AnnualReport 2004 2005 - Canadian Mathematical … · The Director’s Office . . . . . . . . . ....

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Annual Report 2004 2005

Transcript of AnnualReport 2004 2005 - Canadian Mathematical … · The Director’s Office . . . . . . . . . ....

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AnnualReport20042005

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AnnualReport

20042005

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Also available on the CRM’s websitewww.crm.umontreal.ca

c© Centre de recherches mathématiquesUniversité de Montréal, 2006

ISBN 2-921120-42-9

Centre de recherches mathématiquesUniversité de MontréalC.P. 6128, succ. Centre-villeMontréal, QC H3C 3J7Canada

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CENTRE DE RECHERCHES MATHÉMATIQUES

Presenting the Annual Report 2004 – 2005 5

Thematic Program 8Thematic Year 2004 – 2005: The Mathematics of Stochastic and Multiscale Modeling . . . . 9Aisenstadt Chairholders in 2004 – 2005: T.Y. Hou and A.J. Majda . . . . . . . . . . . . . . . . 11Activities Held During the Thematic Year . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Past Thematic Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

General Program 18CRM Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19CRM-ISM Colloquium Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Multidisciplinary and Industrial Program 30CRM Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

CRM Prizes 36CRM – Fields Prize 2005 awarded to David W. Boyd . . . . . . . . . . . . . . . . . . . . . . . 37André Aisenstadt Prize 2005 awarded to Ravi Vakil . . . . . . . . . . . . . . . . . . . . . . . 37CAP – CRM Prize 2005 awarded to Robert C. Myers . . . . . . . . . . . . . . . . . . . . . . . 38CRM – SSC Prize 2005 awarded to Jiahua Chen . . . . . . . . . . . . . . . . . . . . . . . . . . 39

CRM Partnership 40CRM Partners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Joint Initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Mathematical Education 49Institut des sciences mathématiques (ISM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50Others Joint Initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Research Laboratories 54Applied Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55CICMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57CIRGET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60LaCIM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Mathematical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Mathematical Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69PhysNum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Publications 77Recent Titles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78Previous Titles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78CRM Preprints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Scientific Personnel 83CRM Members in 2004-2005 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84Postdoctoral Fellows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85Long-term Visitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86Short-term Visitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Preprints and Research Reports 89

Committees Heading the CRM 95Bureau de direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96Scientific Advisory Committee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

CRM Administrative and Support Staff 100The Director’s Office . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

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CENTRE DE RECHERCHES MATHÉMATIQUES

Administration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Scientific Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Computer Services . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Statement of Revenue and Expenditures for the Fiscal Year Ending on May 31, 2005 102

Mission of the CRM 105

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Presenting the Annual Report 2004 – 2005

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CENTRE DE RECHERCHES MATHÉMATIQUES

THIS year the quan-tity and impact

of the CRM’s diverseactivities are moreimpressive than ever.In the year covered bythis report, the CRMorganized a most pro-ductive thematic yearon the “Mathematicsof Stochastic and Mul-tiscale Modeling” put

together by Anne Bourlioux and Paul Tupperassisted by a high-level international team. TheCRM also organized numerous internationalconferences and workshops, including the ma-jor “Workshop on Computational Biology in thePost Genomics Era,” held at CRM and initiatedby the three Canadian mathematics institutes incollaboration with NRC. This workshop broughttogether, for the first time in Canada, univer-sity researchers with NRC scientists. Thanksto the prestigious NSERC Leadership SupportInitiatives program CRM hosted an “InformalSemester in Symplectic Topology.” Another no-table event was the three-week “Short Pro-gram on Riemannian Geometry” organized byVestislav Apostolov. The CRM also assisted withthe registrations logistics of the “Quatrième col-loque francophone sur les sondages,” a majorinternational colloquium. In fact, in the single2004 – 2005 year, CRM organized 29 events ofwhich 25 were held on its premises! This consistsof four more activities than were offered the pre-vious year, which was already extremely busy.In 2004 – 2005, CRM organized a record numberadvanced training schools, including the SMS(a NATO ASI), the Spring School on “Mini-invasive Procedures in Medicine and Surgery:Mathematical and Numerical Challenges,” a“Summer School on Riemannian Geometry,” the“Summer School on Stochastic Calculus for Ap-plications: Theory and Numerics,” and cred-ited advanced courses such as the one given byClaude LeBris on “Multiscale Systems.” In all,1,459 participants from the four corners of theworld were officially registered in these events.To all this, we must also add the seminar se-ries organized by the centre’s eight research lab-oratories (five of which were held in the CRM’sseminar rooms), the special lectures given by theAisenstadt Chair holders, by CRM prize win-ners (CRM – Fields, Aisenstadt, and CRM – SSCprizes) and those in our two weekly Colloquiumseries (one each in mathematics and statistics).This represents a few thousand participants in

our activities in addition to the 1,459 registeredparticipants in our international workshops andconferences.

The Centre’s scientific programming is struc-tured into a thematic program, a general pro-gram, a multidisciplinary/industrial programand an educational program. In addition thereare the eight research laboratories in which mostof the research work takes place. Our publicationand postdoctoral fellowship programs completethe outline of our activities. Here is a brief de-scription of each:

Thematic program The thematic program isthe principal activity organized by the Centre inthe accomplishment of its national mandate sup-ported by NSERC. In general, themes alternatebetween subjects in pure mathematics and inapplied mathematics, usually where mathemat-ics borders with other sciences where they haveconsiderable impact. In 2004-2005, the themechosen was in the applications of mathematics in“Stochastic and Multiscale Modeling.” It was asplendid program lead masterfully by Bourliouxand Tupper. Let the numbers speak for them-selves: the program drew over 400 participantsfrom around the world, several longterm vis-itors and postdoctoral researchers. It includedseveral workshops, mini courses and two Aisen-stadt Chair lecture series given by Andrew J.Majda (Courant Inst.) and Thomas Y. Hou (Cal-tech).

General program This program is comprisedof the non-thematic events organized by CRM.The Séminaire de Mathématiques Supérieures(a NATO ASI) dealt with “Morse TheoreticMethods in Non-linear Analysis and SymplecticTopology” and drew 80 participants from abouttwenty countries and some 40 local participants.We have already mentioned the Fall 2004 “In-formal Semester in Symplectic Topology” thathad about 40 foreign participants, which greatlybenefited local students and postdoctoral fel-lows. Following this semester, the Institute forAdvanced Study in Princeton held a specialworkshop that largely echoed the semester. Thegeneral program included the Summer 2004short program on Riemannian geometry and theworkshop on K-Theory that inspired the FieldsInstitute’s forthcoming thematic semester of Fall2006; as well as the financing (in collaborationwith the two other Canadian institutes) of ac-tivities organized by AARMS in the Atlanticprovinces. In addition, it includes the four an-nual prizes awarded by CRM and the two col-loquium series in mathematics and statistics or-

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PRESENTING THE ANNUAL REPORT 2004 – 2005

ganized jointly with ISM. These Colloquiums inwhich a world-renowned researcher addresses alarge audience are particularly important for thetraining of graduate students. These activitiesare mainly supported by NSERC and FQRNTgrants.

Multidisciplinary and Industrial Program Eventhough the development of mathematics is at theheart of the Centre’s preoccupations, we havea very wide definition of these and an open-ness to its applications in other scientific fields.CRM is the host institution of the Québec net-work in computation and mathematical mod-eling (ncm2). While NSERC financing of thenetwork ended recently, ncm2 still incorporatesthe Bell University Laboratories and serves tolaunch collaborative efforts. CRM is also a mainpartner of the Mathematics of Information Tech-nology and Complex Systems (MITACS), a fed-erally funded Network of Centres of Excellence.The industrial program organized by CRM in2004 – 2005 was quite full with nine workshops,summer schools and special advanced courses.These activities included the launch of a CRM –CRIAQ – MITACS collaboration in January 2005put together by CRM and held at the Office forAdvanced Research of Bombardier Aerospace;as well as the first major workshop bringing to-gether university and NRC researchers involvedin computational biology, and the “Workshopon Latent Variable Models and Survey Data forSocial and Health Sciences Research” fundedjointly with the American institute, SAMSI (Sta-tistical and Mathematical Sciences Institute), andthe NSERC-funded National Program on Com-plex Data Structures. CRM also continued its ini-tiatives in brain imaging with INSERM and theInstitut universitaire de gériatrie de Montréal.

Research Laboratories In its transformationfrom a FCAR-funded research centre to aFQRNT-funded regroupement stratégique, CRMconsiderably expanded its membership base andcreated eight research laboratories to bring thesemembers together, thus increasing substantiallyits funding base at FQRNT and partner univer-sities. The laboratories, which only completedtheir second year of existence in 2004 – 2005, or-ganized no less than a dozen weekly seminars

and several workshops, in addition to those or-ganized by CRM, including for instance, the“Workshop on Spectral Theory of SchrödingerOperators,” the “Workshop on Dynamics inStatistical Mechanics,” the “Analysis Day,” the“Workshop on Low-dimensional Topology,” the“Workshop on Bayesian Inference and Func-tional Brain Mapping,” the “Montreal ScientificComputing Days,” and several others. Thanks tothe laboratories and the devoted members of theCentre’s Scientific Advisory Committee, morethan ever the CRM’s programs achieve world-class standing.

Publications The CRM has a vigorous publish-ing program with some fifteen new and forth-coming titles. Both the American MathematicalSociety and Springer have a CRM series. Amongthe new titles of the year, of note are a mono-graph by V. Guillemin (MIT) and R. Sjamaar(Cornell) and another by A.J. Majda (CourantInstitute), as well as proceedings edited byJ. Hurtubise (McGill) and E. Markman (Mas-sachusetts) on “Algebraic Structures and Mod-uli Spaces,” by V. Apostolov (UQÀM), A. Dancer(Oxford), N. Hitchin (Oxford) and M. Wang (Mc-Master) on “Perspectives on Riemannian Geom-etry.” See the complete list in this annual re-port. To which we should add the nice collectionfrom the NATO ASI/Séminaire de Mathémati-ques Supérieures published by Springer but en-tirely edited by CRM.

Postdoctoral program Jointly with ISM, theCRM manages a world-renowned postdoctoralfellowship program. In addition, postdoctoralfellowships are offered in our thematic programas well as by the Centre’s research laboratories.In all, 92 postdoctoral fellows were supervisedby CRM members during at least part of the2004 – 2005 year. Of these, 30 fellows were partlyfunded by the CRM and at least 6 came withtheir own fellowship funding; many of thesewere associated with the thematic year. To thisnumber, we could add a dozen postdoctoral fel-lows funded in part by MITACS research teams.

François LalondeDirector

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Thematic Program

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THEMATIC PROGRAM

THE core of each year’s scientific program at the CRM is its thematic program. The Scientific Ad-visory Committee chose for 2004 – 2005 the theme of Mathematics of Stochastic and Multiscale

Modeling because of its importance, timeliness, and impact on the international scientific commu-nity. The thematic program included several workshops and conferences, two Aisenstadt Chair lec-ture series (Andrew J. Majda and Thomas Yizhao Hou), a number of visiting scientists in residence,and some postdoctoral fellowships. In coordination with Montréal universities, CRM offered an ap-propriate short course in order to help graduate students participate in the activities. The reports arepresented in the language in which they were submitted.

Thematic Year 2004 – 2005:The Mathematics of Stochastic and Multiscale Modeling

Organizers: Anne Bourlioux (Montréal), WeinanE (Princeton), Jean-Pierre Fouque (NC State),Thomas Y. Hou (Caltech), Claude Le Bris(ENPC), Andrew J. Majda (Courant Inst.), Ron-nie Sircar (Princeton), Panagiotis T. Souganidis(UT Austin), Andrew Stuart (Warwick), Paul F.Tupper (McGill), Eric Vanden-Eijnden (CourantInst.)

The 2004 – 2005 thematic year was dedicated tothe applied mathematical tools (modeling, anal-ysis, computation) needed to study multiscalesystems which arise in a variety of areas in sci-ence and engineering. These systems presentmany novel challenges for applied mathemati-cians. The central difficulty is how to account forthe wide range of scales and the large numberof degrees of freedom in such systems. In partic-ular, it is necessary to find an appropriate cou-pling between the mathematically distinct mod-els used for the different scales in such a system.

The fields of application where these issuesarise, and which were discussed during thetheme year, include climate modeling, frontpropagation, molecular dynamics, materials sci-ence, financial engineering, and rheological flu-ids.

Despite the diversity of applications, the chal-lenges in these areas have much in common.A fundamental question is: How can one utilizeknowledge about the dynamics of a system so asto design a useful mathematical model that accu-rately captures its global behaviour? One particu-larly promising approach is based on stochasticmodels: this was the topic of the Summer Schooland was also a recurring theme throughout thevarious workshops. These offered opportunitiesfor interaction between applied mathematiciansspecializing in modeling and numerical simula-tion and scientists and engineers in the variousfields of applications.

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CENTRE DE RECHERCHES MATHÉMATIQUES

Retrospective of the Thematic Year

« L’année thématique 2004-2005 sur la modélisationmathématique multiéchelle et stochastique est main-tenant derrière nous, et c’est l’heure des bilans et re-merciements. Une des missions essentielles du CRMest la formation à la recherche des étudiants et sta-giaires postdoctoraux, et l’année thématique a foi-sonné d’occasions en ce sens, en particulier l’Écoled’été, pilotée par Eric Vanden-Eijnden, et le coursISM avancé sous la houlette de Claude Le Bris – deuxactivités à but pédagogique, certes, mais sans compro-mis sur la qualité. Avec un contenu à un niveau d’ex-cellence ils ont réussi à secouer et enthousiasmer lesparticipants, novices ou non.

Ce bilan est donc une occasion très appropriée dedonner la parole à l’un des participants juniors : ci-dessous, le compte-rendu scientifique des activités del’année du point de vue très personnel de Tony Le-lièvre, qui vient de réintégrer son laboratoire au CER-MICS au terme de son année postdoctorale fort pro-ductive à Montréal.

L’heure est aussi aux remerciements : aux organisa-teurs d’ateliers C. Le Bris, P. Tupper, P. Souganidis,R. Sircar et J.-P. Fouque, Weinan E et E. Vanden-Eijnden, en particulier aux deux conférenciers Ai-senstadt Andrew Majda et Tom Hou, très généreuxdans leurs interactions avec les chercheurs locaux ; et,finalement, au personnel du CRM pour l’accueil at-tentif qu’il a réservé aux nombreux participants. Lescommentaires enthousiastes ont abondé pour souli-gner à quel point l’organisation locale soignée a fa-vorisé de façon essentielle la qualité des interactionsscientifiques. »

Anne Bourlioux

Retrospective of the Year by Tony Lelievre

« Les modèles multiéchelles s’attachent à décrire laréalité, en faisant appel à plusieurs échelles de des-criptions : par exemple, dans le domaine de la méca-nique des solides, on cherche à comprendre les liensentre les phénomènes à l’échelle de l’atome et les com-portements de la matière à l’échelle macroscopique.Ces techniques d’intégration multiéchelle font appelà des technologies scientifiques récentes, dans des do-maines très variés.

Les différents cours et ateliers tout au long de l’annéeont mis en lumière un domaine où les mathématiciensappliqués jouent un rôle primordial entre les physi-ciens créateurs de modèle, les mathématiciens moti-vés par des questions plus théoriques et les numéri-ciens soucieux de construire des algorithmes adap-tés au modèle. Une des qualités de ces ateliers étaitd’ailleurs de réunir des chercheurs de tous ces hori-

zons. Le travail du mathématicien appliqué, à l’in-terface de plusieurs communautés, prend toute sonimportance dans ces nouveaux types de modélisationoù des connaissances pluri-disciplinaires sont néces-saires pour progresser.

La variété des techniques mathématiques nécessairesà l’étude de ces modèles (théorie de l’homogénéisa-tion, théorie des larges déviations, théorie ergodique,schémas symplectiques,. . .) ainsi que des domaines dela physique concernés (mécanique statistique, modé-lisation de la turbulence, dynamique moléculaire, cli-matologie,. . .) constituait en soi un attrait majeur decette année thématique pour un postdoctorant cher-chant à ouvrir ses horizons. La conférence organiséepar T.Y. Hou donnait un bon exemple de la variétédes domaines où la modélisation multiéchelle est uti-lisée, et de la diversité des techniques mathématiqueset numériques nécessaires à l’analyse de ces modèles.

Les modèles aléatoires jouent un rôle particulier dansces modèles en plein développement, non pas tant parle fait que la meilleure description de la matière àl’échelle la plus microscopique (mécanique quantique)soit intrinsèquement aléatoire, mais plutôt parce quele passage d’une échelle microscopique à une échellemacroscopique consiste à éliminer des degrés de li-berté ou à considérer des asymptotiques dans leséchelles en temps ou en espace, d’où naît l’aléatoire.L’atelier organisé par A.J. Majda ainsi que ses coursde la Chaire Aisenstadt illustraient particulièrementces aspects pour des applications à la modélisation cli-matique, où l’on cherche justement à bâtir, à partir demodèles précis et très complets mais en très grandedimension, des modèles approximés plus simples quiconservent des propriétés statistiques proches du mo-dèle initial, avec pour objectif de comprendre les phé-nomènes déterminants pour le climat. Les étapes es-sentielles sont alors la détection des degrés de libertéles plus importants, puis la dérivation d’équationséquivalentes sur ces degrés de liberté, en utilisant desrelations de fermeture appropriées. Ceci requiert desoutils liés à la théorie de l’homogénéisation ou en-core à la mécanique statistique. Les modèles aléatoiresétaient également au cœur de la conférence consacréeaux mathématiques financières, organisée par R. Sir-car et J.-P. Fouque.

L’étude numérique et théorique des couplages de mo-dèles est un autre aspect que ces modélisations mul-tiéchelles ont en commun. En particulier, le cou-plage de modèles aléatoires et déterministes soulèvedes questions numériques intéressantes liées aux rela-tions entre les différentes erreurs de discrétisation (entemps, en espace, erreur statistique pour les modèlesMonte Carlo). La conférence organisée par A. Bour-lioux et P. Souganidis sur les modèles de combustionillustrait particulièrement les questions soulevées par

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THEMATIC PROGRAM

les interactions entre modèles stochastiques (décri-vant l’écoulement advectif aléatoire) et modèles dé-terministes (décrivant la chimie de la combustion).Le couplage de modèles peut aussi se faire à des in-terfaces, une zone étant décrite plus finement qu’uneautre. C’est le problème du passage de l’informa-tion aux interfaces qui est alors soulevé. Ce thèmeétait notamment au centre de la conférence organi-sée par Weinan E et E. Vanden-Eijnden sur la mo-délisation multiéchelle dans les solides, où une desquestions récurrentes concernait le choix des condi-tions aux limites entre les modèles de dynamique mo-léculaire essentiellement discrets, et les modèles demécanique des milieux continus. Ce domaine est unexemple où il reste encore beaucoup de questions théo-

riques pertinentes, sur des modèles simplifiés (com-portement d’une chaîne de ressort unidimensionnelpar exemple) : Quelle notion de minimum (localou global) de l’énergie mécanique faut-il consi-dérer ? Quelle est la bonne dynamique ?

Je voudrais terminer ce compte-rendu très informelet personnel en remerciant Anne Bourlioux pourl’organisation de cette année thématique et nos nom-breuses randonnées, les membres de l’administrationdu CRM pour leur accueil, Michel Delfour pourson support financier, Stéphane Dellacherie pour noslongues discussions scientifiques ou autres, et EricVanden-Eijnden avec qui j’ai commencé une collabo-ration fructueuse au cours de cette année. »

Tony Lelièvre

Aisenstadt Chairholders in 2004 – 2005: T.Y. Hou and A.J. Majda

The CRM was honoured to have as Aisenstadtchairholders, during the 2004 – 2005 theme yearMathematics of Stochastic and Multiscale Mod-eling, Professors Thomas Yizhao Hou of Califor-nia Institute of Technology et Andrew J. Majdaof Courant Institute.

Thomas Yizhao Hou

Thomas Yizhao Hou isthe Charles Lee Pow-ell Professor of Ap-plied and Computa-tional Mathematics atCaltech, and one of theleading experts in ap-plied and numericalanalysis for vortex dy-namics and multiscale

problems. In his twenty-year research career hisresearch interests have been centered around de-veloping analytical tools and effective numericalmethods for vortex dynamics, interfacial flows,and multiscale problems.

He was born in Guangzhou, China, and studiedat the South China University of Technology be-fore undertaking his Ph.D. at UCLA. Upon ob-taining it in 1987, he joined the Courant Insti-tute as a postdoctoral fellow and then becamea faculty member in 1989. He moved to theapplied mathematics department at Caltech in1993, and is currently the executive officer inthe department of applied and computationalmathematics. He was awarded the MorningsideGold Medal in Applied Mathematics in 2004, theSIAM Wilkinson Prize in Numerical Analysisand Scientificc Computing in 2001, the François

N. Frenkiel Award from the Division of FluidDynamics, American Physical Society in 1998,the Feng Kang Prize in Scientific Computing in1997, and was a Sloan Foundation Research Fel-low from 1990 to 1992. He was also an invitedplenary speaker at the International Congress onIndustrial and Applied Mathematics in Sydneyin 2003, an invited speaker of the InternationalCongress of Mathematicians in Berlin in 1998,and founding Editor-in-Chief of a SIAM inter-disciplinary journal on Multiscale Modeling andSimulation.

Andrew J. Majda

Andrew J. Majda isthe Morse Professor ofArts and Sciences atthe Courant Instituteof New York Univer-sity. He was born inEast Chicago, Indianaon January 30, 1949. Hereceived a B.Sc. degreefrom Purdue Univer-

sity in 1970 and a Ph.D. degree from StanfordUniversity in 1973.

Majda’s primary research interests are modernapplied mathematics in the broadest possiblesense merging asymptotic methods, numericalmethods, physical reasoning and rigorous math-ematical analysis.

He is well known for both his theoretical contri-butions to partial differential equations and hisapplied contributions to diverse areas such asscattering theory, shock waves, combustion, in-

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compressible flow, vortex motion, turbulent dif-fusion, and atmosphere ocean science.

Majda is a member of the National Academyof Sciences and has received numerous honoursand awards including the National Academy ofScience Prize in Applied Mathematics, the Johnvon Neumann Prize of the Society of Indus-trial and Applied Mathematics, and the GibbsPrize of the American Mathematical Society. Hehas been awarded the Medal of the Collège deFrance and is a Fellow of the Japan Society forthe Promotion of Science. He received an hon-orary doctorate from his undergraduate almamater, Purdue University in 2000.

He began his scientific career as a Courant In-structor at the Courant Institute from 1973 –1975. Prior to returning to the Courant Insti-tute in 1994, he held professorships at PrincetonUniversity (1984-1994), the University of Califor-nia, Berkeley (1978 – 1984), and the University ofCalifornia, Los Angeles (1976 – 1978). In the pastseveral years at the Courant Institute, Majda hascreated the Center for Atmosphere Ocean Sci-ence with a multidisciplinary faculty to promotecross-disciplinary research with modern appliedmathematics in climate modeling and predic-tion.

Majda has recently published with AndreaBertozzi, Vorticity and Incompressible Flow (Cam-bridge University Press). Also, Majda’s lecturenotes, Introduction to PDE’s and Waves for the At-mosphere and Ocean, was recently published in

the Courant Lecture Note Series of the AmericanMathematical Society.

Aisenstadt Chair

The Aisenstadt Chair was endowed by Mont-réal philanthropist Dr. André Aisenstadt. Underits auspices, one or more distinguished mathe-maticians are invited each year for a period ofat least one week, ideally one or two months.During their stay the lecturers present a seriesof lectures on a specialized subject. They arealso invited to prepare a monograph (see thePublications chapter in this report for a list ofthese publications). At the request of Dr. Aisen-stadt, the first of their lectures should be acces-sible to a wide audience. Previous holders of theAisenstadt Chair are: Marc Kac, Eduardo Zaran-tonello, Robert Hermann, Marcos Moshinsky,Sybren de Groot, Donald Knuth, Jacques-LouisLions, R. Tyrell Rockafellar, Yuval Ne′eman,Gian-Carlo Rota, Laurent Schwartz, Gérard De-breu, Philip Holmes, Ronald Graham, RobertLanglands, Yuri Manin, Jerrold Marsden, DanVoiculescu, James Arthur, Eugene B. Dynkin,David P. Ruelle, Robert Bryant, Blaine Law-son, Yves Meyer, Ioannis Karatzas, László Babai,Efim I. Zelmanov, Peter Hall, David Cox, FransOort, Joel S. Feldman, Roman Jackiw, Duong H.Phong, Michael S. Waterman, Arthur T. Win-free, Edward Frenkel, Laurent Lafforgue, GeorgeLusztig, László Lovász, Endre Szemerédi , PeterSarnak, and Shing-Tung Yau.

Activities Held During the Thematic Year

Summer SchoolStochastic Calculus for Applications: The-ory and NumericsAugust 9 – 20, 2004, CRMorganized jointly with MITACS

Organizers: Anne Bourlioux (Montréal), EricVanden-Eijnden (Courant Inst.)Principal Lecturer: E. Vanden-Eijnden (CourantInst.)Supervisor of exercise sessions: I. Fatkullin(Caltech)Invited Lecturers: P. Tupper (McGill),B. Khouider (Victoria), C. Le Bris (ENPC),I. Fatkullin (Caltech)Number of participants: 51

The aim of the summer school was to coverthe essentials of stochastic calculus, includingfundamental concepts such as Markov chains,

Wiener processes, stochastic differential equa-tions, as well as more elaborate ideas such as theGirsanov transformation and path integrals. Thematerial was presented at a semi-rigorous levelby relying only on the standard tools of basicprobability, linear algebra, and advanced calcu-lus. Both theoretical and numerical aspects werecovered and illustrated via examples.

The purpose of the summer school was to serveas an introduction for graduate students andpostdoctoral fellows to one of the main mathe-matical tools at the centre of the thematic yearorganized by the CRM in 2004 – 2005 so that theycould benefit to the maximum from the special-ized workshops to be held subsequently. Thismission was accomplished with success thanksto a combination of daily theoretical courses,four invited lectures on applications represen-tative of some of the themes to be covered in

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the workshops of the thematic program, andby daily, supervised exercise sessions. An in-teresting fact was the great diversity of partici-pants: students, postdocs and researchers frommathematics, physics, pharmacy, chemistry, en-gineering, etc., not only from diverse Montrealuniversities and research centers, but also fromelsewhere in Canada, from the United Statesand from Europe. Participation was assiduousthroughout the two weeks — many participantscommented on how positive the experience wasfrom all points-of-view: i.e., excellence of thecontent and of the organization. The organiz-ers received several queries asking if the activitywould be repeated in the future.

WorkshopMultiscale Rheological Models for FluidsNovember 14 – 17, 2004, CRM

Organizer: Claude Le Bris (ENPC)Speakers: A. Bonito (EPFL), É. Cancès (ENPC),P. Constantin (Chicago), A. Debussche (ENS-Cachan Bretagne), M. Grmela (École Polytech-nique Montréal), Z.-F. Huang (McGill), B. Jour-dain (EPNC), C. Le Bris (EPNC), T. Lelièvre(Montréal), C. Liu (Penn State), A. Lozinski(EPFL), N. Masmoudi (Courant Inst.), F. Otto(Bonn), R.G. Owens (Montréal), J. Ramírez(Politécnica Madrid), P.T. Underhill (MIT), Q.Wang (Florida State), P. Zhang (Beijing)Number of participants: 25

La modélisation multiéchelle du comportementnon newtonien des fluides complexes peut êtreabordée par l’établissement de lois constitu-tives, mais de telles lois sont souvent difficiles àdériver et à valider. Une stratégie alternative estde faire appel à la théorie cinétique pour simulerle comportement des microstructures présentesdans le fluide (chaînes de polymères, particulesen suspension, etc.) et de coupler cette descrip-tion microscopique avec une description macro-scopique du fluide par les équations de la mé-canique du continuum.

Un large spectre de questions reliées à larhéologie des fluides complexes a été abordé:les aspects de modélisation (Owens, Wang,Grmela, Underhill, Huang), les aspects de sim-ulation numérique (Ramírez, Bonito, Lozin-ski), les aspects d’analyse mathématique etnumérique (Constantin, Otto, Cancès, Liu, Mas-moudi, Zhang). Certaines conférences ont étédédiées aux modèles faisant intervenir des équa-tions de nature stochastique (Debussche, Jour-dain, Lelièvre, Le Bris).

L’atelier a réuni environ 25 participants venusassister aux 18 conférences présentées et àune communication courte. La confrontationde compétences aussi diverses a été largementappréciée par les participants, et les longuesplages de discussion ménagées dans l’emploidu temps ont rendu possibles de nombreuxéchanges dont certains seront certainement legerme d’interactions scientifiques à plus longterme.

WorkshopFront Propagation and Nonlinear Stochas-tic PDE’s for Combustion and Other Ap-plicationsJanuary 26 – 29, 2005, CRMorganized jointly with MITACS

Organizers: Anne Bourlioux (Montréal), Panagi-otis T. Souganidis (UT Austin)Speakers: J. Bell (Lawrence Berkeley NationalLab.), K. Bushe (UBC), C. Devaud (Water-loo), Ö.L. Gülder (Toronto), F. Hamel (Aix-Marseille III), S. Heinze (MPI MIS), M. Her-rmann (Stanford), D. Hillhorst (Paris XI), A.Kiselev (UW Madison), J. Nolen (UT Austin),A. Novikov (Penn State), J.-M. Roquejoffre(Toulouse III), A. Stevens (MPI MIS), V. Volpert(Lyon I), A. Zlatos (UW Madison)Number of participants: 22

The development of efficient large-scale mod-els for the numerical simulation of turbulentpremixed flames requires a good understand-ing of the mathematical principles governingthe dynamics of self-propagating fronts. Oneof the most challenging issues is the analysisof the complex interactions, at small scales, be-tween advection, reaction and diffusion, includ-ing stochastic effects due to the media or the ad-vective flow randomness.

This workshop, offered an opportunity for inter-actions between mathematicians at the forefrontof this area and scientists involved in the de-sign of models and numerical methods for var-ious applications, in particular, turbulent com-bustion.

On the theoretical side, exchanges were quiteintense with several speakers presenting veryrecent results on predictions of flame propaga-tion and extinction in response to flows, notablythose in a network of vortices; various estima-tors for PDEs, comparison principles for theirsolutions, and probabilistic methods were fea-tured. Participants appreciated and found justas instructive presentations offering a different

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but complementary perspective to theoretical ef-forts to understand flame fronts. For example,the presentation by A. Stevens highlighted theinteresting and potentially very promising the-oretical connection between models of combus-tion fronts and those in biology with a nicheof, so far, little studied mathematical problems.Presentations of a more numerical and experi-mental nature also led to discussions going bothways: an improved awareness for mathemati-cians of the complexity and richness of the spec-tacular results obtained during physical and nu-merical experiments, but also very frank discus-sions, for instance on the mathematical valid-ity of certain approximations widely used in nu-merical models.

WorkshopRepresenting Unresolved Degrees of Free-dom for the Atmosphere and OceanMarch 2 – 5, 2005, CRM

Organizer: Andrew J. Majda (Courant Inst.)Speakers: P. Bartello (McGill), J. Bowman(Alberta), G. Branstator (NCAR), O. Büh-ler (Courant Inst.), L. Campbell (Carleton),G. Craig (DLR Oberpfaffenhofen), T. DelSole(George Mason), C. Franzke (Courant Inst.),W. Grabowski (NCAR), D.M. Holland (CourantInst.), M. Katsoulakis (UMass Amherst), B.Khouider (Victoria), P.J. Kushner (Toronto), A.Monahan (Victoria), T.G. Shepherd (Toronto),D. Straub (McGill), I. Timofeyev (Houston),B. Turkington (UMass Amherst), G.K. Vallis(GFDL)Number of participants: 49

A central problem in attempts to understandand predict the evolution of atmospheric oroceanic flows is how best to represent the un-resolved scales in these flows. In the jargonof dynamic meteorology or physical oceanog-raphy this is called the parameterization prob-lem, while in the jargon of turbulence it is calledthe closure problem. The most pertinent areasof analysis and applied mathematics are ho-mogenization theory, probability and non-linearstochastic PDEs. The purpose of this workshopwas to explore two complementary issues thatarise in the context of the parameterization prob-lem:1. the extent to which modern techniques in ap-

plied mathematics can be brought to bear onits formulation and partial solution; and

2. the extent to which problems in the represen-tation of atmospheric and oceanic flows cre-ate fertile new areas of mathematical inquiry.

The workshop was genuinely interdisciplinaryand new synergy between mathematics andthese applications emerged throughout themeeting. One prominent example was the themeof multiscale cloud modeling where the mathe-matical talks by Khouider, Katsoulakis, and Ma-jda had serendipity with the disciplinary lec-tures by Grabowski, Craig and Vallis. The youngscientists in attendance were able to observe thisvibrant scientific activity.

Another exciting development was the newmathematical theory for new types of break-ing waves and their impact on mean flows de-veloped by Bühler in his lecture after the gen-eral overview of Shepherd. Another interestingpoint of interaction was the mathematical tech-niques for stochastic mode reduction presentedby Franzke and Timofeyev in contrast to the ob-servational lecture of Branstator and the inter-esting lecture of Delsole on instantaneous op-timal bases for turbulence. Finally, Turkingtonand Bowman gave interesting novel methods forparametrizing turbulent flow at large scales andin the integral range.

WorkshopExtracting Macroscopic Information fromMolecular DynamicsApril 7 – 9, 2005, CRM

Organizer: Paul F. Tupper (McGill), AndrewStuart (Warwick)Speakers: G. Ciccotti (Roma “La Sapienza”), C.Dellago (Wien), A. Dinner (Chicago), W. Hoover,B. Leimkuhler (Leicester), J.H. Maddocks (ETHZürich), C. Schuette (FU Berlin), R.D. Skeel (Pur-due), M.E. Tuckerman (New York), E. Vanden-Eijnden (Courant Inst.), A.F. Voter (Los Alamos),S. Wiggins (Bristol)Number of participants: 31

Models used in molecular dynamics are high-dimensional dynamical systems (or stochasticdynamical systems) with multiple time-scales. Amajor challenge for computational mathematicsis the extraction of accurate macroscopic infor-mation at minimal cost. This workshop concen-trated on two topics:

• the analysis and development of standardtime-stepping algorithms in the context ofmolecular dynamics, with the purpose of theindirect calculation of macroscopic informa-tion;

• the design of new algorithms aimed at extract-ing macroscopic information directly.

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During the workshop some particular areas offocus emerged: Transition path sampling (Bluemoon, the string method), determining reactioncoordinates (theory and practice), stochastic vsdeterministic mechanics for molecular simula-tion (e.g., Langevin or dynamical thermostats),automatic extractions of information from huge,high-dimensional data sets and fast dynamics(“Voter” dynamics).

The workshop was widely considered a success.Because the talks were each an hour long, speak-ers were able to take their time to develop theirmaterial in a clear fashion. Because we limitedthe number of speakers to 12, there was am-ple time between the talks for discussion. Manyparticipants explicitly thanked the organizers forthis relaxed schedule, saying that it was a re-freshing change from the usual format for suchworkshops.

Moreover, since the speakers included mathe-maticians, physicists, and chemists, there wasa wide variety of perspectives on the differ-ent problems addressed. The most valuable out-come was probably the emergence of unfore-seen parallels between different researchers’ ap-proaches to the analysis of molecular dynamicsdata.

WorkshopMultiscale Modeling of SolidsApril 28 – 30, 2005, CRM

Organizer: Weinan E (Princeton), Eric Vanden-Eijnden (Courant Inst.)Speakers: N. Bernstein (US Naval ResearchLab.), W. Cai (Stanford), W.A. Curtin (Brown),E. Kaxiras (Harvard), A.J. Lew (Stanford), X. Li(IMA), W. K. Liu (Northwestern), G. Lu (Cal-ifornia State), M. Marder (UT Austin), R. E.Miller (Carleton), A. Needleman (Brown), H.Park (Vanderbilt), M.G. Reznikoff (Bonn), R.E.Rudd (Lawrence Livermore National Lab.), M.Tang (Lawrence Livermore National Lab.), Y. Xi-ang (Hong Kong University of Science & Tech-nology)Number of participants: 33

This was a very successful workshop. It is quitedifferent from most other workshops on mul-tiscale modeling, since it was quite focused.This workshop concentrated on energetic and ki-netic issues associated with defects, cross-slip,grain boundary migration, and phase bound-ary dynamics in solids. The objective was to de-velop mathematical models for complex multi-scale phenomena such as crystal plasticity, nu-

cleation and reconstruction of stepped surfaces,and the behaviour of nano-materials in general.Most participants were experts in the field. Theworkshop was run in such a way that it pro-moted in-depth, frank and sometimes heateddiscussions.

Several problems, such as issues of boundaryconditions, dislocation dynamics and their rolein plastic deformation, rare events, systematiccoarse-graining procedures were discussed indepth. Most participants enjoyed this style ofworkshop and expressed interest to have moreof such workshops in the future.

WorkshopIntegrative Multiscale Modeling and Simu-lation in Materials Science, Fluids and En-vironmental ScienceMay 11 – 13, 2005, CRM

Organizer: Thomas Y. Hou (Caltech)Speakers: J.E. Aarnes (SINTEF ICT), A.Bourlioux (Montréal), C.J. Budd (Bath), R.E.Caflisch (UCLA), S. Chen (Johns Hopkins), A.J.Chorin (UC Berkeley), P. Constantin (Chicago),L.J. Durlofsky (Stanford), Y. Efendiev (TexasA&M), B. Engquist (PSCI), A.C. Fannjiang (UCDavis), R. Ghanem (Southern California), J.Glimm (SUNY Stony Brook), Y.G. Kevrekidis(Princeton), R. Kuske (UBC), C. Liu (Penn State),W.K. Liu (Northwestern), M. Luskin (Min-nesota), L.R. Petzold (UCSB), H. Tchelepi (Stan-ford), M.F. Wheeler (UT Austin), J. Xin (UTAustin), S. Yip (MIT), D. Zhang (Los Alamos)Number of participants: 44

There were 22 invited speakers from various dis-ciplines. They are all leading experts in theirfields. The workshop also attracted participantsfrom academia and industry. It generated verylively and stimulating discussions during thelectures, and the coffee breaks. People from dif-ferent backgrounds found common research in-terests through the interactions of the workshop.We also identified a number of key challengesthat remain to be resolved in the future. Thesechallenges include the multiscale analysis andcomputational methods for problems withoutscale separation where global information be-comes important, stochastic modeling and howto quantify the uncertainty effect due to thepresence of random noise in modeling, bridgingthe gap between fundamental multiscale anal-ysis for model problems and the engineeringapplications and the dynamic non-linear inter-action across different length scales. Every in-

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vited speaker gave a first-rate lecture. This in-cludes both the senior established leaders inthe field and the younger generation of risingstars. In many cases, the topic of one lecturecomplemented another lecture. As a result, theworkshop generated a lot of interactions amongthe participants. We can see that mathemati-cians talked to engineers, and engineers learnedfrom mathematicians. For example, the lectureby Wing-Kam Liu on applying the immersedboundary method to biological nanofilm depo-sition inspired discussion with Bjorn Engquist,who has done work on improving the accuracyof immersed boundary methods. The lecture ofShiyi Chen on multiscale simulation of fluid-solids interaction also inspired a lot of discus-sions on during the lecture regarding its poten-tial applications to engineering problems andsome of its limitations. The lectures by Durlof-sky, Efendiev, and Arnes gave an admirableoverview on the topic of upscaling of flow inporous media, covering both the state-of-the-artmethodology and the frontier applications in theindustry. Sidney Yip gave an outstanding talkon the dynamic aspect of multiscale modeling inmaterials science applications. Linda Petzold’slecture is an excellent example how an effectivemultiscale algorithm can make a difference in bi-ological applications. Glimm’s talk showed theimportance of high resolution schemes in cap-turing the small scale interfacial instability whilea less accurate method may completely missthese important fine scale details. Finally, Con-stantin’s lecture provided the fundamental the-ory for some non-Newtonian models for com-plex fluids.

Many participants told the organizer how muchthey had enjoyed the workshop. In some sense,we have integrated successfully the different as-pects of multiscale problems and started a veryhealthy and constructive dialogue among ex-perts from different disciplines. If we continuethis type of cross-disciplinary interactions, wewill be able to make significant advances of thefield.

WorkshopStochastic Modeling in Financial Mathe-maticsJune 1 – 5, 2005, CRMorganized jointly with SAMSI and partiallyfunded by MITACS

Organizers: Ronnie Sircar (Princeton), Jean-Pierre Fouque (NC State)Speakers: R. Almgren (Toronto), D. Becherer

(Imperial College London), T. Bielecki (IIT),A. Cadenillas (Alberta), R. J. Elliott (Calgary),J. Fan (Princeton), P. Glasserman (Columbia),U. Haussmann (UBC), E. Hillebrand (LSU), U.Horst (UBC), S. Howison (Oxford), M. Jeanblanc(Évry-Val d’Essone), I. Karatzas (Columbia), S.Kou (Columbia), D. Kramkov (Carnegie Mel-lon), D. Pelletier (NC State), É. Renault (NorthCarolina), P. J. Schönbucher (ETH Zürich), K.Solna (UC Irvine), N. Touzi (CREST), L. Wu(Baruch College), T. Zariphopoulou (UT Austin)Number of participants: 93

The theme of this workshop was emerging direc-tions in financial mathematics, with emphasis onstochastic modeling of market uncertainties, the-oretical and numerical approximations to pric-ing, hedging and portfolio optimization controlproblems, and data estimation issues. The goalwas to bring together researchers in a varietyof disciplines (mathematics, engineering, oper-ations research and economics, for example) toemphasize different techniques and approaches.

The meeting was very successful in bringing to-gether experts from the various fields of finan-cial mathematics, statistics and econometrics. Itgave an opportunity to graduate students to beexposed to a range of interesting and excitingresearch problems and also an opportunity topostdocs to show their work in twenty-minutetalks. The format was extremely successful andmost likely it will be adopted by others: we hadfourty-five minute long talks (including ques-tions) and fifteen-minute breaks during talks forcoffee and further discussions.

The workshop brought forward exciting newdevelopments in (among others): utility-indifference pricing, numerical solution of non-linear partial differential equations, credit risk,multiscale techniques for volatility modeling (incredit, equity and fixed income), estimation ofvolatility and its time-scales and even the occur-rence of the Riemann-Zeta function in finance!

The organizers are delighted to have had the op-portunity to put together such a workshop atCRM, and many of the participants have con-tacted us afterwards to express their gratitudealso.

Advanced CourseMultiscale Systems: Modeling and Simula-tionFall 2004, CRM

Professor: Claude Le Bris (ENPC)

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This course was an introduction to the studyof multiscale problems from the applied mathe-matician’s point of view. Various strategies weredescribed and analyzed, each of them explainedin the framework of a specific application.

Examples of applications::

• Solid Mechanics• Laminated Materials;• Molecular Chemistry;• Polymeric Fluids Dynamics;• Chemical Reactions Kinetics.

Scientific point-of-views:

• Physics• Mathematical Analysis;• Numerical Analysis;• Programming.

This is a very active research area. The courseaimed at establishing the mathematical basisof this discipline so that the student will beequipped to explore various multiscale researchareas.

Past Thematic Programs

The Centre de recherches mathématiques hasorganized thematic activities every year since1993. Before that, starting in 1987, specialsemesters and concentration periods were com-bined with thematic years.

Here follows a list of thematic activities orga-nized by CRM since 1987:2003 – 2004 Geometric and Spectral Analysis2002 – 2003 Math in Computer Science2001 – 2002 Groups and Geometry2000 – 2001 Mathematical Methods in Biology

and Medicine1999 – 2000 Mathematical Physics1998 – 1999 Number Theory and Arithmetic Ge-

ometry1997 – 1998 Statistics

1996 – 1997 Combinatorics and Group Theory1995 – 1996 Applied and Numerical Analysis1994 – 1995 Geometry and Topology1993 – 1994 Dynamical Systems and Applica-

tions1992 Probability and Stochastic Control

(Special Semester)1991 – 1992 Automorphic Forms in Number

Theory1991 Operator Algebras (Special Semester)1990 Nonlinear PDE’s and Applications (Focal

Period)1988 Shimura Varieties (Special Semester)1987 Quantum Field Theory (Special Semester)1987 – 1988 Fractals: Theory and application1987 Structural Rigidity (Special Semester)

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THE CRM’s general program funds a wide variety of scientific events, both on-site and elsewherein Canada. Whether it be for specialized workshops for a small number of researchers or large

meetings for hundreds of participants, the general program promotes research in the mathematicalsciences at all levels. The program is quite flexible, allowing projects to be considered as they arise.The reports are presented in the language in which they were submitted.

CRM Activities

Short Program on Riemannian GeometryJune 28 – July 16, 2004, CRM

Organizers: Vestislav Apostolov (UQÀM), An-drew Dancer (Oxford), Nigel Hitchin (Oxford),McKenzie Wang (Hamilton)Short courses instructors: Michael Anderson(SUNY Stony Brook), Karsten Grove (Mary-land), Nigel Hitchin (Oxford)Invited speakers: M. Anderson (SUNY StonyBrook), O. Biquard (Strasbourg), R. Bielawski(Glasgow), C. Boyer (New Mexico), R. Bryant(Duke), D. Calderbank (Edinburgh), J. Chen(UBC), X. Chen (UW Madison), A. Dancer(Oxford), M. Dunajski (Cambridge), P. Gaudu-chon (École Polytechnique Palaiseau), A. Fraser(UBC), K. Grove (Maryland), M. Herzlich (Mont-pellier II), N. Hitchin (Oxford), C. LeBrun(SUNY Stony Brook), N.C. Leung (Minnesota), J.Lohkamp (Augsburg), C. Margerin (École Poly-technique Palaiseau), M. Min-Oo (Hamilton), A.Nabutovsky (Toronto), D. Page (Alberta), G. Pa-padopulos (Cambridge), H. Pedersen (Odense),P. Petersen (UCLA), C. Pope (Texas A&M), R.Rotman (Toronto), K. Shankar (Oklahoma), X.Wang (MIT), B. Wilking (Münster), W. Ziller(Pennsylvania)Number of participants: 90

This three-week program, held during the sum-mer of 2004 at the Centre de recherches mathé-matiques, focused on the study of Riemannianmetrics whose curvature satisfies constraints(the so-called special geometries). The relationbetween curvature and topology has been of in-terest since the beginning of differential geome-try and, more recently, metrics with special cur-vature properties have come to the fore in phys-ical problems related to string theory. These sub-jects were the leitmotivs of the program that wasattended by over 90 participants.

The program opened with a week of introduc-tory short courses designed for graduate stu-dents and postdoctoral fellows.

Michael Anderson gave a comprehensive surveyon Einstein metrics on open manifolds, whichhave a certain structure at infinity. Asymptoti-

cally, the simplest structures are those of con-stant curvature, and his five lectures coveredboth the asymptotically flat and the hyperbolic(or conformally-compact) cases. He described alarge class of examples of such metrics, and thenfocused on general questions of existence anduniqueness. He explained through his talks theso-called Anti-de Sitter/Conformal Field The-ory correspondence in physics, and gave a num-ber of results on the structure of the map fromthe space of Einstein conformally-compact met-rics to the conformal structures on the bound-ary. These lectures were masterful in their graspof both the physical theories and the rigorousmathematical results related to them.

Karsten Grove gave a four-lecture mini-courseon comparison geometry, from a fairly new andoriginal point of view. The comparison geome-try has its roots in global Riemannian geometry,where it took off in the 1930s through the worksof Hopf, Morse, Schoenberg, Myers and Synge.The real breakthrough came in the 1950s withthe pioneering works of Rauch, Alexandrov, To-ponogov and Bishop. Since then, the simple ideaof comparing the geometry of an arbitrary Rie-mannian manifold with the geometry of con-stant curvature spaces has had a tremendousevolution. First in conjunction with Morse the-ory and convexity, then with Gromov-Hausdorfftopology on spaces of Riemannian manifolds,and the geometry of singular spaces, and mostrecently in the presence of symmetries. All theseaspects were beautifully presented through thelectures which had a great success.

What is special about 6, 7 and 8 dimensions?Why do we study Calabi-Yau threefolds, G2 andSpin(7) manifolds? These were the questions ad-dressed in Nigel Hitchin’s introductory lecturesto these special geometries of great interest instring theory. Based on the fundamental prin-ciple to look at the geometry of open orbits ofLie groups, he presented a truly elegant andoriginal approach to the subject. The orthogo-nal groups SO(n, n) also appear in this settingthrough their spin representations, and this pro-vided an entrance into the exciting world of gen-eralized geometry. His lectures were beautifully

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orchestrated with many examples and construc-tions on moduli spaces.

The audience during this first week was quiteeclectic, ranging from physicists to geometersto topologists. All three lecturers did wonder-ful tutorial work during the office hours theykindly provided to the participants. There weremany fruitful discussions across boundaries,and these led in particular to an informal lectureby Michael Anderson on the celebrated recentwork of Perelman, aiming at a complete resolu-tion of Thurston’s geometrisation conjecture.

The last two weeks of the program included 43one-hour specialized talks, elaborating in partic-ular on the subjects introduced during the firstweek.

Einstein metrics, positive sectional curvature,obstruction theory for positive scalar curvaturewere the main topics during the second week ofthe program.

Michael Anderson presented his new construc-tion of compact Einstein metrics, by using ageneralization of Thurston’s theory of hyper-bolic Dehn surgery and gluing techniques. Hisconstruction provides the first known familiesof 4-dimensional compact Einstein manifoldswhich are neither Kählerian nor locally sym-metric. Christoph Böhm gave a comprehensiveoverview of general existence results for homo-geneous Einstein metrics, including many newexamples. Charles Boyer lectured on his recentworks with K. Galicki and J. Kollár that pro-duce an abundance of new Einstein metrics oncompact manifolds of dimension 2n + 1, includ-ing exotic spheres. Don Page explained how anEuclidean version of the general Kerr-de Sittermetric leads to the construction of amazingly ex-plicit Einstein metrics on Sn−2-bundles over S2.David Calderbank lectured on his recent workswith H. Pedersen and M. Singer that classifyboth locally and globally self-dual Einstein man-ifolds and orbifolds that admit an isometric ac-tion of a 2-torus. Andrew Dancer presented aclassification for superpotentials that have beenused to reduce the Einstein equations to sub-systems. Olivier Biquard explained the relationbetween 3-dimensional CR geometry and Ein-stein geometry, and defined a new eta invariantfor CR manifolds coming from this correspon-dence. David Duchemin presented his workon quaternionic-Kähler fillings of quaternionic-contact structures in dimension 7. Gordon Craigexplained his gluing construction of Einstein fill-

ings of infinitely many topological types of cer-tain 3-dimensional hyperbolic manifolds.

Wolfgang Ziller related the existence of positivesectional curvature metrics on the total space offiber bundles with the recent constructions ofEinstein self-dual orbifolds, due to N. Hitchin,D. Calderbank and M. Singer. Burkhard Wilkingthen presented a classification of the positivelycurved compact manifolds of cohomogeneityone, a result that he, K. Grove and W. Zillerhave recently obtained, and he discussed in de-tail the still open case of a smooth 3-Sasakian 7-manifold constructed out of Hitchin’s Einsteinself-dual orbifolds. Ingi Petursson and AilanaFraser talked about their exciting results on com-pact Riemannian manifolds of (almost) positiveisotropic curvature.

Joachim Lohkamp presented the complete proofof the positive mass theorem that he and U.Christ have recently found. Marc Herzlich thendefined an analogous asymptotic invariant inthe case of asymptotically hyperbolic metrics,called “hyperbolic mass,” and proved the “pos-itive mass property” in this case. MargaritaKraus talked about inequalities which bound theRiemannian curvature tensor with the asymp-totic “mass invariant” of an asymptotically flatLorentzian manifold. Hélène Davaux found anew upper estimate of the scalar curvature of acompact spin manifold in terms of the spectrumof the Laplacian of the universal covering, thusproviding a new obstruction to the existence of apositive constant scalar curvature metrics.

There were also two talks on upper curva-ture bounds during this second week, given byRegina Rotman and Krishnan Shankar. Alexan-dre Nabutovsky gave an excellent overview ofvariational methods in Riemannian Geometry,and Niky Kamran surveyed some long time be-haviour results for solutions of geometric hy-perbolic equations arising in the Lorenzian Kerrspace-time.

The third week of the program was mostly fo-cused around the geometry of metrics with spe-cial holonomy, Kähler and Hermitian metricswith special curvature, and holomorphic meth-ods in Riemannian geometry.

Roger Bielawski lectured on his recent works oninvariant Kähler metrics with prescribed Riccicurvature, on the complexification of a symmet-ric space of compact type. Paul Gauduchon gavea new description of all Kähler metrics with van-ishing Bochner curvature, thus providing an al-ternative approach to R. Bryant’s classification

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of these manifolds. Gideon Maschler presentedhis recent works with A. Derdzinski that clas-sify, both locally and globally, all Einstein man-ifolds which are conformally Kähler. ChristinaTønnesen-Friedman presented an abundance ofnew explicit examples of extremal Kähler met-rics on toric bundles. Yann Rollin talked abouthis very important recent work with M. Singerthat relates existence of scalar-flat Kähler metricsand stability of parabolic vector bundles. Maur-izio Parton and Ruxandra Moraru talked aboutreduction and instanton moduli spaces over cer-tain hyper-Hermitian manifolds.

Gueo Grantcharov, Ana Fino and Helge Joer-gensen explained their classification results ofcertain homogeneous spaces with special holon-omy properties. Bogdan Alexandrov discussedsome fuzzy threads in the literature concern-ing the notion of weak holonomy. Stefan Ivanovpresented a proof of a Goldberg-type conjec-ture concerning Einstein G2-manifolds. GeorgesPapadopoulos introduced the notion of spino-rial cohomology and explained how it can beapplied to study manifolds with special holon-omy. Min-Oo talked about calibrated geome-try in spaces with special holonomy G2 andSpin(7), and its relevance to string theory. Hediscussed various explicit constructions recentlyfound by physicists. His lecture was later fol-lowed by a talk by his collaborator, Spiro Ka-rigiannis, on calibrated cycles in certain bun-dle constructions of metrics with holonomy G2.There were two other talks on calibration the-ory associated to special Lagrangian manifolds,given by Marianty Ionel and Adrian Butscher.Wei-Dong Ruan discussed convergence and de-generation of complete Kähler – Einstein hyper-surfaces in complex tori.

Robert Bryant lectured on complete Riemannianmetrics for which the Ricci tensor is a Hessianof a function. This class of manifolds naturallyappears in the study of Ricci flow on manifolds.

Claude LeBrun gave a very beautiful new proofof all the classical results concerning compactsurfaces with closed geodesics, by using atwistor-theoretic approach to reduce these prob-lems to certain rigidity properties of complex-analytic surfaces. Maciej Dunajski demonstratedhow the twistor-approach can be applied to var-ious nonlinear integrable equations arising inmathematical physics to find solutions via sim-ple algebro-geometric operations on families ofrational curves.

Following Hitchin’s ideas, Marco Gualtieri intro-duced the notion of generalized Kähler geome-try and explained how these structures naturallyappear on 4-manifolds and in connection withtwisted K-theory classes of even dimensional Liegroups.

Thus, in three very intensive weeks, the programsucceeded in tying together most of the new re-sults in the subject and a variety of new projectswere born. The participants affirmed frequentlyand spontaneously that the program was a greatsuccess.

The lecture notes of the short courses given dur-ing the first week of the program, as well asa number of other contributions will be pub-lished as a joint CRM – AMS volume. We wish toacknowledge the National Science Foundation(NSF) for their contribution.

Seminaire de mathematiques superieures –NATO ASI 2004Morse Theoretic Methods in Non-LinearAnalysis and Symplectic TopologyJune 21-July 2, 2004, Université de MontréalThis Seminar was held with financial supportfrom the NATO, the CRM, the Vice-rectorat à larecherche, the Faculté des Sciences and the Dé-partement de mathématiques et de statistique ofUniversité de Montréal

Organizers: Octavian Cornea (Montréal), Paul I.Biran (Tel Aviv)Speakers: A. Abbondandolo (Scuola Nor-male Superiore di Pisa), P. Biran (Tel Aviv),R. Cohen (Stanford), O. Cornea (Montréal),M. Farber (Durham), K. Fukaya (Kyoto), H.Hofer (Courant Inst.), M. Izydorek (Politech-nika Gdanska), Y.-G. Oh (UW Madison), L.Polterovich (Tel Aviv), M. Schwarz (Leipzig),C. Vitebo (École Polytechnique Palaiseau)Number of participants : 65

The talks at this meeting centered on Morse the-oretical techniques which can be used to solvedifficult analytic problems as well as problemsin symplectic topology and in robotics. The keytool in modern symplectic topology is Floer ho-mology techniques, and this has constituted a re-curring theme for the lectures given at the SMS.

In the first week Helmut Hofer talked about thefoundations of symplectic field theory, one ofthe major new “machines” in symplectic topol-ogy whose development has been pursued byHofer, Eliashberg and Givental for a number ofyears now. The origins of symplectic field the-ory lie in Floer’s machinery but it goes much be-

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yond that, and both in applications in complex-ity. Hofer’s lectures were therefore extremelytimely. Matthias Schwarz presented his recentproof for a result of Viterbo relating the Floer ho-mology of the cotangent bundle and the stringtopology of the zero section of this bundle. Thisnotion of string topology has been recently in-troduced by Chas and Sullivan with a purelytopological motivation, and the fact that it fitsperfectly with the quantum product in Floer’stheory is quite remakable. Michael Farber dis-cussed applications to robotics. Paul Biran de-scribed efficient methods to use Floer homologyin the monotone case to prove results concern-ing the topological structure of Lagrangian sub-manifolds. Leonid Polterovich showed how torelate this symplectic topology to dynamics andgeometric group theory methods. Octav Corneapresented higher order Floer type invariants andapplications.

This was an intense first week with lecturesof the highest order of interest for specialistsas well as for beginners in the field. Some ofthe topics discussed (in particular by Hofer,Schwarz, Cornea and Polterovich) were pre-sented publicly for the first time at the SMS –NATO ASI. The second week continued asstrongly: Claude Viterbo talked about gener-ating functions techniques, Alberto Abbondan-dolo discussed Morse theory in Hilbert spaces,Kenji Fukaya talked about a new version of hisA∞ machinery (developed with Oh and Ono)and applications, some of which overlappedwith applications obtained by different meth-ods by Cornea jointly with Lalonde and men-tioned in the first week. Marek Izydorek lec-tured on his approach to the infinite dimensionalConley index and Yong-Geun Oh presented hisrecent spectral invariant techniques and chainlevel Floer methods. Finally, Ralph Cohen de-scribed his topological approach to string topol-ogy and its potential implications for symplectictopology.

Obviously, as it follows from the descriptionabove, many of the talks of different speakerswere strongly interrelated (for example, Hofer’stalks and those of Cornea, those of Schwarzwith those of Cohen, those of Oh and those ofViterbo). This contributed to the overall qualityand strength of the SMS – NATO ASI itself.

Mini-Workshop on Computational Aspectsof Dynamical SystemsJuly 19, 2004, Concordia Universityorganized by the Applied Mathematics Labora-tory

Organizer: Eusebius Doedel (Concordia)Speakers: A. Vanderbauwhede (Gand), B.Krauskopf (Bristol), H. Osinga (Bristol), P. Tup-per (McGill).

The aim of this mini-workshop was to bringtogether theory and application of numericaltechniques for dynamical systems. New devel-opments were demonstrated with case studiesof dynamical systems arising in applications.Problems considered included the continuationand bifurcation of periodic orbits in symmet-ric Hamiltonian systems, and the computationof invariant manifolds, including unstable man-ifolds in delay equations with application to alaser with optical delay, and computation of one-dimensional unstable manifolds when the equi-librium loses its hyperbolicity or the manifold isa strong unstable manifold. The problem of justi-fying long-time large-scale simulations of molec-ular systems was also considered through a con-cept of weak ergodicity.

Conference on Fixed Point Theory and itsApplications in Honour of Andrzej GranasAugust 16 – 20, 2004, CRMorganized by the Mathematical Analysis Labo-ratory, a collaboration with the Département demathématiques et de statistique of Université deMontréal

Organizer: Marlène Frigon (Montréal)Principal speakers: V. Benci (Pisa), B. Bojarski(Polish Academy of Sciences), H. Brezis (Rut-gers), R. Brown (UCLA), B. Cornet (Paris I), E.Fadell (Wisconsin), J. Jaworowski (Indiana), J.W.Lee (Oregon State), F.-C. Liu (Inst. Sinica, Tai-wan), A. Marino (Pisa), J. Mawhin (Louvain),S.B. Nadler Jr. (West Virginia), R. Nussbaum(Rutgers), H. Steinlein Munich)Number of participants: 50

La Conférence sur la théorie des points fixes etses applications a réuni à Montréal du 16 au 20août 2004 une cinquantaine de participants ve-nus célébrer, dans une atmosphère de collégia-lité et de fraternité, le 75e anniversaire du Pro-fesseur Andrzej Granas. Les thèmes principauxde la Conférence étaient la théorie des pointsfixes et ses applications à l’analyse non linéaire,aux équations différentielles et aux systèmes dy-

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namiques. Notamment, les sujets suivants ontété traités : la théorie du degré topologique surdes espaces de Banach ou sur des variétés et lathéorie du degré équivariant, les théorèmes depoint fixe et de point périodique, la théorie deNielsen et celle de Perron-Frobenius, les applica-tions KKM et les théorèmes de type minimax, lesméthodes variationnelles appliquées à des pro-blèmes d’équations aux dérivées partielles.

Workshop on Algebraic K-TheoryOctober 2 – 6, 2004, CRM

Organizers: Eric Friedlander (Northwestern),Dan Grayson (Urbana-Champaign), Rick Jar-dine (Western Ontario), Manfred Kolster (Mc-Master)Speakers: P. Balmer (ETH Zürich), G. Carlsson(Stanford), J.-L. Colliot-Thélène (Paris-Sud 11),T. Geisser (USC), A. Goncharov (Brown), J.Hornbostel (Regensburg), M. Karoubi (ParisVII), M. Levine (Northeastern), I. Madsen(Aarhus), F. Morel (Munich LMU), O. Röndigs(Bielefeld), M. Schlichting (LSU), R. Sujatha (TataInstitute), A. Suslin (Northwestern), B. Totaro(Cambridge), M. Walker (Nebraska), K. Zain-oulline (Bielefeld)Number of participants : 49

The meeting reflected some of the major devel-opments of the past year in the subject, particu-larly in motivic homotopy theory. These includeLevine’s proof of the Voevodsky slice conjecture,Morel’s proof of the unstable connectivity theo-rem for motivic homotopy types (which was de-scribed in his talk as a type of Hurewicz the-orem), and the identification by Röndigs andOstvaer of Voevodsky’s triangulated categoryof motives with the stable category of mod-ules over the cycle-theoretic Eilenberg–MacLanespectrum. Levine’s theorem uses a homotopytheoretic approach to the Chow moving lemma,which was discussed during his talk. The Levineand the Röndigs–Ostvaer results together sub-stantially demystify the relation between themotivic stable category and motivic cohomol-ogy, while Morel’s work points the way to ex-plicit calculations of motivic homotopy groups.Suslin displayed a spectral sequence for the mo-tivic cohomology of an arbitrary Severi-Brauervariety which is built from a decomposition ofthe motive associated to its Cech resolution.

It had been expected that the proof of the Bloch-Kato conjecture relating Galois cohomology tothe Milnor K-theory of a field would be com-pletely written up by the time of this conference,

but this was not to be. Suslin predicts, however,that this proof will be properly written up withina year. The Bloch–Kato conjecture has sensa-tional calculational consequences; these includethe Lichtenbaum–Quillen conjecture which saysthat K-theory can be computed from étale coho-mology.

Informal Semester on Symplectic TopologyFall 2004, CRM

Organizers: Octav Cornea (Montréal), FrançoisLalonde (Montréal)Speakers: M. Entov (Haifa), J.-Y. Welschinger(ENS Lyon), F. Bourgeois (Université Libre deBruxelles), J.-Y. Welschinger (ENS Lyon), M. Pin-sonnault (Toronto), P. Seidel (Chicago), S. Anjos(IST Lisbonne), D. McDuff (SUNY Stony Brook),A.-L. Biolley (Toronto), Y. Ruan (UW Madison),C. Liu (Harvard), K. Wehrheim (Princeton), R.Hind (Notre Dame), V. Ginzburg (UC SantaCruz),Y. Eliashberg (Stanford), E. Kerman (Uof I Urbana-Champaign), Y. Karshon (Toronto),C. Abbas (Michigan State), A. Teleman (Aix-Marseille 1).

This was an informal thematic semester, held inaddition to the official theme year on Multi-scaleStochastic Modelling. With two major thematicprograms going on at the same time in Fall 2004at the CRM, one can easily imagine the inten-sity of activities and febrility during that period.The informal Semester on Symplectic Topologywas a Canadian Leadership Initiative funded byNSERC; it was the natural sequel to the eventsin symplectic topology that had started with theNATO Advanced Study Institute in the Summerof 2004. Our purpose was to invite a number ofresearchers in the field who have made recentremarkable contributions to the subject and weasked them to discuss their work in an infor-mal, flexible, workshop setting. We encouragedthem to be present at the CRM for periods froma week up to a month and, in particular, duringa concentration period in the first two weeks ofNovember. This created to an excellent workingatmosphere and it was very useful to post-docs,students and established researchers alike.

Some of the lecturers have given one lecture ofone hour and some others two or more some-times longer talks. The maximum has been at-tained by Welschinger who gave three lecturesof an average length of two hours each.

Also present and active in the discussions wereJean-Claude Sikorav (ENS Lyon) as well asShengda Hu (Montréal), Alex Ivrii (Montréal)

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and the two organizers. A number of studentsalso participated sporadically: Clement Hyvrier,Remi Leclercq as well as Baptiste Chantraine.Eliashberg’s, Kharshon’s and Seidel’s talks wereorganized jointly with CIRGET’s seminar.

Scientific descriptionA number of talks focused on “hot” topics insymplectic topology: examples are the workon real Gromov-Witten invariants in the pres-ence of symmetry with the two different pointsof view of Welschinger and ChiuChu Liu. InWelschinger’s case, the symmetry is the real in-volution on complex manifolds with fixed locusequal to a Lagrangian submanifold. Really, whatWelschinger is doing is to construct enumerativeinvariants similar to the Gromow – Witten ones,in a way that requires careful gluing of moduliuspaces according to rules that are dictated by anew concept, the “mass.” In Liu’s case, the sym-metry was given by a S1-action whose effect wasto collapse the boundary of a moduli space sothat new invariants could be defined.

The emerging theory of polyfolds, a whole newtheory that would give the right framework todeal with lots of elliptic moduli spaces (i.e.,spaces of solutions to certain underdeterminedpartial differential equations on curved spaces ofarbitrary dimensions), due to Hofer – Wisocky –Zehnder were patiently explained by KatrinWehrheim. Applications of symplectic field the-ory and contact homology were discussed inthe talks of Bourgeois, Hind, Eliashberg as wellas in those of Kerman and Ginzburg who de-scribed their novel way to detect periodic or-bits of Hamiltonian flows by using a Floer the-oretic construction which takes into account pe-riodic orbits belonging to distinct homotopyclasses (the so-called “Floer Branched Homol-ogy”). We also heard about more topologicalpoints of view concerning the space of Hamil-tonian diffeomorphisms as in the talks of An-jos, McDuff, and Pinsonnault. Andrei Telemanand Paul Seidel both discussed topics closerto algebro-geometric problems relevant in sym-plectic topology.

The main support for this semester was pro-vided by a LSI NSERC grant (whose coordi-nator is Steven Boyer). The CRM provided of-fice spaces and computer capabilities as wellas a seminar room and other administrativeassistance. We were also helped by Ms. Di-ane Bélanger, the administrative assistant to theMathematics Canada Research Chairs at Univer-sité de Montréal who kindly took care of the ho-tel reservations.

Montreal Scientific Computing DaysFebruary 26 – 27, 2005, CRMorganized by the Applied Mathematics Labora-tory

Organizers: Tony Humphries (McGill), NilimaNigam (McGill), Robert Owens (Montréal)Invited speakers: J. Gopalakrishnan (Florida), J.S. Hesthaven (Brown)Number of participants: 101

The second edition of this annual event, wasonce again a great success, this year attracting101 participants, mostly from Québec and On-tario, up from 78 participants last year. The ob-jective of this conference is to encourage scien-tific exchange within the scientific computingcommunity in Québec and further afield. Thetwo-day program included two short courses of-fered by international experts, at a level accessi-ble to advanced graduate students.

Jay Gopalakrishnan gave two long lectures onMultigrid methods, a class of numerical tech-niques to solve linear systems arising from dis-cretization of PDEs using a hierarchy of dis-cretization grids. These methods can often com-pute an approximate solution up to a given pre-cision at asymptotically optimal computationalcost. The optimal complexity of multigrid hasbrought within the reach of simulation many sci-entific problems previously thought to be of in-tractable size. The first lecture covered the fun-damental theory and mechanics of multigridmethods, showing how it leads to optimal algo-rithms, and illustrating it on simple examples.The second lecture considered more compli-cated applications, highlighting examples fromelectromagnetics, and investigated the modifica-tions needed to successfully apply the multigridparadigm. The interplay between convergencetheory of discretizations and convergence analy-sis of multigrid was emphasized, especially howone has led to improvements in the other.

Jan Hesthaven gave two long lectures on Dis-continuous Galerkin methods for solving time-dependent PDEs. These discontinuous finite el-ement methods, although proposed first morethan three decades ago, have recently receivedconsiderable attention due to a number of veryattractive properties, e.g., solid theoretical foun-dation, ability to work with high-order andadaptive grids, support for unstructured gridsand very high performance on parallel comput-ers. The first lecture covered the fundamentaltheory of these methods, discussing some keytheoretical results, illustrated by illuminating ex-

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amples. The second lecture focused on more ap-plied aspects and how to develop and imple-ment these methods for a variety of problemsand applications.

Both lecturers gave superb and well appreci-ated presentations, and also made comprehen-sive notes available, Hesthaven even supplieda suite of software routines for implementingthe Discontinuous Galerkin method. There werealso 15 twenty-minute contributed talks, manyby postdoctoral fellows and graduate students,who were especially encouraged to participate,and a pizza and poster session on Saturdayevening.

Workshop on Bayesian Inference and Func-tional Brain MappingMarch 31 – April 2, 2005, CRMorganized by PhysNum and the Statistics Labo-ratory

Organizers: J.-F. Angers (Montréal), J.-M. Lina(ETS)Speakers: A. Mohammad-Djafari (Supélec), C.Bouman (Purdue), C. Phillips (Liège), K. Wors-ley. (McGill), C. Grova (McGill), J. Daunizeau(Montréal)Number of participants: 30

En choisissant d’ancrer l’analyse bayésiennedans le contexte de l’imagerie en neuroscience,les organisateurs avaient comme objectif de sus-citer l’intérêt des jeunes chercheurs quant auxavenues de recherche qui s’offrent aujourd’huidans ce domaine extrêmement dynamique desbiosciences. Les thèmes suivants ont été abor-dés :

• reconstruction d’images selon une approchebayésienne ;

• application des modèles de chaînes de Mar-kov cachées à la modélisation des couleurs ;

• aspect calculatoire des problèmes inverses enimagerie biomédicale ;

• comparaison entre différentes méthodes defusion d’information ;

• comparaison entre différents paradigmesd’estimation ;

• sélection de modèles pour les données enimagerie par résonance magnétique fonction-nelle ;

• estimation à la source pour les électroencépha-logrammes.

Ces sujets couvraient différents aspects des pro-blèmes souvent rencontrés lors de la reconstruc-

tion d’images. Plusieurs méthodes d’estimationet de calculs ont été présentées.

Charles Bouman (Purdue) a fait le point sur lesnouveaux imageurs optiques qui soulèvent au-jourd’hui autant d’intérêt sur le plan des possi-bilités de « voir » l’activité cérébrale que de défisau niveau des méthodologies de reconstructiontomographique. La tomographie bayésienne afait l’objet de l’exposé d’Ali Mohammad-Djafari(Supélec), spécialiste reconnu des questions dereconstruction à partir de données partielles etincomplètes. L’exposé de Keith Worsley (McGill)donnait un point de vue critique sur l’approchebayésienne en la remettant dans une perspec-tive d’étude de groupe pour l’inférence robustede l’activation cérébrale. Cet exposé complé-tait fort bien les deux présentations fouillées deChristophe Phillips (Liège) qui a su remettre enperspective les outils méthodologiques dans lecontexte appliqué de l’imagerie cérébrale quipeut, aujourd’hui, profiter de la fusion de plu-sieurs types d’information. L’atelier a égalementdonné l’occasion à de jeunes chercheurs de pré-senter leurs propres travaux. Christophe Grova(McGill) a ainsi présenté une méthodologied’évaluation pour comparer les performancesdes estimateurs. Jean Daunizeau (Montréal) adonné une solution au problème de fusion mul-timodale qui permet de prendre en compte dif-férentes sources d’information et François Des-trempes (Montréal) a présenté un estimateurbayésien pour les modèles de champs de Mar-kov cachés qui sont largement utilisés en image-rie mathématique.

Le format de cet atelier a permis d’établir unbon échange entre les différents conférenciers etles participants. Plusieurs étudiants ont pu aussiprésenter leurs travaux et en discuter avec leschercheurs plus expérimentés dans ce domaine.

Workshop on Analysis and Computation ofLattice, Delay and Functional DifferentialEquationsApril 25, 2005, McGill Universityorganized by the Applied Mathematics Labora-tory

Organizer: Tony Humphries (McGill)Invited speakers: D. Breda (Universita degliStudi di Udine), D. Pelinovsky (McMaster), P.-L.Buono (UOIT), B. Moore (McGill), T. Humphries(McGill), R. Wilds (McGill)Number of participants: 18

This workshop focused on recent developmentsin the analysis and computation of lattice, de-

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lay and functional differential equations, withparticular emphasis on advanced-retarded dif-ferential delay equations which define travel-ling wave solutions to lattice differential equa-tions, and related problems. It brought togetherresearchers with theoretical, computational andapplications interests. Topics covered includeddetermining stability of solutions via pseu-dospectral approximation of characteristic val-ues, bifurcations of travelling wave solutionsin discrete NLS lattices, and unfolding of lo-cal bifurcations in equations modelling biolog-ical phenomena. Also covered were travellingwaves and propagation failure in problems withinhomogeneous diffusion, as well as numericalcomputation of travelling waves in lattice differ-ential equations including model problems andproblem truncation.

Analysis DayApril 29, 2005, CRMorganized by the Mathematical Analysis Labo-ratory

Organizers: Thomas Ransford (Laval), Chris-tiane Rousseau (Montréal), Alina Stancu (Mont-réal), Galia Dafni (Concordia), Dmitry Jakobson(McGill)Speakers: T. Kaczynski (Sherbrooke), A. Koko-tov (Concordia), F. Nazarov (Michigan State)Number of participants: 27

Le laboratoire a commencé ses activités seule-ment en 2003-2004. Le programme scientifiquede l’année 2003-2004 a été remarquable tantpar sa qualité que par les rapprochements qu’ila permis entre des membres qui se connais-saient peu. Ce laboratoire est celui qui a le plusde membres. Ses membres sont dispersés danstoutes les universités québécoises, ce qui forcedifférents sous-groupes à travailler en paral-lèle. Pour remédier à ce problème, nous avonscommencé en 2004-2005 la tradition d’une jour-née d’analyse à laquelle seront conviés tous lesmembres. À court terme il n’y a pas lieu de fairevenir beaucoup de conférenciers de l’extérieurmais plutôt de laisser la parole aux membres. Leformat incluait des conférences d’une heure etdes conférences d’une demi-heure, en évitant lesconférences en parallèle.

Topics in Low-Dimensional TopologyMay 16 – 17, 2005, UQÀMorganized by CIRGET

Organizers: Steven Boyer (UQÀM), OlivierCollin (UQÀM)Number of participants: 15

Fifteen mathematicians and students partici-pated in this two-day workshop held at UQÀM.Five of the six talks focused on the topologyand geometry of 3-manifolds and one other on4-dimensional topology. The two main themeswere applications of geometric methods in 3-manifolds and the contact topology in dimen-sion 3.

The speakers and their titles were:

• Joseph Masters (SUNY Buffalo), Quasi-Fuchsian surfaces in hyperbolic knot-manifolds

• Baptiste Chantraine, (UQÀM), Isotopies lengen-driennes et cobordismes lagrangiens

• Xingru Zhang, (SUNY Buffalo), Virtual fibringof Montesinos link complements

• David Gay, (UQÀM), Constructing singular Lef-schetz pencils and fibrations

• Olga Plamenevskaya, (MIT), Khovanov homol-ogy, Heegaard Floer invariants, and contact struc-tures

• Michel Boileau, (Toulouse 3), Finiteness of 3-manifolds and non-zero degree mappings.

Analytic Number Theory ConferenceMay 19 – 21, Université Lavalorganized by CICMA

Organizers: Jean-Marie De Koninck (Laval),Claude Levesque (Laval)Speakers: C. Ballot (Caen), W. Banks (Missouri),J. Friedlander (Toronto), V. Garcia (Puerto Rico),A. Granville (Montréal), H. Kadiri (Montréal) , S.Louboutin (Luminy), F. Luca (Morelia), R. Murty(Kingston), C. Pomerance (Dartmouth), L. Sza-lay (Ouest-Hongrie)Number of participants: 43

La conférence portait sur une grande variétéde thèmes en théorie analytique des nombres,dont les fonctions arithmétiques, les séries deDirichlet, les courbes elliptiques, la méthode ducrible, les sommes de diviseurs, les problèmesdu type Waring, les fonctions zêta de Dede-kind, les équations de Pell simultanées, le théo-rème de Polya-Vinogradov, les petits intervallescontenant des premiers en progression arithmé-tique. Le principal objectif de cette rencontre

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GENERAL PROGRAM

était la mise en commun de différents résultatsd’actualité en théorie analytique des nombres.

Quatrieme colloque francophone sur lessondagesMay 24 – 27, 2005, Université LavalOfficial Meeting of the Société Française deStatistique (SFdS), supported by the StatisticsLaboratory

Chair of the scientific committee: Louis-PaulRivest (Laval)Chair of the organizing committee: LouiseBourque (ISQ)Speakers: J. Domingo-Ferrer (Rovira i Cir-gili de Tarragone, Catalogne), J. Baulne (ISQ),L. Des Groseillers (ISQ), E. Gagnon (ISQ), P.St-Cyr (Statistics Canada), R. Orok (StatisticsCanada), P. Collomb (INED), M.-C. Tremblay(Environment Canada), S. Cotter (Office fédéralde la statistique, Suisse), P. Gauthier (Statis-tics Canada), F. Dupont (INSEE), E. Graf (Of-fice fédéral de la statistique, Suisse), E. Rancourt(Statistics Canada), M. Thompson (Waterloo), A.Saïdi (Statistics Canada), C. Boudreau (Medi-cal College of Wisconsin), N. Lavigne (Statis-tics Canada), R. Morrison (Statistics Canada),S. Giroux (Statistics Canada), M.-E. Tremblay(ISQ), N. Plante (ISQ) R. Courtemanche (ISQ), D.Joye (SIDOS), R. Silberman (LASMAS-CNRS), L.Bourque (ISQ), R. Barnabé (Statistics Canada),A. Davison (EPFL), C. Sårndal, J.-D. Opsomer(Iowa State), J.-F. Beaumont (Statistics Canada),P. Bernard (Montréal), D. Lievesley (UNESCO)Number of participants: 240

L’organisation du Colloque de Québec a été as-surée par l’Institut de la statistique du Qué-bec (ISQ) et l’Université Laval, en collaborationavec Statistique Canada, l’Association des statis-ticiennes et statisticiens du Québec (ASSQ), laSociété statistique du Canada (SSC), le Centre derecherches mathématiques et l’Association inter-nationale des statisticiens d’enquête (de l’Insti-tut international de statistique).

Plus de 240 participants, venant de l’Europe etdes Amériques, ont participé à ce colloque quia duré quatre jours. Deux ateliers portant surdes méthodes statistiques spécifiques à l’analysede données d’enquête complexes ont été présen-tés le mardi 24 mai. Environ 75 participants ontpris part à ces ateliers. Le premier était animé

par François Brisebois de Statistique Canada etportait sur l’analyse de données sur la santé, re-cueillies à l’aide d’enquêtes à plans complexesalors que le deuxième, était animé par OlivierSautory de INSEE-CEPE et portait sur les pro-cédures SAS d’échantillonnage et d’analyse dedonnées d’enquête. Le colloque comme tel a dé-buté le mercredi 25 mai au matin par un ex-posé sur le rôle des méthodologistes dans la ges-tion de la qualité par Gordon Brackstone, pré-sident de l’association internationale des statis-ticiens d’enquêtes, une section de l’Institut inter-national de la statistique. Une centaine de com-munications y ont été présentées, 70 libres et 30sur invitation. La plénière de clôture, où M. etMme Mizrahi de l’ARgSES dressaient un histo-rique des enquêtes de santé en France, s’est ter-minée le vendredi 27 mai à 17h00.

Plusieurs séances ont porté sur des dévelop-pements de statistique théoriques motivés parl’analyse de données d’enquête. Le bootstrap,le lissage et l’utilisation de modèles statistiquespour les données d’enquête y ont été abordés.Les enquêtes de santé ont également fait l’objetde nombreuses communications ; on y a traité duchoix du mode de collecte, et de la pondérationdes données, entre autres. La plénière de clôtureprésentait un historique des enquêtes de santéen France. Des thèmes propres à la statistiqueofficielle tels la gestion de la qualité, le recense-ment, l’utilisation de données administratives etle respect de la confidentialité des informationsfournies par les répondants ont été traités dansde nombreuses sessions. Une séance sur l’accès,par les chercheurs, aux micros données confi-dentielles dans les pays francophones s’est ter-minée par une visite du laboratoire CIQSS-Lavaloù les chercheurs de l’université Laval ont accèsaux données d’enquête de l’Institut de la statis-tique du Québec et de Statistique Canada.

Les organisateurs ont reçu de nombreux té-moignages d’appréciation tant pour les aspectsscientifiques qu’organisationnels du colloque.En effet, le programme scientifique chargé et fortrelevé était accompagné d’un programme socialfort intéressant. Quant aux conférences présen-tées dans le cadre du colloque, elles se retrouve-ront dans les actes qui seront publiés chez Du-nod en 2006, assurant ainsi une pérennité à la re-cherche qui y a été présentée.

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CRM-ISM Colloquium Series

The CRM, together with the Institut des sci-ences mathématiques (the Québec universitygraduate mathematics consortium), runs twoMontréal colloquium series, one in mathematicsand another in statistics (the latter jointly withGERAD). These series offer during the academicyear survey talks by distinguished mathemati-cians and statisticians on topics of current inter-est.

CRM– ISM Mathematics Colloquium

Coordinators: Octavian Cornea (Montréal),Dmitry Jakobson (McGill).

April 22, 2005: Isadore Singer (MIT)The Geometry of Twisted K-Theory

April 15, 2005: Kaleem Siddiqi (McGill)Medial Integrals for Shape Analysis

April 8, 2005: Fabio Bagarello (Palermo)Relations between Multi-Resolution Analysis andQuantum Mechanics: Applications to the FractionalQuantum Hall Effect

April 1, 2005: Mark Haiman (UC Berkeley)Macdonald Polynomials

March 18, 2005: Alexander Its (IUPUI, Indianop-olis)On the Asymptotic Analysis of Toeplitz Determi-nants via the Riemann – Hilbert Method

March 11, 2005: Krystyna Kuperberg (Auburn)Wild and 2-Wild Trajectories

March 4, 2005: Matt Gursky (Notre Dame)Some Fully Nonlinear Equations in Geometry

February 18, 2005: Askold Khovanskii (Toronto)Insolvability of Equations in Finite Terms

February 11, 2005: Steven Lu (UQÀM)Positivity Theorems and the Structure of CompactComplex Manifolds

February 4, 2005: Stephan De Bièvre (Lille I)Chaos quantique: au-delà du théorème deSchnirelman

January 28, 2005: David Bryant (McGill)How can a Mathematician Cope with PhylogeneticUncertainty?

January 21, 2005: Jozef Dodziuk (CUNY)Elliptic Difference Operators on Graphs

January 14, 2005: Haynes Miller (MIT)Elliptic Moduli in Algebraic Topology

January 7, 2005: Vladimir Remeslennikov(UQÀM) et Ilya Kazatchkov (Omsk)Free Partially Commutative Groups

December 10, 2004: Vladimir Korepin (SUNYStony Brook)Quantum Correlations and Number Theory

December 3, 2004: Yuri Gurevich (Microsoft)What is an Algorithm?

November 26, 2004: Bruce Reed (McGill)Routed Routing and Graph Minors

November 19, 2004: Alejandro Adem (UBC)Periodic Complexes and Group Actions

November 5, 2004: Claude Le Bris (ENPC)Flots généralisés de solutions pour des équations dif-férentielles déterministes et stochastiques à coeffi-cients irréguliers

October 22, 2004: Jean-Pierre Gazeau (Paris VII)États cohérents et quantification de systèmes simples

October 15, 2004: Stephanos Venakides (Duke)The Nonlinear Analogues of the Fourier Transform,Steepest Descent and Eikonal Analysis

October 8, 2004: Ronald Fintushel (MichiganState)Lagrangian Tori in 4-Manifolds

October 1, 2004: John Harnad (Concordia)Random Matrices, Orthogonal Polynomials and In-tegrable Systems

September 24, 2004: Paul Schupp (Illinois, Ur-bana Champaign)The Uniform Membership Problem, Foldings andPolynomial Time

September 17, 2004: Pengfei Guan (McGill)Convexity of Solutions of Geometric Nonlinear Par-tial Differential Equations

CRM– ISM–GERAD Statistics Collo-quium

Coordinators: Christian Léger (Montréal) main-coordinator, Pierre Duchesne (Montréal), BrendaMacGibbon (UQÀM), Arush Sen (Concordia),Russ Steele (McGill).

April 8, 2005: Hira Koul (Michigan State)Goodness-of-Fit Testing in Interval Censoring Case 1

March 18, 2005: Jeffrey S. Rosenthal (Toronto)Adaptive MCMC: A Java Applet’s Perspective

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March 11, 2005: Ricardas Zitikis, (Western On-tario)Comparing Points in Multi-Dimensional Spaces,Even When They Are Random

March 4, 2005: Debbie Dupuis (HEC)Ozone Concentrations: a Robust Analysis of Multi-variate Extremes

February 25, 2005: Changbao Wu (Waterloo)Empirical Likelihood Approach to Calibration withSurvey Data

February 18, 2005: Edward L. Ionides (Michi-gan)Infectious Diseases: Data Analysis via ContinuousTime Population Models

February 11, 2005: Angelo J. Canty (Toronto)Finding Differentially Expressed Genes fromAffymetrix Microarray Data

February 4, 2005: Richard Cook (Waterloo)Some Robust Methods for Studies Involving Recur-rent Events

January 25, 2005: Hao Yu (Western Ontario)Residual Processes of GARCH Models and Their Ap-plications

December 3, 2004: Subhash Kochar (ISI)Dependence Orderings for Order Statistics andRecords

November 26, 2004: Weidong Tian (Waterloo)Stochastic Volatility Models: A Large Deviation Ap-proach

November 19, 2004: Linyuan Li (New Hamp-shire)

On the Minimax Optimality of Block ThresholdedWavelet Estimators with Long Memory Data

Novembere 12, 2004: Donald Dawson (Carletonet McGill)2004 CRM-Fields PrizeStochastic Dynamics of Evolving Populations

November 5, 2004: Christopher Field (Dal-housie)Robustness Issues in Models for Molecular Evolution

October 29, 2004: Corinne Berzin (Grenoble II)Théorèmes centraux limites pour des fonctionnellesnon linéaires de processus gaussiens et applications

October 22, 2004: Randy Sitter (Simon Fraser)2004 CRM-SSC PrizeResampling in Complex Surveys

October 15, 2004: Qihe Tang (Concordia)Asymptotic Ruin Probabilities in the Presence ofStochastic Returns on Investments

October 8, 2004: Adrian Raftery (Washington)La prévision météorologique probabiliste

October 1, 2004: Xin Gao (York)A Unified Nonparametric Approach for UnbalancedFactorial Design

September 24, 2004: David Haziza (StatistiqueCanada)Approche par modèle de non-réponse pour l’inférenceen présence de données imputées

September 17, 2004: Steven X. Wang (York)Weighted Likelihood Estimation

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Multidisciplinary and Industrial Program

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MULTIDISCIPLINARY AND INDUSTRIAL PROGRAM

THE main vehicles for the CRM’s efforts in this area are the research networks to which it belongs.Principally, MITACS, a national network focusing on the mathematics of information technology

and complex systems, and the National Program on Complex Data Structures (NPCDS). The reportsare presented in the language in which they were submitted.

Activities of the Multidisciplinary and Industrial Program

Workshop on Stochastic NetworksJuly 16 – 26, 2004, CRM

Organizers: Peter Glynn (Stanford), George Ke-sidis (Penn State), Donald A. Dawson (McGill),Raj Srinivasan (Saskatchewan)Number of participants: 90

In July 2004, within the framework of its Mul-tidisciplinary and Industrial Program, the CRMhosted a workshop on Stochastic Networkswith three different activities. The Madison-styleStochastic Network Conference (SNC) includedtwo satellite workshops. The two-day workshopon Economics of Communication Networks pre-ceded the SNC, while the three-day Call Cen-tre Workshop (CCW), partially funded by theWharton Financial Institutions Center, was atthe tail end of the SNC.

Workshop on Economics of CommunicationNetworksOrganizer: George Kesidis (Penn State)

This workshop attracted some of the major fig-ures who are working on increasingly importanteconomic issues related to the theory of commu-nication networking. In particular, two very in-teresting talks on the role of economic incentivesfor emerging peer-to-peer networks drew a greatdeal of discussion during the breaks. Lively dis-cussions also broke out during several talks andparticipants expressed the value of the clarifica-tion of issues that was achieved in this some-times confusing area where a diversity of issuesneed to be considered simultaneously. For exam-ple,• the roles and mathematical definitions of

“fairness” and how they might be interpretedas regulation in a communication networkthat is run more according to free market dy-namics than in current practice;

• how security, pricing & billing, and quality-of-service may be interrelated.

Stochastic Networks ConferenceOrganizer: Peter Glynn (Stanford)

This meeting attracted the major figures who arecontributing to the development of a mathemat-

ical theory for stochastic networks. A large por-tion of the talks related to various challengesthat are arising in the wireless networks set-ting, where key issues include the spatial vari-ation, bandwidth limitations, and the need togenerate distributed control policies. The formatof the conference, in which only four one hourtalks were scheduled over each of the six days(with the exception of the Wednesday session,in which only three talks were scheduled), lentitself to an environment in which participantswere able to pursue significant technical interac-tions. In spite of the lack of opportunity to givefull contributed talks, the meeting attracted asignificant number of attendees, in large part be-cause it provided an opportunity for unhurriedtechnical exchanges amongst all participants.

It should be noted that Alcatel provided finan-cial support to the meeting, in recognition ofthe relevance of the research agenda to its coremission. A number of industrial participants at-tended the meeting. In addition, one of the ma-jor journals in the area, Queuing systems: Theoryand applications, contacted the organizer subse-quent to the meeting to request that a specialinvited issue, consisting of papers based on thetalks given at the meeting, be put together. Thisspecial issue is being pursued, and publicationis expected late in 2005. This journal’s interest inpursuing such a special issue is a clear testimonyto the quality of the talks offered as part of theStochastic Networks Conference.

Call Center WorkshopOrganizer: Raj Srinivasan (Saskastchewan)

To recognize the recent flurry of research ac-tivities in the call center area, the last day ofthe SNC was designated as a joint activity withthe CCW. There were four talks on that dayof the SNC, most of them being concentratedon staffing large call centres using fluid models.This joint activity was very well received by theeighty-two people in attendance. The CCW con-tinued for another two days with twelve talks.There were twenty-eight to forty-two people inattendance for the two-day activity. The talkscovered a wide range of topics including queu-

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ing network with time varying rates, statisti-cal analysis of call centres, workforce planningand profit maximization, revenue managementthrough cross-selling and managing learningand turnover in employee staffing. The work-shop also included a tutorial on call centers.

One of the highlight of the talks was the pre-sentation from Chantal Gagné, the General Man-ager of Bell Canada Holdings, who discussedseveral challenges involved in the managementof call centers at Bell Canada. In particular, sheemphasized the difficulties facing the industryin forecasting call volume over the eighteenmonths planning horizon and training workforce during that period. Active participationfrom the audience resulted in lively and pro-ductive discussions. Besides the annual two-dayCall Center Forum run by the Wharton Finan-cial Institutions Centre for their industrial partic-ipants, the CCW hosted by CRM is the first ma-jor workshop on call centres. Based on the feed-back we have received from the participants, thisworkshop was a very successful one.

MITACS Biomedical WorkshopJanuary 19 – 20, 2005, CRMorganised by MITACS

Organizers: Leon Glass (McGill), MichaelMackey (McGill), Jack Tuszynski (Alberta),David Ritscher (Medtronic), Jeffrey Saltzman(Merck), Colin Hill (Gene Network Sciences),Alain Vinet (Montréal), Gerda de Vries (Alberta),Kevin Hall (National Institutes of Health), Jian-hong Wu (York), Thomas Hillen (Alberta)Speakers: R. McInnes (Institute of Genetics), S.Bull (Toronto), A. Atoyan (Montréal), L. Greller(Biosystemix), M. Weiner (Biophan Technolo-gies), J. Tuszynski (Alberta), J. Saltzman (Merck),C. Hill (Gene Network Sciences), K. Worsley(McGill)Number of participants: 47

A number of MITACS research projects are cur-rently involved in biomedical research with sci-entists and partners drawn from across Canada.Our experience from both research projects andnetworking activities demonstrates that there isconsiderable interest in this area among both in-dustry and government organizations.

The main objectives of the workshop were: tobring together individuals from industry, gov-ernment and academia who are interested inbiomedical research; to share experiences fromindustry and government participants on key is-sues relating to medical devices and drug de-

velopment, design, and testing; to establish fu-ture biomedical research priorities; and finally,to create new opportunities for research col-laborations between industry, government andacademia.

During this workshop, industrial, academicand governmental organizations discussed andidentified keys research areas in the field of (butnot limited to):

Drug development/design/testing

• design issues;• use of signaling networks to aid in intelligent

drug design;• in vitro drug testing;• diabetes drug design;• analysis, interpretation and integration of

biomedical data.

Medical devices

• techniques/devices for arrhythmia detectionand treatment;

• analysis of medical imaging (mri, cat scan, pet,etc.);

• devices for the treatment of diabetes, e.g., pro-grammable implanted pumps;

• analysis of gene chip data;• analysis, interpretation and integration of

biomedical data.

Furthermore, issues concerning public healthwere raised. For instance: device manufactur-ers, drug companies, large data collections fromhuge sets, lack of incentive from drug or devicemanufacturers to develop studies addressing is-sues.

Participants had the opportunity to share theiracademic interests and propose new collabora-tions. Also, various biomedical internship possi-bilities were proposed.

Launching of Aeronautics CooperationCRM– CRIAQ–MITACSJanuary 20, 2005, Dorval

On January 2005, at the initiative of CRM andwith the help of CIRANO’s Director, the firstexploratory day between mathematicians andthe Canadian Aeronautical Industry was heldat the Bombardier offices in Dorval. Presenta-tions were given by the Advanced Research Di-rector at Bombardier, Bombardier researchers,Pratt & Whitney representatives, MITACS Direc-tor and CEO, CRIAQ’s president, and CRM di-rector. Also present were Michel Delfour fromCRM and Neil Stewart from DIRO (Montréal).

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MULTIDISCIPLINARY AND INDUSTRIAL PROGRAM

This event was held in preparation to theToronto MITACS meeting on Aeronautics.

Workshop on Computational Biology in thePost-Genomics EraMarch 19 – 20, 2005, CRM

Scientific committee: Sandrine Dudoit (UCBerkeley), Avner Friedman (Ohio State), MichaelHallet, (McGill), Leah Keshet (UBC), MarkLewis (Alberta), Normand Mousseau (Mont-réal), John Nash (CNRC-ISB), Enrico Purisima(CNRC-IRB), Jamie Stafford (Toronto) and Raj-mund L. Somorjai (CNRC-IBD)Steering committee: Barbara Lee Keyfitz (di-rector, Fields), Ivar Ekeland (director, PIMS),François Lalonde, (director, CRM), WilliamCowley (Senior Program Officer, NRC), IsabelleBlain (Vice-President, CRSNG)Number of participants: 64

The origin of the workshop is the result of long-term discussions between NRC and the mathe-matics institutes, CRM, Fields and PIMS.

Firstly, the workshop was intended to explorepossible joint research activities between theNRC labs and industry on the one hand andresearchers in the Canadian universities, espe-cially those who have developed specific mathe-matical expertise, on the other hand, on the gen-eral subject of computational biology (taken ina broad sense). Thus the workshop provided anopportunity to seek possible common researchinterests and complementary methods or pointsof view between the two milieux. The ultimategoal was to see whether or not there is a gen-uine interest in interacting at a scientific levelThe workshop provided an opportunity to learnabout foreign experiences, especially in the USand in France, where there have been efforts tolaunch initiatives that have led to the emergenceof a genuine “computational community.”

A further purpose of the workshop was tobroaden the scientific interaction between bi-ologists and mathematicians, to address biolo-gists’ concern that their models are so simplis-tic that they will not be challenging to math-ematics; whether mathematics can provide ap-proaches to seemingly intractable problems ofbiology, and to provide direction to mathemati-cians about new domains that will need study.

The main scientific themes of the workshopwere: biomedical data analysis, computationalstructural biology, proteomics and protein mod-eling and genomics analysis.

The topics discussed in the plenary session were:funding agencies, universities and the chal-lenges of interdisciplinary research and the sci-entific collaborations between mathematiciansand biologists. During the first session, the mainthemes were: the challenge of interdisciplinaryresearch, what NSERC is doing and should do,the MITACS model and the US model.

Workshop on Latent Variable Models andSurvey Data for Social and Health SciencesResearchMay 4 – 6, 2005, CRMNPCDS activitysponsored by the CRM, the NPCDS, the SAMSIand Statistics Canada

Organizers: Mary Thompson (Waterloo), ChrisSkinner (Southampton), Paul Biemer (UNCChapel Hill), Jamie Stafford (Toronto), Milo-rad Kovacevic (Statistics Canada), Randy Sitter(Simon Fraser), David Bellhouse (Western On-tario), Roland Thomas (Carleton)Speakers: H.Ariizumi (Wilfrid Laurier), T. As-parouhov (Muthen & Muthen), K.A. Bollen(UNC Chapel Hill), Brault, A. Carle (U.S. Cen-sus Bureau), K. Chantala (UNC Chapel Hill),S. Christ (UNC Chapel Hill), A. Cyr (Statis-tics Canada), A. Davies (Statistics Canada), M.Kovacevic (Statistics Canada), B. Meekins (Bu-reau of Labor Statistics), B. Muthén (UCLA),J. Olsen (Brigham Young), M. Paterson (Sher-brooke), S. Rabe-Hesketh (UC Berkeley), J.N.K.Rao (Carleton), G. Roberts (Statistics Canada), A.Sacker (University College London), C. Skinner(Southampton), A. Skrondal (London School ofEconomics), R.D. Wiggins (City University Lon-don)Number of participants: 65

This workshop was part of the contribution ofthe National Program on Complex Data Struc-tures (NPCDS) to the theme year on Latent Vari-able Models in the Social Sciences (LVMSS) ofthe Statistical and Applied Mathematical Sci-ences Institute (SAMSI) in North Carolina.

The program began with a tutorial by AndersSkrondal and Sophia Rabe-Hesketh based ontheir recent book, Generalized latent variable mod-elling (Chapman and Hall/CRC). The tutorialcovered a great deal of ground, including a thor-ough introduction to the author’s framework forlatent variable models, and a variety of interest-ing applications. It was very valuable for bothexperts and novices.

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The difficulties in adapting latent variable meth-ods to complex survey data are perhaps bestappreciated in the context of multi-level mod-els, and Chris Skinner provided an excellentoverview of progress to date in this area. Papersby Chantala and Suchindran and by Kovacevicand Huang provided further insights into theperformance of currently available techniques.

Bengt Muthén and Tihomir Asparouhov intro-duced Mplus and demonstrated its efficiencyand flexibility for latent variable models. Thesoftware is being developed in conjunction withleading edge research in social science method-ology, and the complex survey project will makeit even more useful. The discussions of the appli-cation papers were also greatly enhanced by thecontributions of the Mplus team.

The workshop provided an opportunity for areview of the accomplishments of the SAMSItheme year on latent variable models, by itsleader, Ken Bollen.

One gratifying feature of the workshop was thehigh quality of the presentations, and of theanalyses put forward. It is very good for statisti-cians and social scientists each to see somethingof the best of what the other has to offer.

Spring School and Workshop on Mini-invasive Procedures in Medicine andSurgery: Mathematical and NumericalChallengesMay 16 – 27, 2005, CRMsponsored by CRM, MITACS and INRIA

Scientific committee and organizers: MichelDelfour (Montréal), André Fortin (Laval), AndréGaron (École Polytechnique Montréal), CharlesPeskin (Courant Inst.), Marc Thiriet (INRIA Roc-quencourt)Main speakers of the School: Charles Peskin(Courant Inst.), Marc Thiriet (INRIA Rocquen-court)Speakers and animators of mini-workshops ofthe School: Miguel Fernandez (INRIA Rocquen-court), Julie Grant (École Polytechnique Mont-réal), Gérard Plante (Institut de Pharmacolo-gie de Sherbrooke), Grégoire Malandain (INRIASophia-Antipolis), Catalin Fetita (Institut Na-tional des Télécommunications)Invited speakers: Y. Bourgault (Ottawa), G.W.Burgreen (Mississippi State), L. Cohen (Paris-Dauphine), M. Delfour (Montréal), C.R. Ethier(Toronto Western Research Institute), C. Fetita(Institut National des Télécommunications), A.Fogelson (Utah), A. Fortin (Laval), A. Garon

(École Polytechnique), R. Lohner (George Ma-son), G. Malandain (INRIA Sophia Antipolis),M. S. Olufsen (NC State), R. Owens (Montréal), J.Peirò (Imperial College London), M. Sorine (IN-RIA Rocquencourt), D. Steinman (Robarts Re-search Institute, London, ON), M. Thiriet (IN-RIA Rocquencourt), J. Urquiza (Montréal), K.Worsley (McGill), J.-P. Zolésio (INRIA, Sophia-Antipolis)Number of participants: 58, including 18 stu-dents.

The object of this combined Spring School andWorkshop was to bring together experts of in-ternational stature on several facets of mini-invasive procedures in medicine and surgeryand to identify the underlying mathematical andcomputing challenges. The main themes of theworkshop were:

• Biology and mechanics of blood flows;• brain imaging and functions;• cardiac pump;• fluid-structure interactions;• image-based computations;• imaging, meshing and computing;• image processing;• immersed boundaries;• medical devices;• mathematical modeling and computer simu-

lation of the circulation and the hearth;• particle flows;• wall transport.

This ambitious project resulted from a sustainedand productive collaboration between MarcThiriet (INRIA, France), André Garon (ÉcolePolytechnique, Canada) and Michel Delfour(CRM and DMS, Canada). The importance ofsuch exchanges between France and Canadawas recognized two years ago by INRIA whichconferred the status of associated group to theresearchers.

The initiative of holding a Spring School in thedays preceding the Workshop proved to be agreat success; student participation was excel-lent and exchanges were useful and animated.We had the privilege to have two exceptionalprincipal speakers whose 12 talks were comple-mentary. Charles Peskin (Courant Institute, NewYork) is one of the pioneers in the field of mathe-matical modeling and in the simulation of flowsand the heart. He his also the father of “im-mersed boundaries” and of the first valve sim-ulations. Marc Thiriet (member of CNRS, Labo-ratoire Jacques-Louis Lions, Université Pierre etMarie Curie), and principal investigator respon-

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sible for the REO project at INRIA, Rocquen-court, France), is a pneumologist by training aswell as a mechanical engineer specializing in flu-ids. He was a tremendous driving force duringthe school, thanks to, in particular, an extraor-dinarily encyclopedic book of more than 300pages titled “Biology and mechanics of bloodflows” which was given in pre-publication toall participants. This work will be published bySpringer. The theme of his lectures was “Frominput data (biologic, medical, physical, rheolog-ical) to blood flow numerical simulations.”

These two series of principal lectures of theschool were completed by three afternoonsof thematic mini-workshops. Miguel Fernan-dez (INRIA, Rocquencourt, Projet REO) ani-mated the one on “Numerical simulations ofthe fluid-structure coupling in physiological ves-sels.” Dr. Gérard Plante (Institut de Pharma-cologie de Sherbrooke) and Julie Grant (ÉcolePolytechnique, Montréal) conducted the sec-

ond one on “Molecule transport in vessel wallsand blood flows.” Finally, Grégoire Malandain(INRIA Sophia-Antipolis, Projet Epidaure) andCatalin Fetita (Institut National des Télécom-munications, Projets Artemis) lead the one on“Medical image processing: from vessel wall ex-tration to surface mesh production.”

The main workshop of the second week broughttogether world-renowned specialists aroundnine of the major themes of the activity. It wasa privileged meeting ground for the American,Canadian and French team, in a very casualQuébécois ambiance. The participation was sus-tained until the very last session on Friday. Stu-dents interested to give a talk gave their presen-tations on Wednesday afternoon and at the endof the other days.

Finally, the organizers would like to tank CRM,INRIA and MITACS for their financial assis-tance.

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CRM PRIZES

CRM– Fields Prize 2005 awarded to David W. Boyd

David Boyd, thisyear’s recipient, isone of Canada’sleading numbertheorists. He hasmade seminal con-tributions to ana-lytic number theory,noteworthy amongwhich are his ex-plorations of thedeep connectionsbetween the Mahler

measure of polynomials and special values oftheir associated L-functions.

Professor Boyd received his B.Sc. from CarletonUniversity in 1963, and his M.A. and Ph.D. fromthe University of Toronto in 1964 and 1966. Hehas taught at the University of Alberta and theCalifornia Institute of Technology, and has beenat UBC since 1971 where he is currently Full Pro-fessor. He is a winner of the E.W.R. Steacie Prize,a Fellow of the Royal Society of Canada, and haswon both the Canadian Mathematical Society’sCoxeter – James and Jeffery – Williams Prize lec-

tures. His service to the Canadian mathemati-cal community includes terms as vice-presidentof the Canadian Mathematical Society, chair ofthe NSERC Mathematics grant selection com-mittee, and Acting Director of the Pacific Insti-tute for the Mathematical Sciences. The recipi-ent outlines the main themes of his research inLe Bulletin du CRM, vol. 11, no 1, pp. 14 – 15.

The CRM– Fields Prize

The Centre de recherches mathématiques andThe Fields Institute established the CRM-Fieldsprize in 1994 to recognize exceptional research inthe mathematical sciences. The recipient is cho-sen by a selection committee made up of mem-bers of the Advisory Committee of the CRM andthe Scientific Advisory Panel of the Fields Insti-tute.

Previous recipients of the prize are H.S.M. (Don-ald) Coxeter (1995), George A. Elliott (1996),James Arthur (1997), Robert V. Moody (1998),Stephen A. Cook (1999), Israel Michael Sigal(2000), William T. Tutte (2001), John B. Friedlan-der (2002), Edwin Perkins (2003), John McKay(2003), and Donald A. Dawson (2004).

Andre Aisenstadt Prize 2005 awarded to Ravi Vakil

The 2005 André-Aisenstadt Prizewas awarded toRavi Vakil of Stan-ford University. Af-ter completing hisB.Sc. and M.Sc. atthe University ofToronto in 1992,Dr. Vakil obtainedhis Ph.D. from Har-vard University in1997 under the su-

pervision of Joe Harris. Dr. Vakil then spent ayear as a postdoctoral fellow at Princeton Uni-versity, and three years at MIT as a C.L.E. MooreInstructor, before becoming an Assistant Profes-sor at Stanford in 2001.

Dr. Vakil works in algebraic geometry, investi-gating the enumerative geometry of projectivealgebraic curves. His most spectacular work hasbeen done in the last years, in his study of degen-erations in a Grassmannian, to solve several oldproblems in Schubert calculus. One of his con-

clusions is that all Schubert problems are enu-merative over the real numbers. This has been amajor goal in the area of real enumerative geom-etry for at least two decades, and Dr. Vakil hasgiven a complete solution.

The exceptional work of Ravi Vakil was recog-nized by several prizes and honors, includinga NSF Career Fellowship, a Sloan Research Fel-lowship, a Centennial Fellowship and a G. deB. Robinson Prize. The Prize was awarded toDr. Ravi Vakil at a ceremony held on April 29,2005 at the CRM. The recipient’s research de-scription can be found in Le Bulletin du CRM, vol.11, no 1, pp. 2 – 3.

The Andre Aisenstadt Prize

Created in 1991, the André-Aisenstadt Mathe-matics Prize is intended to recognize and re-ward research achievements in pure and appliedmathematics by talented young Canadian math-ematicians. This prize consists of a $3,000 awardand a medal. The recipient is chosen by CRM’sadvisory committee. At the time of considera-

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tion, candidates must be Canadian citizens orpermanent residents of Canada, and no morethan seven years from their Ph.D.

The previous recipients of the André-AisensadtPrize are: Niky Kamran (1992), Ian Putnam(1993), Michael Ward (1995), Nigel Higson

(1995), Adrian S. Lewis (1996), Lisa Jeffrey(1997), Henri Darmon (1997), Boris Khesin(1998), John Toth (1999), Changfeng Gui (2000),Eckhard Meinrenken (2001), Jinyi Chen (2002),Alexander Brudnyi (2003), and Vinayak Vatsal(2004).

CAP– CRM Prize 2005 awarded to Robert C. Myers

The Canadian Asso-ciation of Physicists(CAP) and the Centrede recherches mathé-matiques (CRM) werevery pleased to an-nounce that the 2005CAP – CRM Prize inTheoretical and Math-ematical Physics wasawarded to ProfessorRobert C. Myers of the

Perimeter Institute in Waterloo for his outstand-ing contributions to theoretical physics, rangingfrom aspects in gravitational physics to founda-tional aspects of string theory.

After a B.Sc. in Applied Physics in Waterloo in1982, Robert Myers went to Princeton Univer-sity where he completed a M.Sc. (1983) and aPh.D. (1986) under the supervision of Profes-sor M.J. Perry. He then held a postdoctoral po-sition at the Institute for Theoretical Physics ofthe University of Santa Barbara, and he joinedMcGill University in 1989, where he became aFull Professor in 2000. Since 2001, he is a Long-Term Researcher at the new Perimeter Institutefor Theoretical Physics, and also holds a cross-appointment as a Full Professor in the PhysicsDepartment at the University of Waterloo.

Robert Myers has played a pivotal role in thedevelopment of string theory and is one of itsmost broad and creative researchers. We high-light here some of his contributions, which havehad a tremendous impact in theoretical physics.

His work in the 1980s (some in collaborationwith M. Perry) generalized the standard four-dimensional rotating black hole solution in gen-eral relativity to higher dimensions. These met-rics have been the starting point for a number ofrecent constructions of brane solutions in stringtheory. His work on non-critical string theoryshed profound new insights into the dimension-ality of space-time in string theory, by showingthat the string theory made sense in dimensionsother than the critical dimension originally envi-sioned.

His 1999 paper on the dielectric effect for branes,known in the community as the Myers effect, hasbeen highly influential. Guided by duality, heconstructed a consistent action for branes mov-ing in a background field, and thereby discov-ered the Myers effect which describes how in thepresence of background fields, a stack of braneswill become polarized and spread out. This deepinsight has in turn inspired a number of im-portant contributions by some of the leading re-searchers in string theory and quantum gravity.

His very recent work also include significant andexciting contributions in a number of differentareas. With his collaborators, Robert Myers hasfound new constructions of cosmic strings thatcan have a profound consequences in finding ex-perimental support for string theory. This workis one of the few genuine “stringy” predictionsthat have come out of string theory, and opensup the exciting possibility of testing string the-ory by making astronomical observations.

The high quality of the research of Professor My-ers has been recognized by several prestigiousresearch awards, such as the CAP’s HerzbergMedal, and the first award in the Gravity Re-search Foundation Essay Contest (that he wontwice). The 2005 CAP – CRM Prize was awardedto Professor Myers at the Annual Congress of theCAP held in June 2005 at Vancouver.

The CAP– CRM Prize

The Centre de recherches mathématiques (CRM)and the Canadian Association of Physicists(CAP) created in 1995 on the occasion of the 50thanniversary of the CAP, a joint prize in recog-nition of exceptional achievements in theoreticaland mathematical physics. The prize consists ofa $2,000 award and a medal.

Previous winners were Werner Israel (1995),William G. Unruh (1996), Ian Affleck (1997), J.Richard Bond (1998), David J. Rowe (1999), Gor-don W. Semenoff (2000), André-Marie Tremblay(2001), Pavel Winternitz (2002), Matthew Chop-tuik (2003) and Jirí Patera (2004).

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CRM PRIZES

CRM– SSC Prize 2005 awarded to Jiahua Chen

The CRM – SSCPrize in Statisticshas been awardedthis year to Dr. Ji-ahua Chen (Profes-sor, Department ofStatistics and Actu-arial Science, Uni-versity of Waterloo)for his outstandingcontributions to thestatistical sciences.Within 15 years of

his Ph.D. he has made major sustained contri-butions to three areas: design of experiments,inference for mixtures and survey methodology.Professor Chen blends powerful mathematicalability with keen insight into what is importantstatistically. His work combines deep theory andpractical methodology for dealing with difficultissues.

Apart from his three main research areas, JiahuaChen has made notable contributions to manyother areas including fish surveys, empiricallikelihood, fractal images, genetics and robustestimation. Professor Chen applies strong tech-nical and mathematical skill with a remarkableaptitude for handling important and practicalproblems. He has published extensively in theJournal of the Royal Statistical Society, Biometrika,the Journal of the American Statistical Associa-tion, the Annals of Statistics, Biometrics, StatisticaSinica, the Canadian Journal of Statistics and otherinfluential journals.

Jiahua Chen has also made important profes-sional contributions as Associate Editor of theCanadian Journal of Statistics and of Quality Tech-nology and Quantitative Management, and as amember of the Statistical Sciences Grant Selec-tion Committee of the Natural Sciences and En-gineering Research Council. He has been dedi-cated in his service to his department, in par-ticular as Associate Chair for Graduate Stud-ies. He was elected President of the Interna-tional Chinese Statistical Association in 2005.This prize announcement was made at Univer-sity of Saskatchewan in Saskatoon, site of thisyear’s Annual SSC Meeting. The recipient out-lines the main themes of his research in Le Bul-letin du CRM, vol. 11 no 1, pp. 12 – 13.

The CRM– SSC Prize

The Statistical Society of Canada, founded in1977, is dedicated to the promotion of excellencein statistical research and practice. This presti-gious award, jointly sponsored by the SSC andthe Centre de recherches mathématiques (CRM),is given each year to a Canadian statistician inrecognition of outstanding contributions to thediscipline during the recipient’s first 15 years af-ter earning a doctorate. Jiahau Chen is the sev-enth recipient of the CRM – SSC Prize.

Previous winners of the award were Chris-tian Genest (1999), Robert J. Tibshirani (2000),Colleen D. Cutler (2001), Larry A. Wasserman(2002), Charmaine B. Dean (2003) and Randy Sit-ter (2004).

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CRM Partnership

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CRM PARTNERSHIP

THE CRM is strongly committed to its national mission and takes measures to ensure that thelargest possible number of scientists across Canada benefits from its activities and become in-

volved in their planning. For instance, it appoints to its Scientific Advisory Committee eminentCanadian scientists from various parts of the country; it is present at all important forums wherethe future directions of the Canadian mathematical sciences are discussed; it urges its organizers tomake efforts to ensure the participation of the Canadian specialists in their activities; it organizesand supports scientific events across the country; it collaborates with Canadian institutes, societiesand associations. A specific budget is set aside each year for the participation of Canadian gradu-ate students in its programs. The CRM is the only national institute that operates in the two officiallanguages of Canada and it is highly visible on the international scene. In keeping with its nationalrole, it coordinates its activities with the Fields Institute, PIMS, the Canadian Mathematical Society(CMS), MITACS, the Canadian Applied and Industrial Mathematics Society (CAIMS), the StatisticalSociety of Canada (SSC), the Canadian Association of Physicists (CAP), and other societies as wellwith other institute abroad.

CRM Partners

The Fields Institute (FI) and the PacificInstitute for the Mathematical Sciences(PIMS)

Since the early 1990s twoother research institutes havejoined the CRM on the Cana-dian scene: Toronto’s FieldsInstitute (FI), and the PacificInstitute for Mathematical Sci-

ences (PIMS). As well as coordinating theirscientific activities, the three institutes haveworked closely on a variety of initiatives, themost important of which has been the Mathe-matics of Information Technology and ComplexSystems (MITACS).

Other initiatives involvedthese institutes, such as theCRM–Fields prize awarded inrecognition of outstanding ac-complishments in the mathe-matical sciences in Canada. Itwas created in 1994 and start-ing in 2006 will become theCRM–Fields–PIMS prize. Theadministrative responsibility for this prize willalternate each year between the three institutes.

International Collaboration

In 2004–2005, on the international scene, theCRM collaborated or received financial assis-tance from the National Science Foundation(NSF), the Banff International Research Station(BIRS), INSERM in Paris, the Statistical and Ap-plied Mathematical Sciences Institute (SAMSI),the Institute of Electrical and Electronics Engi-

neers (IEEE), Alcatel, and the Institute for Math-ematics and its Application (IMA).

In its publishing activities, the CRM is contin-uing its partnership with the American Math-ematical Society (AMS), in particular with itstwo series of joint publications, the CRM Mono-graph Series and the CRM Proceedings and LectureNotes. It also has two series with Springer, instatistics and in mathematical physics. The CRMhas exchange agreements with the Fields Insti-tute, PIMS, MSRI (Mathematical Sciences Re-search Institute), the Institute for Mathematicsand its Applications, École Normale Supérieure(France), the Isaac Newton Institute, the Institutdes Hautes Études Scientifiques (IHÉS, France),and the Banff International Research Station.

Associations and Professional Societies

The CRM maintains close ties with the differentprofessional societies in the mathematical sci-ences: CMS, CAIMS, SSC, and CAP. The pres-ident of the CMS is an ex-officio member ofthe CRM Scientific Advisory Committee. CRMalso financially supports a number of initiativesof the CMS, such as the mathematical camps,the Canadian Mathematics Education Forum, aswell as the travel grant program for studentswho attended the joint Canada-France meetingin Toulouse in 2004. Together with the other in-stitutes, the CRM organizes or sponsors specialsessions at the CMS, CAIMS, and SSC meet-ings. The CRM awards a prize each year jointlywith the SSC; similarly, with CAP, it awards aprize each year in mathematical and theoreticalphysics. Moreover, the CRM hosted the 2004 An-nual Meeting of the SSC.

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The Mathematics of Information Technol-ogy and Complex systems (MITACS)

MITACS began as a vi-sion of the three Canadianmathematical sciences insti-tutes. They envisioned a pan-Canadian network of projectseach focused on using sophis-ticated mathematical tools formodeling industrial problemsin key sectors of the Canadian

economy. MITACS was officially launched onFebruary 19, 1999. By March 1999, all 21 initialresearch projects were underway.

MITACS leads Canada’s effort in the genera-tion, application and commercialization of newmathematical tools and methodologies within aworld-class research program. The network ini-tiates and fosters linkages with industrial, gov-ernmental, and not-for-profit organizations thatrequire mathematical technologies to deal withproblems of strategic importance to Canada. MI-TACS is driving the recruiting, training, andplacement of a new generation of highly math-ematically skilled personnel that is vital toCanada’s future social and economic well being.

MITACS networks academia, industry and thepublic sector to develop cutting edge mathemat-ical tools vital to a knowledge-based economy.

The only Network of Centres of Excellence(NCE) for the mathematical sciences, MITACScurrently has 305 scientists, 611 students and 169partner organizations working on 32 ongoingprojects, involving 48 Canadian universities.

To improve Canada’s international competitive-ness, MITACS research focuses on five key sec-tors of the economy:

• biomedical and health;• environment and natural resources;• information processing, risk and finance and

communication;• networks and security.

MITACS Inc. is a federally incorporated not-for-profit society formed to administer the MITACSNetwork of Centres of Excellence.

National Program on Complex Data Struc-tures (NPCDS)

This initiative was developed in partnershipwith the three mathematical sciences insti-tutes and the reallocations committee during

the recently completed reallocations exercise atNSERC. The program was funded by NSERC forfour years for a total of $687,000. An additional$200,000 has been committed to the program bythe institutes.

The National Program was conceived as a modelfor a national network in the statistical sciences,in partnership with the mathematics institutes.The broad goal of the proposal is to foster na-tionally coordinated projects with substantial in-teractions with the large community of scientistsinvolved in analysis of complex data sets, andto establish a framework for national network-ing of research activities in the statistical com-munity.

The original proposal targeted the developmentand application of statistical methods for theanalysis of data obtained from complex surveysample designs and longitudinal biological, epi-demiological and medical studies. More specificobjectives of the program include the develop-ment of collaborations between university andextra-university researchers, and the provisionof training for graduate students in importantscientific areas through these collaborations.

NPCDS ProjectsStatistical Methods for Complex Survey DataProject Leader: Changbao Wu (Waterloo)

Canadian Consortium on Statistical GenomicsProject Leader: Rafal Kustra (Toronto)

Data Mining with Complex Data StructuresProject Leaders: Hugh Chipman (Acadia), Anto-nio Ciampi (McGill), Theodora Kourti (McMas-ter), Helmut Kröger (Laval)

Design and Analysis of Computer Experimentsfor Complex SystemsProject Leader: Derek Bingham (Simon Fraser)

Forests, Fires and Stochastic ModelingProject Leaders: John Braun (Western Ontario),Charmaine Dean (Simon Fraser), Dave Martell(Toronto)

NPCDS WorkshopsNPCDS/SAMSI Workshop on the Design andAnalysis of Computer Experiments for Com-plex SystemsBanff, Alberta, July 13–17, 2004Organizers: Jim Berger (Duke, SAMSI), DerekBingham (Simon Fraser), Randy Sitter (SimonFraser), Jamie Stafford (Toronto, NPCDS), WillWelch (UBC)

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Workshop on Missing Data ProblemsFields Institute, Toronto, August 5-6, 2004Organizers: Richard Cook, Don McLeish (Water-loo)

Workshop on Data Mining Methodology andApplicationsFields Institute, Toronto, October 28-30, 2004Organizers: Hugh Chipman (Acadia), AntonioCiampi (McGill), Michael Vainder (Generation5)

Workshop on Latent Variable Models and Sur-vey Data for Social and Health Sciences Re-searchCRM, May 4–6, 2005Organizers: Mary Thompson (Waterloo), ChrisSkinner (Southampton), Paul Biemer (UNCChapel Hill), Jamie Stafford (Toronto), Milo-rad Kovacevic (Statistics Canada), Randy Sitter(Simon Fraser), David Bellhouse (Western On-tario), Roland Thomas (Carleton). A descriptionof this activity can be found in page 33

Workshop on Forest Fires and Point ProcessesFields Institute, Toronto, May 24–28, 2005Organizers: W. John Braun (UWO), David Martel(Toronto), Rick Schoenberg (UCLA)

Atlantic Association for Research in theMathematical Sciences (AARMS)

AARMS was founded in March 1997 at a timewhen the National Network for Research in theMathematical Sciences was being discussed andplanned. AARMS exists to encourage and ad-vance research in all mathematical sciences, in-cluding statistics and computer science, in theAtlantic region. In addition, AARMS acts as aregional voice in discussions of the mathemat-ical sciences on a national level. Since its incep-tion, AARMS has played an important role in theresearch activities in the Atlantic region, spon-soring or co-sponsoring numerous meetings andworkshops. In the summer of 2002, AARMS ini-tiated an annual Summer School for graduatestudents and promising undergraduates.

AARMS is grateful to Canada’s three mathemat-ical institutes, the Centre de recherches mathé-matiques, the Fields Institute, and the PacificInstitute for Research in the Mathematical Sci-ences as well as Acadia University, DalhousieUniversity, Memorial University, and the Uni-versity of New Brunswick (Fredericton) for pro-viding funding for its activities.

AARMS Scientific activitiesCMS/CAIMS Summer 2004 MeetingDalhousie University, June 13–15, 2004Sessions organized by AARMS:• Algebraic Topology

Organizers: Keith Johnson (Dalhousie), RenzoPiccinini (Milano)

• Graphs, Games and the WebOrganizer: Richard Nowakowski (Dalhousie)

• Nonlinear Dynamics in Biology and MedicineOrganizer: Shigui Ruan (Dalhousie and Mi-ami)

• Hopf Algebras and Related TopicsOrganizers: Yuri Bahturin (Memorial), Mar-garet Beattie (Mount Allison), Luzius Grunen-felder (Dalhousie), Susan Montgomery(Southern California), Earl Taft (Rutgers)

• 16th Canadian Symposium on FluidOrganizers: Richard Karsten (Acadia), SerpilKocabiyik (Memorial)

AARMS Workshop on Symbolic ComputationDalhousie, June 16, 2004Organizers: Alan Coley (Dalhousie), Robert Mil-son (Dalhousie), Mark Fels (Utah State)

International Conference on Nielsen Theoryand Related TopicsMemorial University of Newfoundland, June28–July 2, 2004Organizers: Philip Heath (Memorial), EdwardKeppelmann (Nevada)

International Conference on Nonlinear Dy-namics and Evolution EquationsMemorial University of Newfoundland, July 6–10, 2004.Organizers: Andy Foster (Memorial), Brian Slee-man (Leeds), Jianhong Wu (York), Yuan Yuan(Memorial), Xiaoqiang Zhao (Memorial), XingfuZou (Memorial)

2004 AARMS Summer SchoolMemorial University of Newfoundland, July 12–August 16, 2004Director: Edgar Goodaire (Memorial)

APICS 2004: AARMS Symposium on Func-tional Analysis and Operator AlgebraUniversity of New Brunswick, Saint John, Octo-ber 17, 2004Organizers: Dan Kucerovsky (UNB Fredericton),Andrew Toms (UNB Fredericton)

East Coast Combinatorics Conference 2005Lord Beaverbrook Hotel, Fredericton, January22, 2005Organizers: David Bremner (UNB Fredericton),Hugh Tomas (UNB Fredericton)

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Quantum Gravity WorkshopUniversity of New Brunswick, Fredericton,April 28–30, 2005Organisateurs: Arundhati Dasgupta (UNB Fred-ericton), Jack Gegenberg (UNB Fredericton),Viqar Husain (UNB Fredericton)

Academic Partners

All this activity rests on a solid base of cooper-ation with universities in the region, in partic-ular the Montréal universities, and most partic-ularly the Université de Montréal, whose sup-port for the CRM has been unfailing. The Uni-versité de Montréal releases five of its facultymembers to work at the CRM each year, and thesupport of these faculty members is an essentialasset for the CRM’s scientific activities. There isin addition a regular program of teaching releasewith the other Montréal universities, bringingthe equivalent of another two positions to theCRM each year. On an ad-hoc basis linked to thetheme program, the CRM has also been arrang-ing release of research personnel from nearbyuniversities such as Laval, Sherbrooke, Queen’sand Ottawa. The partnerships of the CRM withthe other research institutes in the Montréal areahave been very profitable.

With the financial support of the Universitéde Montréal, McGill University, Université deQuébec à Montréal, Concordia University, andUniversité Laval as well as grants from Fonds derecherche québécois sur la nature et les technolo-gies (FQRNT) of Québec and of NSERC, CRM fi-nances the activities of the eight laboratories rep-resenting the most active branches of the mathe-matical sciences. These laboratories are the sceneof scientific vitality par excellence and serve tofeed the national and international scientific pro-grams of the CRM. Please refer to the chapter“Research Laboratories” for reports describingthe activities of each of these laboratory.

Association with University of Ottawa

In 2003, the Department of Mathematics andStatistics became a member of the Centre derecherches mathématiques (CRM). In partner-ship with the University of Ottawa, the CRMco-finances postdoctoral fellowships, a seriesof CRM–University of Ottawa conferences andteaching releases so that University of Ottawafaculty members can undertake research collab-orations with colleagues in the CRM’s laborato-ries or to participate in CRM scientific activities.

The following research conferences, workshops,and mini conferences were made possiblethrough sponsorship by CRM:CRM–University of Ottawa Distinguished Lec-ture SeriesThe series features talks by prominent mathe-maticians from Canada and abroad on topics atthe forefront of today’s mathematical research.September 10, 2004: Barbara Lee Keyfitz (Hous-ton)Why Are Multidimensional Conservation Laws SoDifficult?

Lie Theory WorkshopMarch 5–6, 2005,Organizers: Erhard Neher (Ottawa), Wulf Ross-mann (Ottawa)

Network for Computing and MathematicalModeling (ncm2)

The CRM is one of founding members thethe Network for Computing and MathematicalModeling, ncm2, a collaboration which allowsthe network to respond to the needs of industryin a large number of fields related to a commonarea of computing and mathematical modeling,mostly around five major themes: risk manage-ment, information processing, imaging and par-allel computing, transport and telecommunica-tions, health and electronic commerce.

The five centres that established the networkwere the CRM, the Centre de recherche en cal-cul appliqué (CERCA), the Center for Interuni-versity Research and Analysis on Organizations(CIRANO), the Center for Research on Trans-portation (CRT), and the Group for Research inDecision Analysis (GERAD). Since then, threenew members joined the network: the Cooper-ative Centre for Research in Mesometeorology(CCRM), the Centre de Recherche Informatiquede Montréal (CRIM) and the Institut National dela Recherche Scientifique-Énergie, Matériaux etTélécommunications (INRS-EMT).

Laboratoires universitaires Bell (LUB)

The CRM is an active participant in the ncm2’sLaboratoires universitaires Bell, part of a jointproject between the ncm2 and Bell. The labora-tories aim at creating innovations in the fieldof multimedia research and applications (mainlyinteractive applications aimed at the generalpublic, electronic commerce applications andnew generations of evolved networks) as well as

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at promoting the training of a highly qualified,international calibre workforce in these areas.

Neuro-imaging initiative in Quebec (RNQ)

In recent years, CRM’s PhysNum laboratoryhas developed a strong collaborative networkwith various partners in neuroimaging in theMontréal area. This network was formalizedwith the constitution of the “Regroupement

Neuro-imagerie Québec” (RNQ) under the um-brella of the Institut Universitaire de Gériatrie inMontréal. RNQ, with its 70 researchers, has re-cently purchased some key equipment in neuro-imaging through a very large grant ($11M). Oneof the strongest alliances of CRM within that net-work is its association with the INSERM labora-tory for brain-imaging at Jussieu–La Salpêtrière,Paris (director: Habib Benali).

Joint Initiatives

The annual meetings of the CMS, SSC andCAIMS, together with some of their training andpromotion activities, are jointly sponsored bythe CRM, the Fields Institute, the PIMS and MI-TACS. The reports of these activities are presented inthe language in which they were submitted.

Annual Meeting of the Statistical Societyof CanadaMay 30 to June 2, 2004, CRM, Université deMontréalOrganizers: Program Committee Chair, Chris-tian Genest (Laval); Local Arrangements Chair,Christian Léger (Montréal)

The thirty-second annualmeeting of the Statistical So-ciety of Canada was hostedby the Université de Mont-réal and the Centre de recher-ches mathématiques. Over550 registrants participated inthe meeting, which featureda wide range of sessions, in-

cluding workshops of three SSC sections: bio-statistics, survey methods, and business and in-dustrial statistics.

The meeting was sponsored by the Centre derecherches mathématiques, the Fields Institute,PIMS, MITACS, Hydro Québec, the Universitéde Montréal, Pfizer, Bell University Laborato-ries, and the Institut de la statistique du Québec.

The scientific program was extremely rich with109 invited papers and 142 contributed papers.Among the invited papers, the following ad-dresses are especially noteworthy.

Presidential Invited AddressKathryn Roeder (Carnegie Mellon)Discovering haplotype blocks in the human genome

Gold Medal AddressMary Thompson (Waterloo)

Understanding associations: implications for the de-sign and analysis of longitudinal surveys

Special Invited Addresses of the Sections• Raymond Chambers (Southampton)

Informative sampling and sampling information.• Daryl Pregibon (Google, Inc.)

Graph Mining• Richard Simon (US National Cancer Institute)

Key features in the design and analysis of DNAmicroarray studies

Pierre Robillard Award Address (Best Thesis):Rachel MacKay Altman (Washington)Hidden Markov Models: Multiple Processes andModel Selection

Canadian Journal of Statistics Award Address:Belkacem Abdous (Laval), Kilani Ghoudi(United Arab Emirates), Bruno Rémillard (HECMontréal)Nonparametric Weighted Symmetry Tests

CMS/CAIMS Summer 2004 Meeting

June 13–15, 2004, Dalhousie UniversityMeeting Directors: Richard Wood (Dalhousie),Raymond Spiteri (Dalhousie)

The CMS/CAIMS Summer 2004 Meeting washeld at Dalhousie University on June 13–15,2004, and welcomed 432 participants. The Pub-lic Lecture, entitled “Getting at the truth,” wasgiven by Ed Barbeau on June 14 and was verywell attended.

Other special events included plenary talks de-livered by: Peter Cameron (Queen Mary), CraigFraser (Toronto), Mark Lewis (Alberta), Alan C.Newell (Arizona/Warwick), Peter Olver (Min-nesota), Frank T. Smith (University College Lon-don), Mikhail Zaicev (Moscow State)

The Canadian Mathematical Society waspleased to present lectures from their research

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prize winners, specifically the CMS Jeffery-Williams Lecture, given by Joel Feldman (UBC),and Leo Jonker (Queen’s), who received the firstCMS Excellence in Teaching Award. The CAIMSResearch Prize Lecture was given by Robert D.Russell (Simon Fraser) and the CAIMS CecilGraham Doctoral Dissertation Award Lecturewas given by Ramadan Akila (Guelph).

A wide variety of fields of interest were repre-sented in the symposia topics detailed below.Most of these are fields that are well representedby researchers in Atlantic Canada:

16th Canadian Symposium on Fluid DynamicsOrganizers: Richard Karsten (Acadia), Serpil Ko-cabiyik (Memorial)

Applications of Invariant Theory to Differen-tial GeometryOrganizers: Robert Milson (Dalhousie), MarkFels (Utah State)

Classical Analysis in honour of David Bor-wein’s 80th BirthdayOrganizers: Jonathan Borwein (Dalhousie), MikeOverton (Courant Inst.)

Dynamical SystemsOrganizer: Michael A. Radin (Rochester Instituteof Technology)

Financial MathematicsOrganizers: Joe Campolieti (Wilfrid Laurier),David Vaughan (Wilfrid Laurier), Yongzeng Lai,(Wilfrid Laurier)

General Topology and Topological AlgebraOrganizers: Ilijas Farah (York), Vladimir Pestov(Ottawa)

Graphs, Games and the WebOrganizers: Anthony Bonato (Wilfrid Lau-rier), Jeannette Janssen (Dalhousie), RichardNowakowski (Dalhousie)

History of MathematicsOrganizer: Thomas Archibald (Acadia)

Hopf Algebras and Related TopicsOrganizers: Yuri Bahturin (Memorial), MargaretBeattie (Mount Allison), Luzius Grunenfelder(Dalhousie), Susan Montgomery (Southern Cali-fornia), Earl Taft (Rutgers)

Mathematical EducationOrganizers: Richard Hoshino (Dalhousie), JohnGrant McLoughlin (UNB Frederecton)

Nonlinear Dynamics in Biology and MedicineOrganizer: Shigui Ruan (Dalhousie)

Numerical Algorithms for Differential Equa-tions and Dynamical SystemsOrganizer: Tony Humphries (McGill)

Qualitative Behaviour and Controllability ofPartial Differential EquationsOrganizer: Holger Teismann (Acadia)

TopologyOrganizers: Keith Johnson (Dalhousie), RenzoPiccinini (Milano)

Topos TheoryOrganizer: Myles Tierney (Rutgers and UQÀM)

The NExTMAC Workshop was organized sepa-rately from the meeting and took place on June12, 2004.

The Meeting Committee would like to acknowl-edge with much thanks the financial supportof the following: Atlantic Association for Re-search in the Mathematical Sciences, le Centre deRecherches Mathématiques, the Fields Institutefor Research in Mathematical Sciences, Math-ematics of Information Technology and Com-plex Systems, Pacific Institute for the Mathemat-ical Sciences, Acadia University, Dalhousie Uni-versity, Memorial University of Newfoundland,Mount Allison University, Saint Mary’s Univer-sity, Maplesoft, Springer, Unisys Canada Inc.

Toulouse 2004 : First Joint Canada-FranceMeeting of the Mathematical Sciences

July 12–15, 2004, Centre de congrès PierreBaudis, ToulouseScientific Director: Francis Clarke (Lyon I)

The first Canada-France congress involved thethree Canadian societies: CMS, CAIMS, SSC,and their French counterparts: SMF, SMAI andSFdS. Four hundred and thirty delegates regis-tered with a significant number of students andpostdoctoral fellows. Several lectures were givenin French.

The plenary lectures were given by LaurentLafforgue (IHES), Grégoire Allaire (École Poly-technique Palaiseau), Maïtine Bergounioux (Or-léans), Jonathan Borwein (Dalhousie), DavidBrillinger (UC Berkeley), Walter Craig (Mc-Master), Henri Darmon (McGill), EmmanuelGiroux (ENS-Lyon), Gabor Lugosi (PompeuFabra), Mikhail Lyubich (Toronto), ChristopheReutenauer (UQÀM), Alain-Sol Sznitman (ETH

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CRM PARTNERSHIP

Zürich), Murad Taqqu (Boston) and HenryWolkowicz (Waterloo). Michèle Artigue (ParisVII) gave the education lecture.

There were 16 special sessions: Operator alge-bras, Symplectic topology and geometry, Num-ber theory, Spectral and geometric analysis, Par-tial differential equations, Dynamical systems,Differential Equations and Control, VariationalAnalysis and optimization, Stochastic Analysis,Multifractals and long memory processes, theProbability/Statistics interface, Statistical analy-sis of functional data, Numerical analysis, Lowdimensional topology and geometrical grouptheory, Mathematical biology, Complex dynam-ical systems. Eric Muller (Brock) organized apanel on the popularization of mathematics.Discussions are under way for a second Canada-France meeting to be held in the summer of 2008in Montreal.

CMS Winter 2004 MeetingDecember 11–13, 2004, McGill UniversityMeeting Director: Olga Kharlampovich (McGill)

The Meeting welcomed 450participants. Following theusual format of the CMS Win-ter Meeting, the program in-cluded a wide variety of ses-

sions, a contributed paper session, plenary andprize lectures, and a public lecture. Most ac-tivities and all scientific talks were held at theHilton Bonaventure Hotel. The meeting beganwith Alexei G. Myasnikov (McGill) deliveringa public lecture entitled, “Complexity of Com-putations and Cryptography.” The event, heldat the Best Western Hotel Europa, drew a largeaudience and was followed by a welcoming re-ception.

Plenary talks were delivered by: Michael Ben-nett (UBC), Persi Diaconis (Stanford), RostislavGrigorchuk (Texas A&M), François Lalonde(Montréal) and Rainer Steinwandt (Karlsruhe).

The Canadian Mathematical Society waspleased to present lectures from their researchprize winners, namely, the CMS Coxeter-JamesPrize Lecture, given by Izabella Laba (UBC), theCMS Doctoral Prize Lecture, given by NicolaasSpronk (Waterloo) and the CMS Adrien PouliotPrize lecture, given by Jean-Marie De Koninck(Laval).

A wide variety of fields of interest were repre-sented in the symposia topics detailed below.Algebraic CombinatoricsOrganizers: François Bergeron (UQÀM), Ric-

cardo Biagioli (UQÀM), Peter McNamara(UQÀM), Christophe Reutenauer (UQÀM)

Approximation TheoryOrganizers: Richard Fournier (Dawson), PaulGauthier (Montréal)

Arithmetic GeometryOrganizers: Eyal Goren (McGill), Adrian Iovita(Concordia)

Combinatorial and Geometric Group TheoryOrganizers: Inna Bumagin (Carleton), Dani Wise,(McGill)

Commutative AlgebraOrganizers: Sara Faridi (Ottawa), Sindi Sabourin(York), Will Traves (US Naval Academy), Adamvan Tuyl (Lakehead)

Discrete GeometryOrganizers: Karoly Bezdek (Calgary), RobCalderbank (Princeton), Robert Connelly (Cor-nell), Bob Erdahl (Queen’s)

Dynamical Systems and ApplicationsOrganizer: Michael A. Radin (Rochester Instituteof Technology)

Groups, Equations, Non-commutative Alge-braic GeometryOrganizers: Olga Kharlampovich (McGill),Alexei G. Myasnikov (McGill)

Harmonic AnalysisOrganizer: Galia Dafni (Concordia)

History of MathematicsOrganizers: Thomas Archibald (Acadia), RichO’Lander (St. John’s), Ron Sklar (St. John’s),Alexei Volkov (UQÀM)

Interactions between Algebra and ComputerScienceOrganizers: Olga Kharlampovich (McGill),Alexei G. Myasnikov (McGill), Vladimir Shpil-rain (CUNY-City College)

Mathematical Methods in StatisticsOrganizers: Russell Steele (McGill), Alain Vandal(McGill), David Wolfson (McGill)

Mathematics for Future TeachersOrganizer: Leo Jonker (Queen’s)

Number TheoryOrganizers: Chantal David (Concordia), AndrewGranville (Montréal)

Special Structures in Differential GeometryOrganizers: Gordon Craig (Bishop’s), Spiro Kari-giannis (McMaster)

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Universal Algebra and ComplexityOrganizers: Jennifer Hyndman (UNBC), BenoitLarose (Concordia), Denis Therien (McGill)

Contributed papers session was organized byWilliam G. Brown (McGill)

The Meeting Committee would like to acknowl-edge with much thanks the financial support of

the following: McGill University Provost, McGillUniversity Dean of Science, McGill UniversityDepartment of Mathematics and Statistics, Cen-tre de recherches mathématiques (CRM), CRMAnalysis Laboratory, Fields Institute, MITACSand Pacific Institute for the Mathematical Sci-ences.

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IN its mission to promote and stimulate research in the mathematical sciences, at all levels, the CRMprovides funding and support for many activities and programs related to mathematical education

and researcher training. Many of these activities and programs are coordinated jointly with the ISM(Institut des sciences mathématiques). The ISM text that follows was only available in French.

Institut des sciences mathematiques (ISM)

Fondé en 1991 par les départements de mathé-matiques et de statistique des quatre univer-sités montréalaises, l’Institut des sciences ma-thématiques est un consortium des six uni-versités québécoises (Concordia, Laval, McGill,l’Université de Montréal, l’UQÀMet l’Univer-sité de Sherbrooke) qui offrent un programmede doctorat en mathématiques. S’appuyant surl’ensemble des chercheurs universitaires qué-bécois travaillant en sciences mathématiques,il coordonne un grand nombre de ressources,aussi bien matérielles qu’intellectuelles, pour at-teindre la masse critique qui fait de Montréalet du Québec un pôle nord-américain de for-mation et de recherche en sciences mathéma-tiques. L’Institut est financé par le ministère del’Éducation du Québec et par les six universitésmembres.

Voici un aperçu des activités et programmes del’ISM :

• Coordination et harmonisation des pro-grammes d’étude de 2e et 3e cyclesC’est la principale raison d’être de l’ISM, quivise à réunir les forces de ses départementsmembres pour en faire une grande école demathématiques. Ainsi, l’Institut coordonne lesprogrammes d’étude de 2e et 3e cycles des uni-versités membres et favorise la mise en com-mun des expertises des chercheurs ainsi quela circulation interuniversitaire des étudiants.

• Bourses d’excellence et soutien financierL’ISM offre aux étudiants et jeunes chercheursdivers moyens matériels de poursuivre leursrecherches dans les meilleures conditions pos-sibles.

• Activités scientifiquesL’ISM a depuis sa création mis en place plu-sieurs événements qui font désormais partiedu paysage scientifique québécois.

• Promotion des sciences mathématiques

Le CRM a plusieurs activités communes avecl’ISM, en particulier un programme conjoint debourses postdoctorales, deux colloques CRM-ISM, un en mathématiques et un en statistiqueet l’organisation de cours avancés liés à la pro-grammation thématique. Depuis l’été 2003, leCRM participe également au programme debourses d’été pour les étudiants de premier cyclequi permet aux stagiaires postdoctoraux de su-perviser ces étudiants.

CRM-ISM Postdoctoral Fellowships

Les bourses postdoctorales CRM-ISM offrent àdes jeunes chercheurs prometteurs la chance deconsacrer la majeure partie de leur temps à leurstravaux de recherche. Le processus de sélectionde ces boursiers est très rigoureux : en orga-nisant un seul concours pour les six universi-tés membres de l’ISM, l’institut reçoit un grandnombre de candidatures qui sont ensuite éva-luées par les 150 professeurs membres de l’Ins-titut. Il s’agit d’un concours extrêmement com-pétitif où environ un candidat sur quarante estchoisi. De plus, le CRM et l’ISM ont débutél’informatisation du processus de demande debourse. Dès la prochaine année, les dossiers se-ront acheminés électroniquement, facilitant ainsila gestion de ces nombreuses candidatures etréduisant considérablement la quantité de res-sources utilisées dans le processus.

Nous ne pouvons surestimer l’importance de cesstagiaires postdoctoraux dans nos universités :ils stimulent et collaborent avec les chercheursbien établis, ils sont une source d’idées nouvellesprovenant d’autres grands centres, et ils créentun lien essentiel entre les professeurs et les étu-diants, organisant souvent de leur propre grédes groupes de travail sur des sujets de pointe.

2004-2005 Postdoctoral Fellows :

Mostafa Gabbouhy (Ph.D. 2000, Université IbnTofaïl, Maroc) travaille avec Daniel Leroux (GI-REF, Laval), et Jean-Loup Robert (GIREF, La-val) sur l’étude d’un modèle de Saint Venant 3-D avec couplage de la convection thermique etadaptation de maillage.

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David Gay (Ph.D. 1999, UC Berkeley) a travailléavec Vestislav Apostolov (UQÀM), Olivier Col-lin (UQÀM) et François Lalonde (Montréal) surla topologie symplectique et de contact de bassedimension. David Gay a pris un poste de profes-seur à l’University of Cape Town en Afrique duSud, débutant en juillet 2005.

Harald Helfgott (Ph.D. 2003, Princeton) a tra-vaillé avec Andrew Granville (Université deMontréal) en théorie des nombres, courbes el-liptiques, formes automorphes et combinatoire.Harald Helfgott a accepté un poste de professeurà l’University of Bristol en Angleterre.

Alexander Ivrii (Ph.D. 2003, Stanford) travaillesur la topologie symplectique et les courbesholomorphes-J avec Octav Cornea (Montréal),François Lalonde (Montréal) et Iosif Polterovich(Montréal).

Shannon Starr (Ph.D. 2001, UC Davis) a travailléen physique mathématique et mécanique statis-tique avec Vojkan Jaksic (McGill) et John Toth(McGill). Shannon Starr est maintenant profes-seur à l’University of California à Los Angeles.

Ye Tian (Ph.D. 2003, Columbia) travaille avecHenri Darmon (McGill) sur la théorie desnombres.

Stephan Tillmann (Ph.D. 2002, Melbourne) tra-vaille sur la topologie de basse dimension et lesdégénérescences des structures hyperboliquesavec Steven Boyer (UQÀM).

Michèle Titcombe (Ph.D. 1999, UBC) travailleavec Jacques Bélair (Montréal) sur l’analyse ap-pliquée (analyse asymptotique, méthodes deperturbation), l’analyse numérique, la modélisa-tion mathématique, la biologie mathématique, ladynamique des fluides et la dynamique non li-néaire.

Undergraduate Summer Scholarships

En collaboration avec le CRM et les professeursmembres de l’ISM, la bourse d’été de premiercycle est offerte par l’ISM aux étudiants de pre-mier cycle prometteurs qui désirent faire unstage de recherche en mathématiques et éven-tuellement poursuivre des études aux cycles su-périeurs. La supervision des boursiers d’été estassurée par des stagiaires postdoctoraux pourlesquels il s’agit généralement d’une première

expérience en supervision de recherche. Lesboursiers cette année étaient :

Lory Ajamain (McGill)Responsable de stage : Brian E. Moore

Dominique Brunet (Laval)Responsable de stage : Mario Roy

François Charette (Montréal)Responsables de stage : Alina Stancu et Octav Cor-nea

Maria Dorokhina (McGill)Responsable de stage : Pete Clark

Wai Chit Lam (McGill)Responsable de stage : Emily Dryden

Yuedan Liu (McGill)Responsable de stage : Pete Clark

Clarence Simard (Montréal)Responsable de stage : Harald Helfgott

“Sur la route” ISM Colloquium

October 1–3, 2004, Université de SherbrookeOrganizing committee: Jennifer Bélanger, Syl-vain Bérubé, Julie Dionne, Jean-Philippe Morin,Charles Paquette, Jean-Simon Sénécal, DavidSmith, Anik Trahan.Plenary speakers: Michael Barot (UNAM), JoëlFoisy (SUNY Potsdam), Jean Goulet (Sher-brooke), Claude Le Bris (ENPC)Speakers: M. Valley (Laval), G. Chênevert(McGill), P. Poulin (McGill), A. Rémillard (Mont-réal), J.-P. Morin (Sherbrooke), D. Smith (Sher-brooke), H. Bac (UQÀM), G. Paquin (UQÀM), X.Provençal (UQÀM).Number of participants: 38

Inspiré par le colloque pan-québécois des étu-diants, un groupe d’étudiants de l’Université deSherbrooke a décidé de lancer cette année le« Colloque ISM sur la route », un « mini » col-loque pan-québécois qui s’est déroulé du 1 au 3octobre 2004 à l’Université de Sherbrooke. Dansla tradition des colloques ISM, cette rencontreétait organisée par des étudiants et était desti-née à l’ensemble de la communauté étudianteaux cycles supérieurs. En plus de pouvoir pré-senter leurs plus récents travaux, les participantsont eu le plaisir d’assister à quelques conférencesplénières. Le Colloque a attiré une quarantained’étudiants des universités de l’ISM.

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Others Joint Initiatives

ESSO/CMS Math Camps 2004

The ESSO/CMS Math Camp Program startedin 1999 with three camps, and the program hasnow grown to include at least one camp in everyprovince. The support received from the spon-sors enables the Canadian Mathematic Societyto ensure these camps are accessible to studentsfrom across Canada who demonstrate en excel-lence and interest in mathematics.

In 2004, there were thirteen regional math campsin ten provinces, as well as a national camp, inwhich 350 students participates

Organized by Thomas Griffiths (Waterloo), thenational camp was held at University of West-ern Ontario from June 5 to 12, 2004. The Na-tional Camp is designed primarily for youngerCanadian students with at least two years re-maining in high school and with the potentialto compete at the mathematical Olympiad level.Students are invited based upon their resultsin various mathematics competitions. Presenta-tions on particular topics and the various prob-lem solving sessions are runs by local area teach-ers and faculty member as well as former IMOteam members.

The Regional Camps are intended to providesome mathematics enrichment in a fun and re-warding environment. Each camp invites be-tween 20 and 30 students (from grade 9 to 11)on the basis of national or regional mathematicscompetition as well as recommendations fromteachers. The 2004 regional camps took place atthe University of Regina, Sir Wilfred GrenfellCollege, the University of New Brunswick, theUniversity of Prince Edward Island, Universitédu Québec à Rimouski, Simon Fraser University,Dalhousie University, the University of Ottawa,the University of Western Ontario, Brock Uni-versity, the University of Alberta, and the Uni-versity of Manitoba.

The sponsors of the 2004 math camp programwere: Imperial Oil Foundation, Canadian Math-ematical Society, NSERC PromoScience, theFields Institute, the Centre de recherches mathé-matiques, the Pacific Institute for the Mathemat-ical Sciences, the Association Mathématique duQuébec, the host universities, the governmentsof New Brunswick, Alberta, Northwest Territo-ries, Newfoundland and Labrador, Nova Scotia,Québec, Ontario, and Saskatchewan.

2004 AMQ Mathematics CampMay 23 – June 4, UQÀM

Organizer: Pierre Bouchard (UQÀM)

For the fourth year in a row, the Camp was heldat UQÀM. Participants are primarily prizewin-ners of the Quebec Mathematics Contest, on theCEGEP level. For about twelve days, they hadthe chance to meet with mathematicians andpeople who use mathematics in their work. Ev-ery day, one or more lecturers presented a topicthat would be of interest to the students. Partici-pants shared in an unforgettable experience withmore than twenty other mathematics enthusi-asts. They also had access at all times to UQÀM’scomputers.

2004 IMO Training SeminarJune 25 – July 4, UQÀMOrganizer: Matthieu Dufour (UQÀM)

The International Mathematical Olympiad(IMO) is the World Championship Mathemat-ics Competition for High School students and isheld annually in a different country. The CMShas been sending a team of Canadian studentsto the annual IMO since 1981. Canadian stu-dents have always done extremely well, ob-taining a total of 93 medals (14 Gold, 27 Silverand 52 Bronze). In 2004 the Olympiad was heldat Athens and the Canadian team obtained 4medals, 1 Gold and 3 Bronze.

As with all competition, training is vital for suc-cess. The Canadian Team of six high school stu-dents chosen from more than 200,000 studentswho have participate in various local, provincial,national and international contests. Team mem-bers and their coaches attended a training sem-inar at UQÀMfor two weeks prior to their de-parture to Athens. A few select students fromQuébec, who have excelled in mathematics com-petitions, also attended the IMO training semi-nar as observers for the first few days.

The 2004 Canadian Olympiad “mathletes” were:Oleg Ivrii (Toronto), János Kramár (Toronto),Dong Uk Rhee (Edmonton), Peng Shi (Toronto),Jacob Tsimerman (Toronto) et Yufei Zhao(Toronto).

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Canadian Mathematics Education ForumMay 6–8, 2005, University of Toronto

Co-chairs: Florence Glanfield (Saskatchewan),Frédéric Gourdeau (Laval), Bradd Hart (McMas-ter)

The 2005 Canadian Mathematics Education Fo-rum (CMEF2005) was organized by the Cana-dian Mathematics Society (CMS). The Forumwas held at the University of Toronto with someactivities at the nearby Fields Institute. This Fo-rum follows the one held in 2003 in Montréal.The 2005 Forum is the third organized by theCMS, the first national forum in mathematicaleducation being held in Québec in May 1995.

The purpose of the 2005 invitational forum wasto develop a national on-going conversation,among educators at all levels of schooling, aboutimportant issues and concerns in the develop-ment and future of mathematics education inCanada. The overall theme of the 2005 Forumwas Why teach Mathematics? The Forum wasthought of as a working meeting and includedplenary panel sessions and talks as well elevenworking groups.

The Forum brought together some 200 partici-pants coming from all sectors connected to edu-cation in mathematics and from all the provincesand territories of Canada: teachers and instruc-tors of mathematics at all the levels, researchersin mathematics and mathematics education,consultants and education advisers, representa-tives of associations of teaching and teachersof mathematics, representatives of the provin-cial ministries for education, representatives ofother groups having a particular interest for theteaching of mathematics: industry representa-tives, parents, administrators, editors, textbookwriters, etc.

It was the intent that groups working together inthis forum will develop projects, initiatives, andstatements that will outline ways in which Cana-dians may address these issues and concerns.The projects, initiatives, and statements devel-oped during this forum will be shared widelywith policy makers, school divisions, universi-ties, colleges, parents, students, and the generalpublic in a variety of ways.

Working groups

• Mathematics education in the aboriginal com-munity,

• Early numeracy: developing mathematical lit-eracy in the early years,

• Why is mathematics relevant in our society,• Supporting student success — Helping stu-

dents reach their potential,• Creating a curriculum that affords learners

opportunity to develop powerful mathemat-ics,

• Learning in the presence of technology,• Mathematics through the eyes of a child,• Classroom practice and mathematics educa-

tion research,• Developing a national mathematics teaching

community,• Supporting teacher success.

Partners

• Canadian Mathematical Society• Alberta Education• Fields Institute• Ministère de L’Éducation, du Loisir et du

Sport du Québec• University of Saskatchewan• Nova Scotia Department of Education• Pacific Institute for the Mathematical Sciences• Yukon Department of Education• McMaster University• Centre de recherches mathématiques• Institut des sciences mathématiques• Toronto District School Board• Ontario Ministry of Education• Saskatchewan Learning• Nunavut Department of Education• Canadian Applied and Industrial Mathemat-

ics Society• Statistical Society of Canada• Université Laval• Nova Scotia Mathematics Teachers’ Associa-

tion• Ontario Association for Mathematics Educa-

tion• BC Association of Mathematics Teachers• Saskatchewan Mathematics Teacher Society• Association Mathématique du Québec• Groupe des responsables en mathématiques

au secondaire

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RESEARCH LABORATORIES

THE CRM now encompasses eight research laboratories at the heart of the Québec mathematicalcommunity. These research groups act as focal points for local scientific activity and participate

actively in the scientific programs of the CRM.

Applied Mathematics

Description

Applied and computational mathematics is avery active area of research with a long tradition,as well as many young faculty members in thegreater Montreal area. With modern computingequipment, it has become possible to simulateproblems and compute solutions which one wasonly able to dream of a few decades ago: this hasbeen a tremendous driving force in recent devel-opments in applied and computational mathe-matics.

The objective of the laboratory is to further en-courage scientific exchanges both amongst itsmembers and outside the group. It is character-ized by the intensity of its multidisciplinary col-laborations, with all the members working onthe development of mathematical models andnumerical methods for applications to scienceand engineering. The members of the labora-tory work in a wide range of applications (flu-ids, solids, physics, biology, etc.) using a widevariety of tools (optimization, numerical anal-ysis, dynamical systems, etc), and are very ac-tive in both research and training, supervisinga large number of graduate students and post-

doctoral fellows. One characteristic of this labo-ratory is the sustained collaboration of its mem-bers with researchers in other fields: for in-stance, André Bandrauk and Nilima Nigam aremembers of RQMP (Regroupement québécoisdes matériaux de pointe), Sebius Doedel andJacques Bélair are members of the Centre forNonlinear Dynamics in Physiology at McGill,Martin Gander and Michel Delfour are mem-bers of GIREF, Anne Bourlioux collaborates withcomputer scientists and mechanical engineersin an industrial project sponsored by MITACS,while Peter Bartello, André Bandrauk, and Se-bius Doedel hold positions completely or partlyoutside mathematics departments.

The laboratory organizes the annual MontrealScientific Computing Days each February, aswell as other workshops. It has two regularseminars running during the academic year, aweekly applied mathematics seminar and a bi-weekly computational science and engineeringseminar. It also supports postdoctoral fellowsand summer students as well as Canadian andinternational visitors.

Activities of the laboratory in 2004–2005

Seminars

The regular core activity of the laboratory isthe weekly applied mathematics seminar whichusually takes place on Mondays at McGill. Thisyear it was organized by Paul Tupper, wholined up 32 speakers covering a very wide rangeof interesting topics in applied mathematics.Though most seminars were at McGill, therewere also seminars at Université de Montréaland one at Concordia. The series included jointseminars with the Analysis laboratory and withthe McGill departement of Atmospheric andOceanic Sciences and Computational Scienceand Engineering. The seminar series was wellattended not just by laboratory members along

with their students and postdoctoral fellows, butwith significant participation of the Montréal-wide applied mathematics community.

Complementary to that core seminar, and in linewith the strong multidisciplinary orientation ofthis group, the laboratory was also involved inorganizing and sponsoring the bi-weekly Com-putational Science and Engineering (CSE) Sem-inar at McGill, organized this year by DennisGiannacopoulos (Electrical and Computer Engi-neering, McGill), which included 13 speakers, inaddition to the three joint “Applied Mathemat-ics/CSE” seminars.

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Workshops, special sessions and others

Besides its regular activities, the laboratory or-ganized the second Montréal Scientific Com-puting Days in February. The objective of thisconference is to encourage scientific exchangewithin the scientific computing community inQuébec and further afield. The two-day programincluded two short courses offered by interna-tional experts, at a level accessible to advancedgraduate students, as well as oral and postercontributed sessions. Students and postdoctoralresearchers were especially encouraged to par-ticipate. The event was once again a great suc-cess, this year attracting over 100 participants,mostly from Québec and Ontario.

Two one-day workshops were also organizedby the laboratory on “Computational Aspects ofDynamical Systems” and “Analysis and Com-putation of Lattice, Delay and Functional Differ-ential Equations.” Michel Delfour was a mem-ber of the organizing committee for the SpringSchool and Workshop “Mini-invasive proce-dures in medicine and surgery: mathematicaland numerical challenges.” Details on thesethree workshops as well as on the Montreal Sci-entific Computing Days can be found in the sec-

tions “General Program” and “MultidisciplinaryProgram.”

In addition to these laboratory events, the labo-ratory members were very active in the organi-zation of activities related to the Theme Year.

• Anne Bourlioux was the principal organizerfor the CRM Thematic Year on “The Math-ematics of Stochastic and Multiscale Model-ing,” and also organized the workshop “FrontPropagation and Nonlinear Stochastic PDEsfor Combustion and other Applications” andthe Summer School “Stochastic Calculus forApplications: Theory and Numerics.”

• Paul Tupper organized another workshop,“Extracting Macroscopic Information fromMolecular Dynamics.”

Details about all these activities can be found inthe chapter “Thematic program” of this report.

With over 30 seminar speakers from outsideQuebec, the laboratory members were alsohosts to a number of scientific visitors includ-ing Dimitri Breda (Udine), Chris Elmer (NJIT),McKay Hyde (Rice), Olivier Lafitte (Paris 13),Peter Monk (Delaware) et David Nicholls (NotreDame).

Members of the laboratory

Highlights of its members

During the year we welcomed three new mem-bers; Jacques Bélair (Montréal), Robert Owens(Montréal) and Paul Tupper (McGill).

The laboratory members were visible at the na-tional and international levels in applied and in-dustrial mathematics.

• Anne Bourlioux served on the board of di-rectors of CAIMS, and several members ofthe laboratory were involved in organizingand participating in various symposia dur-ing the Joint 2004 CAIMS/CMS meeting in-cluding Peter Bartello, Jacques Bélair, TonyHumphries, Sebius Doedel, Martin Ganderand Sherwin Maslowe.

• Eusebius Doedel organized workshops on“Analysis and Continuation of Bifurcations,”at University of Seville in May 2004, and

“Qualitative numerical analysis of high-dimensional nonlinear systems,” at Univer-sity of Bristol in March 2005.

• Martin Gander organized two minisymposiaat 16th International Conference on “DomainDecomposition Methods,” New York, January2005 on “Optimized Schwarz Methods” and“Space-Time Parallel Methods for PDE’s.”

• Robert Owens organized a minisymposiumon “High Order Methods for Complex Fluids”at the International Conference on ““Spectraland High-Order Methods,” Brown, June 2004.

• Paul Tupper has been chosen as finalist for the2005 Fox Prize in Numerical Analysis.

During the year 2004–2005, 17 master’s students,20 Ph.D. students and 8 postdoctoral fellowswere supervised by laboratory members.

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Regular members

Tony Humphries (McGill) DirectorNumerical analysis, differential equations.

Paul Arminjon (Montréal)Numerical methods in fluid mechanics.

André Bandrauk (Sherbrooke)Quantum chemistry.

Peter Bartello (McGill)Turbulence, CFD.

Jacques Bélair (Montréal)Dynamical systems in physiology.

Anne Bourlioux (Montréal)Modeling, numerical simulation in turbulentcombustion.

Michel Delfour (Montréal)Control, optimization, design, shells, calculus,biomechanics.

Eusebius J. Doedel (Concordia)Numerical analysis, dynamical systems, differ-ential equations, bifurcation theory, scientificsoftware.

Martin Gander (Geneva and McGill)Domain decomposition, preconditioning.

Sherwin A. Maslowe (McGill)Asymptotic methods, fluid mechanics.

Nilima Nigam (McGill)Applied analysis, numerical methods in electro-magnetism.

Robert G. Owens (Université de Montréal)Mechanic and numerical simulation of complexfluids.

Georg Schmidt (McGill)Control of partial differential equations.

Paul Tupper (McGill University)Numerical analysis, stochastic processes, andstatistical mechanics.

Jian-Jun Xu (McGill)Asymptotics and numerical analysis, non-linearPDEs material science.

Jean-Paul Zolésio (INRIA)Control, optimization.

CICMA

Description

This centre comprises researchers working innumber theory, group theory and algebraic ge-ometry. Contemporary number theory followstwo major courses. On the one hand, there isthe theory of special values of L-functions at-tached to arithmetic objects, originating in thework of Gauss and Dirichlet and leading to themodern conjectures of Deligne, Beilinson andBloch–Kato. On the other hand, the Langlandsprogram postulates a close link between arith-metic L-functions and automorphic representa-tions. An area where these two currents inter-sect is the study of elliptic curves. The center isparticularly well represented in this regard withDarmon, Iovita, and Kisilevsky. CICMA also ac-quired a new expertise in many aspects of an-alytic number theory with the recent arrival of

Andrew Granville, one of the leaders in the field.On the group theory side, Kharlampovich andMiasnikov are world-renowned specialists ongroup varieties and McKay is one of the origi-nators of the moonshine program.

Among the problems to be studied by the groupin the coming years include the construction ofrational points on elliptic curves both from al-gorithmic and theoretical viewpoints; Zeta func-tions of varieties over finite fields on the al-gorithmic approach; canonical lifting of ellip-tic curves and Abelian varieties; cryptography,Abelian varieties, and many aspects of analyticnumber theory, as averages of special values ofL-functions, distribution of prime numbers andprime divisors, and problems of additive num-ber theory.

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Activities of the laboratory in 2004–2005

Seminars

The main scientific activity of the CICMA labo-ratory is the Québec–Vermont Number TheorySeminar, which is held every second Thursdayfor a full day, with about 30 regular participantsfrom Montréal, Vermont, Québec and Ottawa.

One can see from that list that the invited speak-ers to the QVNTS are among the most prominentresearchers in number theory, arithmetic geom-etry and related topics. In the academic year2004–2005, the invited speakers to the QVNTSincluded: Haruzo Hida (UCLA) who gave a se-ries of lectures on his fundamental work on p-adic families of modular forms, which has pro-foundly infuenced the development of the sub-ject and plays a key role in the work of Iovitaand Darmon (in collaboration with Bertolini);and Akshay Venkatesh (Clay Fellow, NYU), oneof the young leaders in number theory today,who came to talk about his new and outstand-ing work on equidistribution, subconvexity andspectral theory.

The complete list of invited speakers for2004–2005 is: Dino Lorenzini (Georgia), Kar-tik Prasanna (UCLA), Haruzo Hida (UCLA),Jean-Louis Colliot-Thélène (Paris-Sud), MarvinKnopp (Temple), Akshay Venkatesh (Clay Fel-low, NYU), Mark Kisin (Chicago), Jordan Ellen-berg (Wisconsin), Gabor Kun (Eotvos Univer-sity, Budapest), Romyar Shari (McMaster), Wen-zhi Luo (Ohio State), David McKinnon (Wa-terloo), Denis Thérien (McGill), Farshid Hajir(Amherst), Jason Lucier (Waterloo), AlexandruPopa (Princeton), Jorge Devoto (Buenos Aires),Nora Ganter (Urbana-Champaign), Ali Ozluk(Maine), Pierre Charollois (Bordeaux), John Cre-

mona (Nottingham), Gergely Harcos (Texas),Nyandwi Servat (University Tunis El Manar),R. Sujatha (Tata Institute), John Coates (Cam-bridge), Gregory Freiman (Tel Aviv) et ManfredEinsiedler (Wien and Princeton).

A number of talks were also given by the localparticipants, and an important facet of QVNTSis to give to CICMA members an occasion topresent to each other their latest research. TheQVNTS are also important for the postdoctoralfellows, allowing them to present their researchto the number theory community, and to sharetheir expertise. One of the QVNTS day was en-tirely dedicated to the recent spectacular workof C. Khare proving Serre’s conjecture. The talkswere given by David Savitt, a CICMA postdoc-toral fellow whose work was important in theproof of Khare.

In addition to the main scientific event, theQVNTS, the members of CICMA are also in-volved in more informal and specialized sem-inars, or working seminars, among smallergroups of postdoctoral fellows, graduate stu-dents and faculty members. Those include:

• The “Séminaire de Théorie analytique desnombres,” organized since 2003–2004 by agroup of postdocs and graduate students. Thetopics covered in the seminars are influencedby the research interests of the participants.

• A Working Seminar organized by AdrianIovita on the p-adic Banach spaces, and the L-invariants associated to modular forms. Theparticipants included some faculty members,and several postdocs and graduate students.

Workshops, special sessions and others

Organized by CICMA members, the followingactivities took place in the province:

A conference on Analytic number theory, or-ganized by Jean-Marie De Koninck at UniversitéLavalMay 19–21, 2005

One of the goals of the conference was to encour-age scientific exchanges between researchers inQuébec and Mexico, following the collabora-tion of Florian Luca (UNAM, Mexico) and Jean-Marie De Koninck. This conference was fundedin part by the Ministère des relations interna-

tionales (division Amérique latine) and the cor-responding institution in Mexico. More detailscan be found in page 26.

The annual “Québec–Maine Number Theory”Conference which was held in Québec Cityin October 2004, was organized by ClaudeLevesque.

In addition to (and including some of) the in-vited speakers of the QVNTS mentioned above,a number of long-term visitors, involved inresearch projects with the CICMA members,were in Montreal during the year 2004–2005.

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RESEARCH LABORATORIES

We mention a few here: Nora Ganter (Urbana-Champaign), Jorge de Voto (Buenos Aires),Haruzo Hida (UCLA), Alina Cojocaru (Prince-

ton), Samit Dasgupta (Harvard), Pierre Charol-lois (Bordeaux) et Kristin Lauter (Microsoft).

Members of the laboratory

Highlights of its members

Other conferences and workshops organized byCICMA members include:

• A 5-day Workshop at BIRS entitled “Dio-phantine Approximation and Analytic Num-ber Theory” which was held on November 20–25, 2004, and whose organizers included An-drew Granville. Several faculty member andpostdoctoral fellows from Montréal partici-pated to the event.

• Two special sessions at the CMS Winter Meet-ing held at McGill University in Decem-ber 2004. A session on Arithmetic geometrywas organized by Eyal Goren and AdrianIovita, and a session on Number theory was

organized by Chantal David and AndrewGranville. Both sessions were funded by theCMS.

C. David, A. Iovita, H. Darmon (principal appli-cant), and E. Goren obtained a NSERC Leader-ship Support Initiative Grant.

C. David, H. Kisilevsky, F. Thaine, H. Darmon(director), and E. Goren obtained a FQRNT TeamGrant.

During the year 2004–2005, 21 master’s students,23 Ph.D. students and 12 postdoctoral fellowswere supervised by laboratory members.

Regular members

Henri Darmon (McGill) DirectorAlgebraic number theory, geometry, arithmetic,L-functions, Diophantine equations, ellipticcurves.

Chris J. Cummins (Concordia)Group theory, modular functions, Moonshine.

Chantal David (Concordia)Analytical number theory, L-functions

Jean-Marie De Koninck (Laval)Analytic number theory: distribution of primenumbers, factorisation of numbers, asymptoticbehaviour of arithmetic functions, Riemann zetafunction.

Dave Dummit (Vermont)Algebraic number theory, arithmetic algebraicgeometry, computational mathematics.

David Ford (Concordia)Computational number theory, algorithmicnumber theory.

Eyal Goren (McGill)Arithmetic geometry, algebraic number theory,moduli spaces of abelian verieties, Hilbert mod-ular forms, p-adic modular forms.

Andrew Granville (Montréal)Analytic number theory, arithmetic geometry,combinatorics.

Adrian Iovita (Concordia)Number theory, p-adic cohomology.

Olga Kharlampovich (McGill)Combinatorial theory of groups and Lie alge-bras.

Hershy Kisilevsky (Concordia)L-functions, Iwasawa theory, elliptic curves,class field theory.

Claude Levesque (Laval)Algebraic number theory, units, class number,cyclotomic fields.

Michael Makkai (McGill)Mathematical logic.

John McKay (Concordia)Computational group theory, sporadic groups,computation of Galois groups.

Alexei Miasnikov (McGill)Group theory.

M. Ram Murty (Queen’s)Number Theory: Artin’s conjecture, ellipticcurves, modular forms, automorphic forms,Langlands program, Selberg’s conjectures, Sievemethods, cryptography.

Jonathan Pila (McGill)Number theory, especially algorithmic and Dio-phantine problems.

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Damien Roy (Ottawa)Transcendental number theory.

Peter Russell (McGill)Algebraic geometry.

Francisco Thaine (Concordia)Cyclotomic fields, cyclotomy, rational points oncurves.

CIRGET

Description

Geometry and topology are fundamental disci-plines of mathematics whose richness and vital-ity have been evident throughout human historyand reflect their deep link to our experience ofthe universe. They are at a crucial crossing pointof modern mathematics and in effect several do-mains of mathematics have recently shown astrong trend towards a geometrization of ideasand methods: two cases in point are mathemati-cal physics and number theory.

During the last twenty-five years, a group ofresearchers of international calibre in geometry

and topology has been hired by Québec univer-sities. The research centre, based at UQÀM, nowcomprises seventeen professors-researchers to-gether with a large number of postdoctoral fel-lows and graduate students.

The main themes to be pursued in the comingyears include Dehn surgery and Thurston ge-ometrization; quantization of Hitchin systemsand geometric Langlands program; classifica-tion of special Kähler metrics; the study of sym-plectic invariants, especially in dimension 4;Hamiltonian dynamical systems.

Activities of the laboratory in 2004–2005

Workshops, special sessions and others

CIRGET members have organized variousevents in the Montreal area this year funded byCIRGET, the CRM and other sources. A com-plete description of all these activities can befound in the chapter “General Program .”

• Short Program on Riemannian GeometryJune 28 to July 16, CRMOrganizers: Vestislav Apostolov (UQÀM), An-drew Dancer (Oxford), Nigel Hitchin (Ox-ford), McKenzie Wang (McMaster)

The theme of this program was the study ofspecial geometries (metrics whose curvaturesatisfies constraints), as well as the relation be-tween curvature and topology.

• Special Semester on Symplectic Geometryand TopologyFall 2004, CRMOrganizers: Octavian Cornea (Montréal),François Lalonde (Montréal)

This began with the Séminaire de Mathéma-tiques Supérieures (SMS), the annual NATOsponsored summer school held at the Univer-sité de Montréal. This year’s topic was “Morsetheoretic methods in non-linear analysis andsymplectic topology.” The School was heldfrom June 21 to July 2 with 91 students par-ticipating. In the framework of this informalsemester, between October 14 and December7, 17 invited lectures were given, with an in-tensive two-week workshop held November2 to November 12.

• Topics in Low-Dimensional TopologyMay 16–17, 2005, UQÀMOrganizers: Steven Boyer (UQÀM), OlivierCollin (UQÀM)

The two main themes of the Workshopwere applications of geometric methods in 3-manifolds and the contact topology in dimen-sion 3.

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Niky Kamran invited Stephan De Bièvre (Lille)to give a full-term course this winter on quan-tum field theory in curved space-time at McGillto provide students and postdoctoral fellowswith the background for a workshop he is plan-ning in 2005-2006. The course was a rigorousconstructive quantum field theory course thatcovered the classical theorems on CCR algebrasand concluded with a discussion of the Unruheffect for accelerated observers near black holes.This was the first time that a course on this im-portant topic has been given in Montreal. Thelectures will be published as a book.

Added to the many seminar and conferencevisitors listed above, CIRGET also welcomed :Daryl Cooper (UCSB), Xingru Zhang (SUNY),Michel Boileau (Toulouse), Felix Finster (Re-gensburg), Alexander Its (IUPUI), Gabriele Vez-zosi (Florence), Michael Batanin (Sidney), Marie-Françoise Ouedraougo (Ouagadougou), ViktorEnolskii (Heriot-Watt) and Michael Gekhtman(Notre-Dame).

The CIRGET Summer Scholarship program, thatencourages promising undergraduate students

to continue in graduate studies, began to bearfruit. Indeed, Apostolov’s two summer fellowsstarted a master’s in geometry in 2004. Further-more, each year, we receive many applicationsfrom French students from the ENS, which isa good indication of the international spread ofthe CIRGET.

One can see how well the CIRGET is known in-ternationally by looking how many postdoctoralCRM-ISM applications it received: the third ofall the applications were send to CIRGET mem-bers (110 to 330). Four of these candidate willjoint the CIRGET next year. The presence of post-doctoral fellows enhance CIRGET dynamism,they participate in organizing event, they invitemany collaborators whom presence is benefic forall CIRGET members, they work with gradu-ate students and collaborate with regular mem-bers. Two publications resulted from these col-laborations: Hu and Lalonde published a paperin symplectic geometry and Tillmann and Boyerwill publish soon a paper in low-dimensionaltopology.

Seminars

The three weekly CIRGET Seminars have beenquite active.• The Geometry-Topology Seminar is the main

regular activity of the laboratory, attended byall CIRGET members. Organized by OlivierCollin, the seminar hosted 24 speakers ofwhom 17 were from outside Montreal.

• The Geometric Group Theory Seminar, a morespecialized seminar organized by Dani Wise,met 17 times over this period with 11 talksgiven by speakers from outside Montreal.

• Finally, the CIRGET Junior Seminar, orga-nized by Baptiste Chantraine for CIRGET stu-dent members, met 23 times.

Members of the laboratory

New members of the laboratory

CIRGET welcomed two new members this year.Steven Lu (Ph.D. Harvard 1990) accepted a posi-tion at UQÀM after spending four years in Ger-many at the Max Plank Institute and two yearsat the University of Essen. Pengfei Guan (Ph.D.Princeton 1989) came to McGill as a senior CRCafter spending many years at McMaster Univer-sity.

Both have integrated smoothly into the Mon-treal mathematical scene and have played an ac-

tive role in CIRGET. Their presence will rein-force the geometrical analysis domain, in whichApostolov and Kamran already work. With nowfour researchers working in the area, geometri-cal analysis will become an important CIRGETresearch nucleus.

During the year 2004–2005, 22 master’s students,15 Ph.D. students and 10 postdoctoral fellowswere supervised by laboratory members.

Regular Members

Steven Boyer (UQÀM) DirectorTopology of manifolds, low-dimensional geom-etry and topology.

Syed Twareque Ali (Concordia)Coherent states, wavelets, quantization tech-niques, harmonic analysis, Wigner functions.

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Vestislav Apostolov (UQÀM)Complex geometry, Kähler geometry.

Abraham Broer (Montréal)Algebraic transformation groups, invariant the-ory.

Olivier Collin (UQÀM)Invariants of knots and 3-manifolds arising fromglobal analysis.

Octavian Cornea (Montréal)Algebraic topology, dynamical systems.

Pengfei Guan (McGill)Partial differential equations, geometric analy-sis, several complex variables.

John Harnad (Concordia)Mathematical physics, classical and quantumphysics, geometrical methods, integrable sys-tems, group theoretical methods, random ma-trices, isomonodromic deformations, isospectralflows.

Jacques Hurtubise (McGill)Algebraic geometry, integrable systems, gaugetheory, moduli spaces.

André Joyal (UQÀM)Algebraic topology, category theory.

Niky Kamran (McGill)Geometric approach to partial differential equa-tions.

François Lalonde (Montréal)Symplectic topology and geometry, global anal-ysis on manifolds, infinite dimensional transfor-mation groups.

Steven Lu (UQÀM)Chern number inequalities, semi-stability of ten-sorial sheaves, log jets, log and hyperbolic geom-etry, algebraic degeneracy.

Iosif Polterovich (Montréal)Geometric applications of spectral geometry.

Peter Russell (McGill)Algebraic geometry.

John A. Toth (McGill)Microlocal analysis, partial differential equa-tions.

Daniel T. Wise (McGill)Geometric group theory, low-dimensional topol-ogy.

LaCIM

Description

LaCIM is a research lab-oratory of the Universitédu Québec à Montréal,which was officially es-tablished in 1989. Its re-search activities concen-trate on enumerative al-gebra, algebraic combi-natorics, computer sci-

ence and their applications to other scientific do-mains, such as the analysis of algorithms, sta-tistical mechanics and computational biology.Since 2002, LaCIM is one of the eight researchlaboratories of the CRM.

Research areas

Discrete mathematics has lately become an im-portant field of practical research, witness thenew heading in Mathematical Reviews 05E of al-gebraic combinatorics with subheadings indicat-ing interactions with the newest areas of math-ematics, such as group representations, quan-tum groups, discrete algebraic geometry, spe-cial functions. Combinatorics benefits from the

revival of the concrete computational aspect inmathematics after decades of abstract structural-ism. Algebra is enriched in a fundamental man-ner by combinatorics, as the commutative alge-bra book by Eisenbud demonstrates, highlight-ing constructive geometric methods. Moreover,combinatorics applies to computer science (the-ory of automata, analysis of algorithms), to sta-tistical physics (computation of configurationspaces and of critical exponents, discrete mod-els), bio-informatics (combinatorics of words ap-plied to genomic sequences). The youth, dy-namism, utility and applicability of this researchdomain are highlighted in the modern world,where discrete structures (trees, graphs, permu-tations) are more and more present in communi-cations, networks and research engines, of whichthe use is growing exponentially in this 21st cen-tury.

The researchers

The laboratory is comprised of thirteen principalresearchers, ten of them professors at UQÀM,one at McGill, one at Université de Montréal

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and one at École Polytechnique de Montréal; oftwelve collaborator and five associated mem-bers in North America, one in Chile and twoin Europe. Notably, Christophe Reutenauer (reg-ular member) and Nantel Bergeron (associatemember) hold Canadian research chairs. A teamof four LaCIM members is supported by agrant from FQRNT. André Joyal, past memberof LaCIM and current member of CIRGET, isinvolved in several activities at LaCIM, bothformal and informal. LaCIM is the largest re-search group in combinatorics in Canada and isknown worldwide in its field. The UQÀM teamhas contributed to the emergence and establish-ment of combinatorics as a mathematical dis-cipline. For example, several LaCIM membershave played and continue to play an importantrole in the organization of the international col-loquium “Formal Power Series and AlgebraicCombinatorics,” which is bilingual and is heldyearly, alternately in Europe and North Amer-ica. Its success is without question.

Research activities at LaCIM

André Joyal enriched the counting theory ofPolya by including the theories of group repre-sentations and symmetric functions. Under thename of theory of species, this theory marked

the emergence of the UQÀM combinatoricsgroup about twenty years ago. From that timeresearch has diversified greatly at LaCIM:

• classical enumerative combinatorics and itsapplications (counting of discrete configura-tions and planar maps);

• algebraic combinatorics;• theoretical computer science;• bio-informatics.

Seminars and others

The LaCIM Combinatorics and Theoretical In-formatics Seminar is an important and suc-cessful integrating element. Cédric Chauve andChristophe Reutenauer are the organizers. Theseseminars were held on Fridays 25 times duringthe year and about 25 people attended the talks.

During 2004 – 2005, the LaCIM hosted sev-eral visitors: David Barrington (Amherst), Jean-Pierre Borel (Limoges), Ricard Gavalda (UPCBarcelona), Mark Haiman (Berkeley), CristofferHansen (Århus), Christian Kassel (Strasbourg),Michal Koucky (Prague), Clemens Lautemann(Mainz), Francois Lemieux (UQÀC), Julia Mi-tacki (Bielefeld), Mathieu Raffinot (Paris), KlausReinhardt (Tübingen)and Jens Stoye (Bielefeld).

Members of the laboratory

Highlights of its members

Denis Thérien is a James McGill Professor atMcGill University (2002–2009) and ChristopheReutenauer has a Canada Research Chairin “Combinatorial Algebra and MathematicalComputing ” (2001–2008).

Two former members of the LaCIM, MarniMishna (Ph.D.) and Sara Faridi (postdoctoral fel-low) received this year a NSERC Faculty Sup-port Programs (Each year, only 25 candidate arechosen). Also, Marni Mishna received in 2004the Governor General’s Academic Medal for herPh.D. Thesis.

LaCIM integrated a new regular member: JohnMullins, Professor at the Computer Engineer-ing Department of the École Polytechnique deMontréal; he is director of CRAC (Conceptionet réalisation des applications complexes). He al-ready collaborates with Srecko Brlek.

During the year 2004–2005, LaCIM memberswere active in the organization of many large-scale events:

• François Bergeron, in collaboration with SaraFaridi (former LaCIM postdoctoral fellow), Ric-cardo Biagioli (LaCIM postdoctoral fellow) andTony Geramita, organized, in January 2005, theSecond Invariants and Combinatoric Workshop, heldin Ottawa (the first took place in Kingston in Jan-uary 2004).

The main achievement of this event has been theestablishment of an on-going dialogue betweentwo separate research communities that hadbeen using similar techniques to study differentmathematical problems. The two groups are al-gebraic combinatorialists working on the repre-sentation theory of symmetric groups, and com-mutative algebraists studying resolutions andinverse systems. The connections between thesetopics were highlighted in a successful meetingthat took place in January 2004 at Queen’s Uni-versity in Kingston. In this meeting, through aseries of expository lectures by Tony Geramitaand François Bergeron, among others, it was

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made evident that interesting special cases of thenotion of Macaulay’s inverse systems of commu-tative algebra are essentially the same objects ascoinvariants spaces studied in algebraic combi-natorics and representation theory. This year’smeeting will continue in the same tradition.

• Vladimir Makarenkov was president of theScientific Committee (which also include AnneBergeron and Cédric Chauve) of the Société fran-cophone de Classification Colloquium, which tookplace at UQÀM in May 2005.

Beside the usual classification thematic, the fol-lowing themes were privileged in Montréal:Bioinformatics, evolution and phylogenic anal-ysis, consensus methods, data search and sym-bolic data analysis.

Invited speakers: Francisco De Carvalho (Univer-sidade Federal de Pernambucol), Pierre Hansen(HÉC), Melvin F. Janowitz (DIMACS Center,Rutgers University), Sabine Krolak-Schwerdt(Universität des Saarlandes), Bruno Leclerc(École des Hautes Études en Sciences Sociales),Maurizio Vichi (Universitá “La Sapienza” diRoma).

• A special session on “Algebraic Combina-torics” of the CMS Meeting, held at McGill in De-cember 2005, was organized by François Berg-eron and Christophe Reutenauer, together withthe two postdoctoral fellows Peter MacNamaraand Riccardo Biagioli. Topics included all as-pects of algebraic combinatorics and their rela-tions with other parts of mathematics. One par-ticular focus was on recent work concerning re-lations among symmetric functions.

Invited speakers: Nantel Bergeron (York),Francesco Brenti (Tor Vergata), Sergey Fomin(Michigan), Adriano Garsia (UC San Diego), IanGoulden (Waterloo), David Jackson (Waterloo),Mercedes Rosas (York), Mark Skandera (Dart-mouth), Richard Stanley (MIT), John Stembridge(Michigan), Stephanie van Willigenburg (UBC)et Mike Zabrocki (York).

• The 2004 International JOBIM Conference(Journées Ouvertes en Biologie, Informatique etMathématiques) included in its program com-

mittee Anne Bergeron, Sylvie Hamel, CédricChauve and Vladimir Makarenkov.

JOBIM is a multidisciplinary event that bringstogether experts in biology, computer science,mathematics and physics. In 2004, the pro-gram was divided in six sessions on: repetitions,patterns, gene expression and regulation net-works; comparative genomic, predictions, mod-els; data bases, exploration, classification andvisualization; phylogeny, evolution and popu-lation; structure and families of ARN or pro-teins; and metabolism classification, biologicalsystems.

The program included 20 long presentations,33 “flash" presentations and 6 invited talks.This year the invited speakers were Tom Hud-son (McGill), Bernard Dujon (Institut Pasteur),Hervé Philippe (Montréal), Mathieu Blanchette(McGill), David Sankoff (Ottawa) and ShoshanaWodak (Hospital for Sick Children, Toronto). JO-BIM also held a poster session: around 40 posterswere presented.

• An Invited Minisymposia on “Genome Rear-rangements” was organized by Anne Bergeronin June 2004 during the SIAM conference Dis-crete Mathematics held at Nashville, Tennessee.

The recent spectacular growth of genome se-quencing projects provides a fertile ground fornew problems that are both relevant to biolo-gists, and challenging to mathematicians andcomputer scientists. In an unexpected way, chro-mosomes happen to be ordering devices for thevarious genes that encode information aboutspecies. The content and order of these genesvaries from species to species, and differentgenomes are modeled as permutations andwords. This symposium will focus on the issuesraised by whole genome comparisons: Theserange from central applied problems such asgene function prediction or phylogeny recon-struction, to hard combinatorial problems whosesolution requires the development of new theo-retical tools.

During the year 2004–2005, 34 master’s students,22 Ph.D. students and 7 postdoctoral fellowswere supervised by laboratory members.

Regular members

Christophe Reutenauer (UQÀM) DirectorAlgebraic combinatorics, non-commutative al-gebra, automata, codes, free algebras.

Robert Bédard (UQÀM)Representations of finite groups, Lie theory.

Anne Bergeron (UQÀM)Bio-informatics.

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François Bergeron (UQÀM)Combinatorics, algebras, representations of fi-nite groups.

Srecko Brlek (UQÀM)Combinatorics of words, algorithmics.

Cedric Chauve (UQÀM)Enumerative combinatorics, trees, bio-informatics.

Sylvie Hamel (Montréal)Bio-informatics and algorithms, language andautomaton theory, algebraic combinatorics.

Gilbert Labelle (UQÀM)Enumerative combinatorics, analysis

Pierre Leroux (UQÀM)Enumerative and algebraic combinatorics.

Vladimir Makarenkov (UQÀM)Computational biology, mathematical classifica-tion.

John Mullins (École Polytechnique de Mont-réal) Logic and Algebra applications to mod-elization, concurrent systems analysis, in partic-ular, safety systems analysis.

Denis Thérien (McGill)Theory of complexity of computation, logic,combinatorics, probability.

Timothy Walsh (UQÀM)Algorithmics, enumerative combinatorics,graphs.

Associate members

Michel Bousquet (Cegep du Vieux-Montréal)

Alain Goupil (Cegep du Vieux-Montréal)Combinatorics, algebra, finite group representa-tions, symmetrical groups and extensions.

Pierre Lalonde (Cegep Maisonneuve)Enumerative and bijective combinatorics, sign

alternating matrices, involution enumeration re-lated to divers parameters, use of pfaffiens anddeterminants in enumeration.

Cédric Lamathe (UQÀM)

Luc Lapointe (University of Talca, Chili)Algebraic Combinatorics, symmetrical func-tions, integrable systems, supersymmetries.

Collaborating members

Marcello Aguiar (Texas A&M University)Algebraic Combinatorics, non-commutative al-gebra, Hopf algebras and quantum groups, cat-egory theory.

Luc Bélair (UQÀM)Mathematical logic, model theory.

Nantel Bergeron (York Univ.)Applied algebra.

Pierre Bouchard (UQÀM)Commutative algebra, algebraic geometry andcombinatorics.

Yves Chiricota (UQÀC)

Sylvie Corteel (CNRS)Enumerative and bijective combinatorics, inte-gers partitions and q-series.

Adriano Garcia (University of California at SanDiego)

Algebraic combinatorics, symmetrical func-tions, Harmonic and co-invariant spaces, quasi-harmonic and quasi-invariant functions.

André Joyal (UQÀM)Algebraic topology, Category theory.

Jacques Labelle (UQÀM)Combinatorics, topology.

Louise Laforest (UQÀM)Data structures, combinatorics, asymptoticalanalysis, quaternary trees.

Simon Plouffe

Xavier G. Viennot (Université Bordeaux I)Enumerative, algebraic and bijective combina-torics, interaction between combinatorics, theo-retical informatics and theoretical physics.

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Mathematical Analysis

Description

At the same time classical and central to modernmathematics, analysis involves studying contin-uous systems from dynamical systems to solu-tions of partial differential equations and spec-tra of operators. The analysis laboratory wasformed three years ago. Currently the laboratoryhas 36 (regular and associate) members work-ing at eight different universities in Quebec,the USA and France. The research areas of themembers of the laboratory are harmonic analy-sis, complex analysis and several complex vari-

ables, potential theory, functional analysis, Ba-nach algebras, microlocal analysis, analysis onmanifolds, nonsmooth analysis, spectral theory,partial differential equations, geometric analy-sis, ergodic theory and dynamical systems, con-trol theory, mathematical physics, applied math-ematics, probability, nonlinear analysis, nonlin-ear differential equations, topological methodsin differential equations, fluid dynamics and tur-bulence.

Activities of the laboratory in 2004–2005

Workshops, special sessions and others

Workshop on Spectral Theory of SchrödingerOperatorsJuly 26-30, 2004, CRMOrganizers: Vojkan Jaksic (McGill), Yoram Last(Hebrew)

This workshop, organized in the framework ofthe 2003 – 2004 CRM theme year, focused onthe spectral theory of random and quasiperiodicSchrödinger operators. In solid state physicsrandom and almost periodic Schrödinger opera-tors serve as models of disordered systems, suchas alloys, glasses and amorphous materials. Thedisorder of the system is reflected by the depen-dence of the potential on some random parame-ters.

This workshop brought together the world lead-ers in spectral theory of random and quasiperi-odic Schrödinger operators. Its goal was to re-view the state of the art of the field and tomap new directions of the research. The pro-gramme included short courses given by M.Aizenman (Princeton), B. Simon (Caltech), andS. Jitomirskaya (Irvine). The workshop was heldin conjunction with the following one.

Workshop on Dynamics in Statistical Mechan-icsAugust 2-6, 2004, CRMOrganizers: Vojkan Jaksic (McGill), Claude-AlainPillet (Toulon)

This workshop, also organized in the frameworkof the 2003 – 2004 CRM theme year, was devotedto the study of dynamical properties of (classi-cal and quantum) open systems. In particular,through the study of noisy or forced dissipativesystems, or Hamiltonian systems with a largenumber of degrees of freedom, our understand-ing of the mathematical structure of nonequilib-rium statistical mechanics has greatly improved.

The aim of this meeting was to present the latestresults and discuss the possible future directionsof research in this area. The program includedshort courses to be given by H. Araki (Kyoto), B.Derrida (École Normale), J. Froehlich (ETH), J.-P. Eckmann (Geneva). The workshop was heldin conjunction with the preceding one.

Conference on Fixed Point Theory and its Ap-plications in Honour of Andrzej GranasAugust 16-20, 2004, CRMOrganizer: Marlène Frigon (Montréal)

The Centre de Recherches Mathematiques(CRM), in collaboration with the Departmentof Mathematics and Statistic of the Université deMontréal, organized this conference in honourof Andrzej Granas on the occasion of his 75thbirthday. The main themes of the conferencewere fixed point theory and its applications toproblems arising in non-linear analysis, differ-ential equations and dynamical systems. Details

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about this activity can be found in page of thisreport.

Analysis Day29 April 2005, CRMOrganizers: Thomas Ransford (Laval), Chris-tiane Rousseau (Montréal), Alina Stancu (Mont-réal), Galia Dafni (Concordia), Dmitry Jakobson(McGill).

This laboratory is one of the most numerous andis present in all the universities of the province.This forces sub-groups of the laboratory to workin parallel. To remedy the problem, and sincea lot of the members do not know each other,we started in 2004–2005 a tradition of organiz-ing each year an Analysis Day, to which all themembers will be invited. For the moment, there

is no need to invite many speakers from abroad,but to let the members give the talks, so they willknow each other’s research areas.

During 2004–2005, the Mathematical AnalysisLaboratory hosted several visitors: H. Araki (Ky-oto), J. Artes (Barcelona), L. Bruneau (Warsaw),M. Cojocaru (Queen’s), S. De Bievre (Lille), J.Derezinski (Warsaw), F. Dumortier (LimburgsUniversitair Centrum), A. Fedotov (Physics In-stitute, St-Petersbourg), B. Helffer (Paris Sud), V.Ivrii (Toronto), F. Klopp (Paris Nord), Y. Last,(Hebrew), J. Llibre (Barcelona) M. Mrozek (Jag-ellon), N. Nadirashvili (CNRS, Marseille), C.-A.Pillet (Toulon), L. Rey-Bellet (UMass Amherst),N. Vulpe, (Moldavian Academy), A. Sobolev(Sussex), S. Zelditch (Johns Hopkins) et E.S. Ze-ron (Cinvestav-IPN).

Seminars

Several Analysis Seminars take place in Québecuniversities. The following were organized bythe members of the laboratory in 2004–2005.

Analysis (Laval): 20 talks in the regular seminarand 18 in the working group.

Analysis (McGill/Concordia)Organizers: Galia Dafni, Dmitry Jakobson, 22talks.

Analysis (Montréal)Organizers: Paul Gauthier, Richard Fournier.This weekly seminar focused on complex analy-sis, organized mainly for students, 20 talks.

Seminar in Nonlinear Analysis and DynamicalSystems (Montréal)Organizers: Christiane Rousseau, Alina Stancu,25 talks.

Analysis and Related Topics (Sherbrooke/Bishop’s)Organizers: Madjid Allili, Tilak Bhattacharya,François Dubeau, Tomasz Kaczynski, 15 con-férences.

Student Analysis Seminar (McGill)Organizer: Eugene Kritchevski

Members of the laboratory

Highlight of the members

• P. Guan (McGill), A. Kokotov (Concordia)have recently become associate members ofthe laboratory and A. Shnirelman (Concordia)has become regular member.

• P. Guan (McGill) and A. Shnirelman (Con-cordia) have recently been awarded SeniorCanada Research Chair Positions.

• Christiane Rousseau (Montréal) organized, incollaboration with Pavao Mardesic, a Confer-ence for the 60th anniversary of Robert Rous-sarie in June 2004 at Luminy.

• Christiane Rousseau (Montréal) organized, incollaboration with Robert Roussarie, the ses-sion “Dynamical systems ” during the firstFrance-Canada Colloquium in July 2004 atToulouse. She was also member of the Meet-

ing Organization Committee, together withthe presidents of the Canadian and Frenchmathematical societies.

• Paul Gauthier (Montréal) and RichardFournier (Dawson) organized a sessions inApproximation theory and Galia Dafni (Con-cordia) organized a session in Harmonic anal-ysis at the 2004 CMS Winter Meeting in Mon-treal.

• Pengfei Guan (McGill) organized a Geometricanalysis session at AMS Meeting in Newark,Delaware, April 2005.

During the year 2004–2005, 30 master’s students,26 Ph.D. students and 6 postdoctoral fellowswere supervised by laboratory members.

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Regular members

Dmitry Jakobson (McGill) DirectorPure mathematics, global analysis, spectral ge-ometry, quantum chaos, harmonic analysis,eigenvalues and eigenfunctions

Line Baribeau (Laval)Complex and functional analysis, Banach alge-bras, holomorphic iterations, discrete groups.

Abraham Boyarsky (Concordia)Dynamical systems

Francis Clarke (Lyon I)Nonlinear and dynamic analysis, control theory,calculus of variations.

Galia Dafni (Concordia)Harmonic analysis, partial derivative equations,complex variables.

Donald Dawson (Carleton)Probability, stochastic process.

Stephen Drury (McGill)Harmonic analysis, matrix theory.

Richard Fournier (Collège Dawson)Probability, stochastic processes.

Marlène Frigon (Montréal)Nonlinear analysis, differential equations, fixedpoint theory, critical point theory, multivalentanalysis.

Paul Gauthier (Montréal)Complex analysis, holomorphy, harmonicity, an-alytic approximation.

Pawel Góra (Concordia)Ergodic theory, dynamic systems, fractal geom-etry.

Frédéric Gourdeau (Laval)Banach algebras, cohomology, amenability, func-tional analysis.

John Harnad (Concordia)Mathematical physics, classical and quantumphysics, geometrical methods, integrable sys-tems, group theoretical methods, random ma-trices, isomonodromic deformations, isospectralflows.

Vojkan Jaksic (McGill)Quantum mechanics, statistics, randomSchrödinger operators.

Tomasz Kaczynski (Sherbrooke)Topological methods, Conley index, applica-tions to dynamical systems.

Niky Kamran (McGill)Geometric approach to partial differential equa-tions.

Ivo Klemes (McGill)Harmonic analysis, trigonometric series.

Paul Koosis (McGill)Analyse harmonique.Harmonic analysis.

Dmitry Korotkin (Concordia)Integrable systems, isomonodromic deforma-tions, classical and quantum gravity, Frobeniusvarieties.

Javad Mashreghi (Laval)Complex analysis, harmonic analysis, Hardyspaces.

Iosif Polterovich (Montréal)Geometric applications of spectral geometry.

Thomas Ransford (Laval)Complex and harmonic analysis, functionalanalysis and theory of operators, spectral anal-ysis, potential theory.

Dominic Rochon (UQTR)Numbers, analysis, dynamic complexes.

Jérémie Rostand (Laval)Complex analysis, experimental mathematics.

Christiane Rousseau (Montréal)Dynamical systems, bifurcations, qualitativetheory, polynomial systems, analytic invariants,integrable systems.

Dana Schlomiuk (Montréal)Global analysis, dynamical systems, singulari-ties, bifurcations, algebraic curves, primary inte-gral.

Alexander Shnirelman (Concordia)Applications of geometrical analysis to fluidsand “weak” solutions of the Euler and Navier–Stokes equations.

Ron Stern (Concordia)AFunctional analysis and theory of operators,linear and non-linear systems, non-smooth anal-ysis, stability, optimal order.

John Toth (McGill)Spectral theory, semi-classical analysis, micro-local analysis, Hamiltonian mechanics.

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Associate members

Richard Duncan (Montréal)Ergodic theory, probability.

Kohur GowriSankaran (McGill)Potential theory.

Pengfei Guan (McGill)Geometric analysis.

Alexei Kokotov (Concordia)

Nilima Nigam (McGill)Applied analysis, numerical methods in electro-magnetism.

Yiannis Petridis (CUNY, Lehman College)Automorphic forms and spectral theory. L-Functions, quantum chaos.

Samuel Zaidman (Montréal)

Mathematical Physics

Description

The mathematical physics group is one of theoldest and most active at the CRM. It consistsof nineteen regular members, all full-time fac-ulty at five Quebec Universities, and four asso-ciate members. A new associate member wasadded this year: Alexander Shnirelman, whowas named to a Canada Research Chair inApplied Mathematics at Concordia University.The Laboratory also includes two attachés derecherches, fourteen postdoctoral fellows (some,jointly with the Analysis and CIRGET Labo-ratories), and lab members supervise, or co-supervise the thesis work of about forty mastersand doctoral students.

The group carries out research in many ofthe currently most active areas in mathemati-

cal physics: Coherent nonlinear systems in flu-ids, optics and plasmas; classical and quantumintegrable systems; the spectral theory of ran-dom matrices; percolation phenomena; confor-mal field theory; quantum statistical mechan-ics; spectral and scattering theory of randomSchrödinger operators; quasi-crystals; relativ-ity; spectral transform methods; asymptotics ofeigenstates; foundational questions in quanti-zation; coherent states; wavelets; supersymme-try; the symmetry analysis of PDE’s and dif-ference equations; representation theory of Liegroups and quantum groups; and the mathemat-ical structure of classical and quantum field the-ories.

Activities of the laboratory in 2004–2005

Workshops, special sessions and others

Much of the year was spent in preparation forthe CRM “Short Program on Random Matrices,Random Processes and Integrable systems,” or-ganized by two Lab members: John Harnad andJacques Hurtubise, which took place as part ofthe CRM General Program on June 20 – July 8,2005. Details about this activity will be found inthe 2005 – 2006 CRM annual report.

The members of the laboratory maintain activeties and ongoing collaborations with other re-searchers from centers in mathematical physicsaround the world. The list of scientific visitors tothe laboratory this academic year included: A.

Arefijamaal (Meshhed), H. Braden (Edinburgh),L. Chekhov (Moscow), S. De Bièvre (Lille), R.Conte (Paris), C. Eilbeck (Edinburgh), A. ElGradechi (Artois), V. Enolskii (Heriot-Watt), B.Eynard (Saclay), M. Fels (Utah State), F. Fin-ster (Regensburg), R. Floreanini (IFIN Trieste),M. Gekhtman (Notre Dame), A. Its (IUPUI), C.Klein (Bonn), M. Knopp (Temple), A. Kokotov(St. Petersburg), D. Levi (Rome), D. Majard (Aix-Marseille), N. Nadirashvili (Chicago), S. Norton(Cambridge), E. Previato (Boston), I. Rivin (Tem-ple), Nasser Saad (UPEI), A. Safapour (Mesh-hed), A. Sergyeyev (Silésie), M.K. Tavassoly (Is-pahan), P. Tempesta (SISSA Trieste), Z. Thomova

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(SUNY Syracuse), S. Venakides (Duke), N. Witte(Melbourne) and Ismet Yurdusen (Middle EastTechnical).

In addition, within the framework of ISM spon-sored doctoral level courses, two special seriesof lectures were given by visiting researcherswho were at the CRM for the Fall and Wintersemesters, while on sabbatical leave from theirhome institutions: Professors Michael Gekht-man (Notre Dame) and Stefan De Bièvre (Lille).

The titles of these courses were:

Integrable systems, exactly solvable latticesand Lie groupsConcordia, Michael Gekhtman.September to December 2004.

Topics in Analysis V : An Introduction to freeBose fieldsMcGill, Stephan De Bièvre.January to April 2005.

Seminars

• The regular CRM Mathematical Physics semi-nar series was continued throughout the aca-demic year, with weekly talks given bothby invited visitors and local members of theLab, including postdoctoral fellows and some

graduate students near to completion of theirdoctorates.

• From January until April, 2005, a second“Working Seminar in Mathematical Physics”was organized by V. Jaksic at McGill.

Members of the laboratory

Highlights of the members

• Jacques Hurtubise was elected a Fellow of theRoyal Society of Canada.

• Alexander Shnirelman, our new AssociateMember, was named a Tier I Canada ResearchChair at Concordia University.

In addition the following conferences/workshopswere organized by members of the laboratory:Special Session “In the Wake of Hamilton andJacobi 200 Years Later”AMS Joint Mathematics MeetingJanuary 5–8, 2005, Atlanta, GeorgiaOrganizers: Maria Clara Nucci (Perugia), PavelWinternitz (Montréal).

“Wavelets 2005,” VIIth International Work-shop on Wavelets, Differential Equations, andQuantizationFebruary 21–25, 2005, University of HavanaOrganizer: Syed Twareque Ali (Concordia).

Research in teams program “Random Matrices,Multi-orthogonal Polynomials and Riemann–Hilbert Problems”April 30–May 14, 2005, BIRSOrganizer: John Harnad (Concordia).

Regular members

John Harnad (Concordia) DirectorMathematical physics, classical and quantumphysics, geometrical methods, integrable sys-tems, group theoretical methods, random ma-trices, isomonodromic deformations, isospectralflows.

Syed Twareque Ali (Concordia)Coherent states, wavelets, quantization tech-niques, harmonic analysis, Wigner functions.

Marco Bertola (Concordia)Axiomatic quantum field theory, invarianttheory of discrete groups, random matrices,isomonodromic deformations.

Chris Cummins (Concordia)Group theory, modular functions, Moonshine.

Alfred Michel Grundland (UQTR)Symmetry of differential equations in physics.

Richard L. Hall (Concordia)Spectra of Schrödinger, Klein-Gordon, Dirac,and Salpeter operators; many-body problems,relativistic scattering theory, iterative solution toode’s and boundary-value problems.

Jacques Hurtubise (McGill)Algebraic geometry, integrable systems, gaugetheory, moduli spaces.

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Véronique Hussin (Montréal)Group theory, Lie algebra and application inphysics, supersymmetries in classic and quan-tum mechanics.

Dmitry Jakobson (McGill)Pure mathematics, global analysis, spectral ge-ometry, quantum chaos, harmonic analysis.eigenvalues and eigenfuntions.

Vojkan Jaksic (McGill)Mathematical physics, quantum statistical me-chanics, random Schrödinger operators.

Niky Kamran (McGill)Geometric approach to partial differential equa-tions.

Dmitry Korotkin (Concordia)Integrable systems, isomonodromic deforma-tions, classical and quantum gravity, Frobeniusvarieties.

Jean LeTourneux (Montréal)Symmetry properties of systems, special func-tions.

Pierre Mathieu (Laval)Conformal field theory, classical and quantumintegrable systems, affine Lie algebras.

Jirí Patera (Montréal)Applications of group theory, quasi-crystals, Liealgebras.

Yvan Saint-Aubin (Montréal)Conformal field theory, statistical mechanics, 2-dimensionalphase transition model.

John Toth (McGill)Microlocal analysis, partial differential equa-tions.

Luc Vinet (McGill)Symmetric properties of systems, special func-tions.

Pavel Winternitz (Montréal)Methods of group theory in physics, nonlinearphenomena, symmetries of difference equations,superintegrability.

Associate members

Stéphane Durand (Collège Edouard-Montpetit)Classical and quantum physics, mathemati-cal physics, symmetries, parasupersymmetries,fractional supersymmetries, KdV, quantum me-chanics, relativity.

François Lalonde (Montréal)Symplectic topology and geometry, global anal-ysis on manifolds, infinite dimensional transfor-mation groups.

Carolyne Van Vliet (Miami)Non-equilibrium statistical mechanics, fluctua-tions and stochastic processes, quantum trans-port in condensed matter, electronic behavior insubmicron quantum devices.

Alexander Shnirelman (Concordia)Applications of geometrical analysis to fluidsand “weak” solutions of the Euler and Navier–Stokes equations.

PhysNum

Description du laboratoire

En tant que laboratoire propre au CRM, Phys-Num est un laboratoire dont une grande partdes activités de recherche est hébergée par leCRM. Cette particularité, qui contribue à la vi-sibilité du Centre dans le champ des mathéma-tiques appliquées, explique sa taille relativementréduite par rapport à l’étendue de ses collabo-rations dans les milieux de la neuro-imagerie à

Montréal et ailleurs : le Regroupement Neuroi-magerie Québec (piloté par Yves Joanette et Ju-lien Doyon), le GRENE (dirigé par Franco Le-pore, Département de psychologie, Montréal)et le groupe d’Imagerie Quantitative de l’Unité494 de l’INSERM (Paris), (dirigé par Habib Be-nali). La plupart des ressources financières sontconsacrées à des étudiants qui poursuivent leurrecherche au CRM. Notre recherche avec cesgroupes porte sur l’imagerie mathématique, es-sentiellement dans le domaine médical, avec lesthèmes suivants :

• l’analyse et la modélisation en ondelettes(formalisme thermodynamique, modèles gra-phiques),

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• l’analyse fractale et multifractale (analyse desmatériaux, angiogénèse, signaux turbulents),

• l’approche probabiliste pour la résolution deproblèmes inverses (inférence par Maximumd’Entropie, graphes d’indépendance).

Ces outils sont utilisés dans plusieurs domainescliniques et cognitifs. Les différentes équipes,mentionnées plus haut, centrées sur la neurolo-gie, sont intéressées à voir se développer de la“méthodologie fine” dans leur problématique etdonc, une interaction à long terme avec notreéquipe est envisagée.

Principaux themes de recherche du laboratoire pour l’annee 2004–2005

Maximum d’entropie et inference en Magneto-EncephaloGraphie (MEG)

Le travail a porté sur la version “bayésien em-pirique” du MEM qui permet de mieux contrô-ler la loi de référence présente dans le for-malisme du MEM. Des algorithmes itératifs,proches d’algorithmes d’apprentissage de typeEM (Expectation-Maximisation), ont été évaluéssur des simulations en MEG à temps fixe et surdes données EEG en épilepsie. Le formalisme dumaximum d’entropie continue de démontrer sastabilité et sa robustesse dans l’estimation dessources dipolaires distribuées (10 000 sources)sur le cortex (Erwig Lapalme, Jean-Marc Lina, Jé-rémie Mattout, 2005). Dernière étape dans ce vo-let de recherche, l’estimation des séries tempo-relles en MEG et l’évaluation des performancesdu MEM sur des données réelles sont actuelle-ment en cours et font l’objet de la rédaction d’unarticle (Erwig Lapalme, Jean-Marc Lina, BernardGoulard, 2005). Les travaux ont fait l’objet de lathèse de doctorat d’Erwig Laplame (directeurs :Jean-Marc Lina, Bernard Goulard).

Estimateur du signal EEG en presence d’arte-facts oculaires

Ce volet de recherche est une collaboration entrePhysNum (Lina, Goulard, Basile-Bellavance) etle département de Pédo-psychiatrie de l’HôpitalSainte-Justine (Robey, Liang, Basile-Bellavance).Le problème consiste à réduire le nombre de ré-pétitions de stimuli dans les expériences EEG enneuropsychiatrie chez les enfants, en proposantune méthode robuste de détection et d’élimina-tion des artefacts oculaires dans les signaux. Cesartefacts sont la principale source de difficultéd’interprétation des signaux, voire du rejet desmesures. Le contrôle oculaire chez les jeunes en-fants demeurant difficile a obtenir, la solutionproposée par la collaboration consiste a détec-ter les mouvements oculaires dans les signauxbruts projetés dans le plan temps-échelle parune analyse en ondelettes continues. Les évalua-tions de la méthode sur des signaux cliniques

démontrent que celle-ci permet de mieux inter-préter les expériences, avec beaucoup moins designaux collectés.

Localisation de sources en MEG/EEG

La détection des activités cérébrales en IRMfet EEG/MEG reste un problème ouvert. En ef-fet, en IRMf, les modèles linéaires multidimen-sionnels, actuellement utilisés, ne prennent pasen compte les corrélations spatio-temporelles dubruit présent dans les données. Souvent, cescorrélations ne peuvent être négligées car ellesrisquent d’engendrer une mauvaise estimationde la carte d’activité fonctionnelle. Pour en te-nir compte, nous avons récemment proposé desmodèles non séparables de covariance spatio-temporelle du bruit et calculé des cartes statis-tiques d’activation plus robustes. En MEG, pourextraire les distributions spatio-temporelles desactivités neurales, nous avons montré, au tra-vers de la thèse de Jérémie Mattout (directeurs :Habib Benali, Line Garnero), l’intérêt de combi-ner les informations spatiales issues de l’IRMfet les informations temporelles issues du signalMEG. Ce travail se poursuit actuellement à par-tir d’acquisitions simultanées IRMf/EEG et faitl’objet de la thèse de doctorat de Jean Dauni-zeau (Thèse en cotutelle avec l’Université deMontréal ; directeurs : Habib Benali, Jean-MarkLina et Bernard Goulard). L’intégration des in-formations IRMf (imagerie de Résonance Ma-gnétique Nucléaire fonctionnelle) dans la détec-tion de sources en MEG/EEG (Magnéto-Electro-Encéphalographie) est l’objectif de ce volet derecherche. L’étude d’une méthodologie d’infé-rence sur le décours temporel des sources d’unmodèle dipolaire distribué, capable de prendreen compte des connaissances a priori multi-modales, est actuellement dans sa phase d’éva-luation de performance. Le modèle retenu parJean Daunizeau (doctorant en cotutelle entreMontréal et Paris 11, codirection Benali, Gou-lard, Lina) s’apparente à celui développé dansle cadre du Maximum d’entropie en exprimantla dépendance temporelle à l’échelle de « par-

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RESEARCH LABORATORIES

celles » (construites à partir des données) quicontiennent des sources élémentaires qui sontcontrastées localement par la méthode d’infé-rence (Daunizeau, Mattout, Goulard, Lina, Be-nali, 2004). Soulignons que ces méthodes ont faitl’objet d’une évaluation de performance dans uncas clinique bien défini (Grova, Daunizeau, Lina,Benali, Gotman, 2004, 2005).

Activité 2005 liée à ce thème :

Atelier (deux journées) Inférence bayésienne etImagerie cérébrale (en collaboration avec Jean-François Angers)Conférenciers : Ali Mohammad-Djafari (SupE-lec, France), Charles A. Bouman (Purdue, USA),Christophe Phillips (Liège, Belgique), KeithWorsley (McGill), Christophe Grova (McGill),Jean Daunizeau (Montréal).

Atelier qui mit l’accent sur la modélisation del’activité cérébrale et les aspects liés à la connec-tivité. Aspects méthodologiques et implémenta-tion numérique. Les détails de l’activité peuventêtre trouvés au chapitre « Programme général ».

Etudes de la connectivite fonctionnelle en IRMf

Les modèles pour l’étude des connectivités entrepopulations de neurones à partir du signal IRMfet MEG/EEG sont en plein essor. La connec-tivité fonctionnelle est définie comme étant lacorrélation entre deux régions du cerveau. Afinde mesurer les connectivités directes entre ré-

gions, nous avons introduit une nouvelle défini-tion de la connectivité qui donne un rôle centralà la notion de corrélation partielle. Nous avonsproposé un modèle théorique original, auto-adaptatif aux données et guidé par des connais-sances a priori sur le réseau fonctionnel étudié.Ce modèle repose sur les modèles graphiquesd’association et le principe de l’échantillonnagebayésien. Il permet une évaluation statistique ra-pide et robuste des différents graphes de connec-tivité possibles. Cette méthode a été validée surdes données de simulation et des données réellesissues de protocoles cognitifs. Nous la validonsactuellement sur des données cliniques (chirur-gie de tumeurs cérébrale). Ce travail a fait l’ob-jet de la thèse de G. Marrelec (directeur : H.Benali). Le modèle de connectivité développénécessite l’identification préalable du réseau derégions fonctionnellement connectées. Pour cefaire, nous avons développé une méthode de dé-tection du réseau spatial basée sur le calcul descorrélations entre les fluctuations lentes du si-gnal IRMf (< 0.1 Hz) et le signal d’une région« cible » préalablement identifiée. Ainsi, nousavons pu construire un réseau de régions plusétendu que celui de la carte d’activation, et indé-pendant de la tâche sensori-motrice considérée.Seul, le niveau de corrélation entre les noeudsdu réseau identifié semble varier d’une tâche àl’autre. Ce travail fait l’objet de la thèse de PierreBellec (directeur : Habib Benali).

Membres du laboratoire

Durant l’année 2004–2005, 2 étudiants à la maîtrise et 4 étudiants au doctorat ont été encadrés par lesmembres québécois du laboratoire.

Membres reguliers

Jean-Marc Lina (ETS) responsableOndelettes, modélisation statistique et imageriecérébrale, algorithmes d’apprentisage.

Alain Arnéodo (CNRS)Fractales et ondelettes.

Habib Benali (CHU Pitié-Salpêtrière)Analyse quantitative en imagerie cérébrale, ima-gerie médicale et systèmes multi-modaux

Line Garnero (CHU Pitié-Salpêtrière)Magnéto-Encéphalo-Graphie (MEG)

Bernard Goulard (Montréal)Imagerie cérébrale

Fahima Nekka (Montréal)Analyse fractale, systèmes poreux, ondelettes

Frédéric Lesage (Montréal)Théorie conforme, systèmes intégrables, pro-blèmes inverses imagerie optique.

Membre associe

Keith J. Worsley (McGill)Géométrie et analyse d’images aléatoires enmédecine et en astrophysique

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CENTRE DE RECHERCHES MATHÉMATIQUES

Statistics

Description

Statistics is central to many endeavours in soci-ety. Whether it be through surveys from sam-pling, clinical trials to study various biomedi-cal treatments or experimental designs in agri-culture or industry, statistical methodology canbe found everywhere in science. Recently, statis-tics has been undergoing a revolution in its tech-niques and its approaches. This revolution hasbeen driven by the need to analyze very largedata sets, data with more complex structure, andby the advent of powerful computers. For ex-ample, statistical methodology is now address-ing problems whose structure is more complex,such as brain images or genome data and newmethodology is developed for large data sets.

Data-mining is one of the tools used. The labora-tory aims at structuring the Québec communityto engage with this revolution at a time of animportant renewal of academic personnel. Thisstructure allows the Québec community to ben-efit from a new pan-Canadian program in analy-sis of complex data organized by the three Cana-dian mathematics institutes. The laboratory iscomposed of the leaders of the Québec schoolof statistics who work on subjects such as sta-tistical learning and neuronal networks, surveysampling, analysis of functional data, statisti-cal analysis of images, dependence structures,Bayesian analysis, analysis of time series and fi-nancial data, as well as resampling methods.

Activities of the laboratory in 2004–2005

Workshops, special sessions and others

Many activities organized by the Statistic Labo-ratory were held in Montréal and in Québec in2004–2005. A detailed description of these activ-ities can be found in the “General Program” andthe “Joint Initiatives” sections of this report.

The annual meeting of the Statistical Society ofCanada took place at the CRM in June 2004.The Program Committee was chaired by Chris-tian Genest; Local Arrangements were coordi-nated by Christian Léger. Many commented onthe highquality of several aspects of the meet-ing organized by “the two Christian” Meeting.Notably, with more than 550 participants, it wasfinancially the most profitable.

The Laboratory is proud of its association withthe PhysNum Laboratory in the organizationof the joint Workshop “Bayesian Inference andFunctional Brain mapping.” Organized by Jean-François Angers and Jean-Marc Lina, this two-day workshop attended by 30 participants,aimed to promote interaction between the spe-cialists and researchers in functional brain im-agery.

The Laboratory organizes NPCDS workshops incollaboration with the Fields and PIMS and isinvolved in its research projects. The Workshop

on “Latent Variable Models and Survey Data forSocial and Health Sciences Research” organizedby the NPCDS, in collaboration with SAMSI,took place at the CRM in May 2005. With morethan 80 participants coming from the Nether-lands, the United Kingdom, the United Statesand the Canada, the workshop was a success,notably considering the diversity of the partic-ipants. Beside the experienced researchers par-ticipation, the workshop was also attended byscientists working in statistical agencies, for in-stance: Statistique Canada, US Census Bureau,Bureau of Labor Statistics, together with re-search groups such as the Research Unit on Chil-dren’s Psychosocial Maladjustment (GRIP) andla Direction de santé publique (Québec).

The major scientific activity of the laboratory thisyear was the Quatrième Colloque francophonesur les sondages held in Québec City in May.With more than 225 participants, this interna-tional Congress welcomed world-renowed spe-cialists in survey methods. The Scientific Com-mittee was chaired by Louis-Paul Rivest; ThierryDuchesne and Christian Léger were members ofthe Organizing Committee. Proceedings will bepublished.

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RESEARCH LABORATORIES

Seminars

The scientific life of the laboratory is fed, ona weekly basis, with the CRM–ISM–GERADStatistics Colloquium in Montréal and the Statis-tics Seminar at Université Laval. As one can see,GERAD joined CRM and ISM in the financial

support and the organization of the StatisticsColloquium. This collaboration between CRMand GERAD is mutually beneficial for the twocentres and their members. The complete list ofthe talks is given in page 28 of this report.

Members of the laboratory

Highlights of its members

• This year, ten new members joined the labora-tory: Belkacem Abdous (Laval), Masoud As-gharian (McGill), Pierre Duchesne (Montréal),Thierry Duchesne (Laval), Charles Dugas(UdeM), Debbie Dupuis (HEC), Sorana Froda(UQÀM), Arush Sen (Concordia), Russ Steele(McGill) and Alain Vandal (McGill).

• During its annual meeting in June, the Sta-tistical Society of Canada (SSC) granted aGold Medal to Keith Worsley. This Medalis awarded to a Canadian mathematician inrecognition of his exceptional achievement

and work in Statistics. He gave a lecture at theSSC meeting.

• In December, Russ Steele, Alain Vandal andDavid Wolfson organized a session on “Math-ematical Methods in Statistics” during theWinter 2004 Meeting of the Canadian Mathe-matic Society. There was a strong participationfrom the members of the laboratory.

During the year 2004–2005, 63 master’s students,44 Ph.D. students and 4 postdoctoral fellowswere supervised by laboratory members.

Regular Members

Christian Léger (Montréal) DirectorResampling methods, adaptive estimation,model selection, robustness, applications in datamining.

Belkacem Abdous (Laval)Biostatistics, health research methodology, con-struction and validation of measuring tools inthe health sector.

Jean-François Angers (Montréal)Decision theory, Bayesian statistics, robustnesswith respect to prior information, function esti-mation.

Masoud Asgharian (McGill)Survival analysis, change-point Problems, simu-lated annealing and its variants, optimization.

Yoshua Bengio (Montréal)Statistical learning algorithms, neural networks,nucleus models, probabilistic models, data min-ing, applications in finance and statistical lan-guage modeling.

Martin Bilodeau (Montréal)Multivariate analysis, decision theory, asymp-totic methods.

Yogendra Chaubey (Concordia)Sampling, linear models, resampling, survivalanalysis.

Pierre Duchesne (Montréal)Time series, sampling, multivariate analysis.

Thierry Duchesne (Laval)Survival analysis, longitudinal data analysis,missing data, modeling of losses, insurance ofcatastrophic incidents, nonparametric inference,model selection, warranty.

Charles Dugas (Montréal)Actuarial science, finance, learning algorithms,neural networks, universal approximation, sur-vival analysis.

Debbie Dupuis (HEC)Extreme values, robustness.

René Ferland (UQÀM)Probability, statistic processes, applications tomathematical finance.

Sorana Froda (UQÀM)Nonparametric methods in function estimation,applications of stochastic modeling in biologyand medicine.

Christian Genest (Laval)Multidimensional data analysis, dependencemeasures, nonparametric statistics, decision the-ory, applications in actuarial science, finance andpsychology.

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CENTRE DE RECHERCHES MATHÉMATIQUES

Nadia Ghazzali (Laval)Multidimensional data analysis, neural net-works and genetic algorithms, applications inastrophysics and biostatistics.

Brenda MacGibbon (UQÀM)Mathematical statistics, decision theory, bio-statistics.

François Perron (Montréal)Decision theory, multidimensional data analysis,Bayesian statistics.

James Ramsay (McGill)Functional data analysis, smoothing and non-parametric regression, curve registration.

Bruno Rémillard (HEC Montréal)Probability, empirical processes, time series,nonlinear filtering, applications in finance.

Louis-Paul Rivest (Laval)Linear models, robustness, directional data,sampling, applications in finance.

Roch Roy (Montréal)Time series analysis, predictive methods, appli-cations in econometrics and epidemiology.

Arush Sen (Concordia)Statistical inference of truncated data, nonpara-metric function estimation.

Russ Steele (McGill)Bayesian approaches to mixing modeling, mul-tiple imputation.

Alain Vandal (McGill)Biostatistics, nonparametric survival estimationand graph theory, imaging, capture-recapture.

David B. Wolfson (McGill)Changepoint problems, survival analysis,Bayesian statistics, optimal design, applicationsin medicine.

Keith J. Worsley (McGill)Statistics of brain mapping, geometry of randomimages in medicine and astrophysics.

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Publications

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CENTRE DE RECHERCHES MATHÉMATIQUES

THE CRM publishes monographs, lecture notes, proceedings, software, videos and research re-ports. It has several collections. The in-house collection Les Publications CRM offers titles in

both English and French. The CRM also has publishing agreements with the American MathematicalSociety (AMS) and Springer. Since 1992, two collections, edited by CRM, have been published anddistributed by the AMS. They are the CRM Monograph Series and the CRM Proceedings and LectureNotes. Springer publishes the CRM Series in Mathematical Physics and the Subseries of the SpringerLecture Notes in Statistics. An asterisk preceding an author indicates that this is a monograph from anAisenstadt Chair holder.

Recent Titles

The following list of Recent Titles contains booksthat appeared in 2004 – 2005 or that will be pub-lished soon.

AMSCRM Monograph Series

Olga Kharlampovich & Alexei Myasnikov, Alge-braic Geometry for a Free Group (to appear).

Victor Guillemin & Reyer Sjamaar ConvexityProperties of Hamiltonian Group Actions, vol. 26,2005.

*Andrew J. Majda, Rafail V. Abramov & Mar-cus J. Grote, Information Theory and Stochastics forMultiscale Nonlinear Systems, vol. 25, 2005.

Dana Schlomiuk, Andrei A. Bolibrukh, SergeiYakovenko, Vadim Kaloshin & AlexandruBuium, On Finiteness in Differential Equations andDiophantine Geometry, vol. 24, 2005.

Prakash Panangaden & Franck van Breugel(eds.), Mathematical Techniques for Analyzing Con-current and Probabilistic Systems, vol. 23, 2004.

Montserrat Alsina & Pilar Bayer, Quaternion Or-ders, Quadratic Forms, and Shimura Curves, vol. 22,2004.

AMSCRM Proceedings & Lecture Notes

Vestislav Apostolov, Andrew Dancer, NigelHitchin & McKenzie Wang (eds.), Perspectives inComparison, Generalized and Special Geometry (toappear).

Pavel Winternitz, David Gomez-Ullate, AriehIserles, Decio Levi, Peter J. Olver, Reinout Quis-pel, & Piergiulio Tempesta, Group Theory and Nu-merical Analysis, vol. 39, 2005.

Jacques Hurtubise & Eyal Markman, AlgebraicStructures and Moduli Spaces, vol. 38, 2004.

Piergiulio Tempesta, Pavel Winternitz, John Har-nad, Willard Miller Jr., Georgo Pogosyan &Miguel A. Rodriguez, Superintegrability in Clas-sical and Quantum Systems, vol. 37, 2004.

Hershy Kisilevsky & Eyal Z. Goren, Number The-ory, vol. 36, 2004.

H. E. A. Eddy Campbell & David L. Wehlau, In-variant Theory in All Characteristics, vol. 35, 2004.

Pavel Winternitz, John Harnad, C.S. Lam & JiríPatera, Symmetry in Physics, vol. 34, 2004.

Previous Titles

AMSCRM Monograph Series

Andrei Tyurin, Quantization, Classical and Quan-tum Field Theory and Theta Functions, vol. 21,2003.

Joel Feldman, Horst Knörrer & EugeneTrubowitz, Riemann Surfaces of Infinite Genus,vol. 20, 2003.

*Laurent Lafforgue, Chirurgie des grassmanni-ennes, vol. 19, 2003.

*George Lusztig, Hecke Algebras with Unequal Pa-rameters, vol. 18, 2003.

Michael Barr, Acyclic Models, vol. 17, 2002.

*Joel Feldman, Horst Knörrer & EugeneTrubowitz, Fermionic Functional Integrals and theRenormalization Group, vol. 16, 2002.

Jose I. Burgos, The Regulators of Beilinson andBorel, vol. 15, 2002.

Eyal Z. Goren, Lectures on Hilbert Modular Vari-eties and Modular Forms, vol. 14, 2002.

Michael Baake & Robert V. Moody (eds.), Direc-tions in Mathematical Quasicrystals, vol. 13, 2000.

Masayoshi Miyanishi, Open Algebraic Surfaces,vol. 12, 2001.

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PUBLICATIONS

Spencer J. Bloch, Higher Regulators, AlgebraicK-Theory, and Zeta Functions of Elliptic Curves,vol. 11, 2000.

James D. Lewis, A Survey of the Hodge Conjecture,2e édition, vol. 10, 1999 (with an appendix byB. Brent Gordon).

*Yves Meyer, Wavelets, Vibrations and Scaling,vol. 9, 1997.

*Ioannis Karatzas, Lectures on Mathematics of Fi-nance, vol. 8, 1996.

John Milton, Dynamics of Small Neural Popula-tions, vol. 7, 1996.

*Eugene B. Dynkin, An Introduction to BranchingMeasure-Valued Processes, vol. 6, 1994.

Andrew M. Bruckner, Differentiation of Real Func-tions, vol. 5, 1994.

*David Ruelle, Dynamical Zeta Functions for Piece-wise Monotone Maps of the Interval, vol. 4, 1994.

V. Kumar Murty, Introduction to Abelian Varieties,vol. 3, 1993.

Maximilian Ya. Antimirov, Andrei A. Kolyshkin& Rémi Vaillancourt, Applied Integral Transforms,vol. 2, 1993.

*Dan V. Voiculescu, Kenneth J. Dykema &Alexandru Nica, Free Random Variables, vol. 1,1992.

AMSCRM Proceedings & Lecture Notes

André D. Bandrauk, Michel C. Delfour & ClaudeLe Bris (eds.), Quantum Control: Mathematical andNumerical Challenges, vol. 33, 2003.

Vadim B. Kuznetsov (ed.), The Kowalevski Prop-erty, vol. 32, 2002.

John Harnad & Alexander R. Its (eds.), Isomon-odromic Deformations and Applications in Physics,vol. 31, 2002

John McKay & Abdellah Sebbar (eds.), Proceed-ings on Moonshine and Related Topics, vol. 30, 2001.

Alan Coley, Decio Levi, Robert Milson, ColinRogers & Pavel Winternitz (eds.), Bäcklund andDarboux Transformations, vol. 29, 2001.

John C. Taylor (ed.), Topics in Probability and LieGroups: Boundary Theory, vol. 28, 2001.

Israel M. Sigal & Catherine Sulem (eds.), Nonlin-ear Dynamics and Renormalization Group, vol. 27,2001.

John Harnad, Gert Sabidussi & Pavel Winternitz(eds.), Integrable Systems: From Classical to Quan-tum, vol. 26, 2000.

Decio Levi & Orlando Ragnisco (eds.), SIDEIII — Symmetry and Integrability of DifferenceEquations, vol. 25, 2000.

B. Brent Gordon, James D. Lewis, Stefan Müller-Stach, Shuji Saito & Noriko Yui (eds.), The Arith-metic and Geometry of Algebraic Cycles, vol. 24,2000.

Pierre Hansen & Odile Marcotte (eds.), GraphColouring and Applications, vol. 23, 1999.

Jan Felipe van Diejen & Luc Vinet (eds.), Al-gebraic Methods and q-Special Functions, vol. 22,1999.

Michel Fortin (ed.), Plates and Shells, vol. 21, 1999.

Katie Coughlin (ed.), Semi-Analytic Methods forthe Navier – Stokes Equations, vol. 20, 1999.

Rajiv Gupta & Kenneth S. Williams (eds.), Num-ber Theory, vol. 19, 1999.

Serge Dubuc & Gilles Deslauriers (eds.), SplineFunctions and the Theory of Wavelets, vol. 18, 1999

Olga Karlampovich (ed.), Summer School inGroup Theory in Banff, 1996, vol. 17, 1998.

Alain Vincent (ed.), Numerical Methods in FluidMechanics, vol.16, 1998.

François Lalonde (ed.), Geometry, Topology andDynamics, vol. 15, 1998.

John Harnad & Alex Kasman (eds.), The Bispec-tral Problem, vol. 14, 1998.

Michel Delfour (ed.), Boundaries, Interfaces andTransitions, vol. 13, 1998.

Peter G. Greiner, Victor Ivrii, Luis A. Seco &Catherine Sulem (eds.), Partial Differential Equa-tions and their Applications, vol. 12, 1997.

Luc Vinet (ed.), Advances in Mathematical Sci-ences: CRM’s 25 Years, vol. 11, 1997.

Donald E. Knuth, Stable Marriage and Its Relationto Other Combinatorial Problems, vol. 10, 1996.

Decio Levi, Luc Vinet, & Pavel Winternitz (eds.),Symmetries and Integrability of Difference Equa-tions, vol. 9, 1995.

Joel S. Feldman, Richard Froese & Lon M.Rosen (eds.), Mathematical Quantum Theory II:Schrödinger Operator, vol. 8, 1995.

Joel S. Feldman, Richard Froese, & Lon M. Rosen(eds.), Mathematical Quantum Theory I: Field The-ory and Many-Body Theory, vol. 7, 1994.

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CENTRE DE RECHERCHES MATHÉMATIQUES

Guido Mislin (ed.), The Hilton Symposium 1993,vol. 6, 1994.

Donald A. Dawson (ed.), Measure-Valued Pro-cesses, Stochastic Partial Differential Equations andInteracting Systems, vol. 5, 1994.

Hershy Kisilevsky & M. Ram Murty (eds.), Ellip-tic Curves and Related Topics, vol. 4, 1994.

Andrei L. Smirnov & Rémi Vaillancourt (eds.),Asymptotic Methods in Mechanics, vol. 3, 1993.

Philip D. Loewen, Optimal Control via NonsmoothAnalysis, vol. 2, 1993.

M. Ram Murty (ed.), Theta Functions, vol. 1, 1993.

SpringerCRM Series in Mathematical Physics

David Sénéchal, André-Marie Tremblay &Claude Bourbonnais, Theoretical Methods forStrongly Correlated Electrons, 2003.

*Roman Jackiw, Lectures on Fluid Dynamics, 2002.

Yvan Saint-Aubin & Luc Vinet (eds.), TheoreticalPhysics at the End of the Twentieth Century, 2001.

Yvan Saint-Aubin & Luc Vinet (eds.), AlgebraicMethods in Physics, 2000.

Jan Felipe van Diejen & Luc Vinet (eds.),Calogero – Moser – Sutherland Models, 1999.

Robert Conte (ed.), The Painlevé Property, 1999.

Richard MacKenzie, Manu B. Paranjape & Woj-ciech J. M. Zakrzewski (eds.), Solitons, 1999.

Luc Vinet & Gordon Semenoff (eds.), Particlesand Fields (Banff, 1994), 1998.

SpringerCRM Subseries of the Lecture Notes inStatistics

Marc Moore (ed.), Spatial Statistics: Methodologi-cal Aspects and Applications, 2001.

S. Ejaz Ahmed & Nancy Reid (eds.), EmpiricalBayes and Likelihood Inference, 2001.

CRM Publications

Luc Lapointe, Ge Mo-Lin, Yvan Saint-Aubin &Luc Vinet, Proceedings of the Canada-China Meet-ing on Theoretical Physics, 2003.

Armel Mercier, Fonctions de plusieurs variables :Différentiation, 2002.

Nadia El-Mabrouk, Thomas Lengauer & DavidSankoff (eds.), Currents in Computational Molecu-lar Biology, 2001.

James G. Huard & Kenneth S. Williams (eds.),The Collected Papers of Sarvadaman Chowla Vol-ume I 1925-1935; Volume II 1936-1961; Vol-ume III 1962-1986, 2000.

Michael Barr & Charles Wells, Category Theory forComputing Science, 1999.

Maximilian Ya. Antimirov, Andrei A. Kolyshkin& Rémi Vaillancourt, Mathematical Models forEddy Current Testing, 1998.

Xavier Fernique, Fonctions aléatoires gaussiennes,vecteurs aléatoires gaussiens, Montréal, 1997.

Faqir Khanna & Luc Vinet (eds.), Field Theory, In-tegrable Systems and Symmetries, Montréal, 1997.

Paul Koosis, Leçons sur le théorème de Beurling atMalliavin, 1996.

David W. Rand, Concorder Version Three, 1996(software and user guide).

Jacques Gauvin, Theory of Nonconvex Program-ming, 1994.

Decio Levi, Curtis R. Menyuk & Pavel Win-ternitz (eds.), Self-Similarity in Stimulated RamanScattering, 1994.

Rémi Vaillancourt, Compléments de mathématiquespour ingénieurs Montréal, 1993.

Robert P. Langlands & Dinakar Ramakrishnan(eds.), The Zeta Functions of Picard Modular Sur-faces, 1992.

Florin N. Diacu, Singularities of the N-Body Prob-lem, 1992.

Jacques Gauvin, Théorie de la programmationmathématique non convexe, 1992.

Pierre Ferland, Claude Tricot, & Axel van deWalle, Analyse fractale, 1992 (software and userguide).

Stéphane Baldo, Introduction à la topologie des en-sembles fractals, 1991.

Robert Bédard, Groupes linéaires algébriques, 1991.

Rudolf Beran & Gilles R. Ducharme, AsymptoticTheory for Bootstrap Methods in Statistics, 1991.

James D. Lewis, A Survey of the Hodge Conjecture,1991.

David W. Rand & Tatiana Patera, Concorder, 1991(software and user guide).

David W. Rand & Tatiana Patera, Le Concordeur,1991 (software and user guide).

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PUBLICATIONS

Véronique Hussin (ed.), Lie Theory, DifferentialEquations and Representation Theory, 1990.

John Harnad & Jerrold E. Marsden (eds.), Hamil-tonian Systems, Transformation Groups and SpectralTransform Methods, 1990.

M. Ram Murty (ed.), Automorphic Forms and An-alytic Number Theory, 1990.

Wendy G. McKay, Jirí Patera & David W. Rand,Tables of Representations of Simple Lie Algebras.Volume I. Exceptional Simple Lie Algebras, 1990.

Anthony W. Knapp, Representations of Real Re-ductive Groups, 1990.

Wendy G. McKay, Jirí Patera & David W. Rand,SimpLie, 1990 (software and user guide).

Francis H. Clarke, Optimization and NonsmoothAnalysis, Montréal, 1989.

Samuel Zaidman. Une introduction à la théorie deséquations aux dérivées partielles, 1989.

*Yuri I. Manin, Quantum Groups and Noncommu-tative Geometry, Les Publications CRM, 1988.

Lucien Le Cam, Notes on Asymptotic Methods inStatistical Decision Theory, 1974.

Les Presses de l’Universite de MontrealAisenstadt Chair Collection

Laurent Schwartz, Semimartingales and TheirStochastic Calculus on Manifolds, 1984.

*Yuval Ne′eman, Symétries, jauges et variétés degroupe, 1979.

*R. Tyrrell Rockafellar, La théorie des sous-gradients et ses applications à l’optimisation, fonc-tions convexes et non convexes, 1979.

*Jacques-Louis Lions, Sur quelques questionsd’analyse, de mécanique et de contrôle optimal, 1976.

*Donald E. Knuth, Mariage stables et leurs relationsavec d’autres problèmes combinatoires, 1976.

*Robert Hermann, Physical Aspects of Lie GroupTheory, 1974.

*Mark Kac, Quelques problèmes mathématiques enphysique statistique, 1974.

*Sybreen de Groot, La transformation de Weyl et lafonction de Wigner: une forme alternative de la mé-canique quantique, 1974.

Other Collaborations with Publishers

Marc Moore, Sorana Froda & Christian Léger(eds.), Mathematical Statistics and Applications:Festschrift for Constance van Eeden, LectureNotes – Monograph Series, vol. 42, 2003 (a col-laboration with the Institute of MathematicalStatistics).

Duong H. Phong, Luc Vinet & Shing-Tung Yau(eds.), Mirror Manifolds and Geometry, AMS/IPStudies in Advanced Mathematics, vol. 10, 1998(a collaboration with the AMS and the Interna-tional Press).

Pierre Ferland, Claude Tricot & Axel van deWalle, Fractal Analysis User’s Guide, 1994 (a col-laboration with the AMS).

Hedy Attouch, Jean-Pierre Aubin, FrancisClarke & Ivar Ekeland (eds.), Analyse non linéaire,1989 (a collaboration with Gauthiers-Villars).

Videos

Efim Zelmanov, Abstract Algebra in the 20th Cen-tury, 1997.

Serge Lang, Les grands courants, 1991

Robert Bédard, Brouiller les cartes, 1991.

Serge Lang, Les équations diophantiennes, 1991.

Laurent Schwartz, Le mouvement brownien,1990.

Laurent Schwartz, Une vie de mathématicien, 1989.

CRM Preprints

Bertola, M., Eynard, B., Harnad, J., Semiclas-sical orthogonal polynomials, matrix models andisomonodromic tau functions, Centre de recher-ches mathématiques, CRM-3169, October 2004;arXiv:nlin.SI/0410043.

Bertola, M., Gekhtman, M., Biorthogonal Laurentpolynomials, Töplitz determinants, minimal Toda or-bits and isomonodromic tau functions, Centre derecherches mathématiques, CRM-3182, March2005.

Cornea, O., Lalonde, F., A universal Floer theory,localization and applications, Centre de recherchesmathématiques, CRM-3172, 2004.

Dryanov, D., Fournier, R., On a discrete vari-ant of Bernstein’s polynomial inequality, Centre derecherches mathématiques, CRM-3178, January2005.

El Boukili, A., Madrane, A., Vaillancourt, R.,Multifrontal solution of sparse unsymmetric matri-ces arising from semiconductor equations, Centre

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CENTRE DE RECHERCHES MATHÉMATIQUES

de recherches mathématiques, CRM-3125, June2004.

Ghidaoui, M. S., Kolyshkin, A. A., Vaillancourt,R., Transient turbulent flow in a pipe, Centre derecherches mathématiques, CRM-3176, January2005.

Grundland, A. M., Strasburger, A., Zakrzewski,W. J. M., Surfaces immersed in su(N + 1) Lie alge-bras obtained from the CPN sigma models, Centre derecherches mathématiques, CRM-3180, February2005.

Mélard, G., Roy, R., Saidi, A., Exact maximumlikelihood estimation of structured or unit root mul-tivariate time series models, Centre de recherchesmathématiques, CRM-3129, June 2004.

Nguyen-Ba, T., Kolyshkin, A. A., Vaillancourt,R., Hermite – Birkhoff differential equation solvers,Centre de recherches mathématiques, CRM-3175, December 2004.

Ratnarajah, T., Vaillancourt, R., Quadratic formson complex random matrices and channel capac-ity, Centre de recherches mathématiques, CRM-3126, June 2004.

Ratnarajah, T., Vaillancourt, R., Alvo, M., Com-plex random matrices and Rician channel capac-ity, Centre de recherches mathématiques, CRM-3174, October 2004.

Rousseau, C., Christopher, C., Modulus of analyticclassification for the generic unfolding of a codimen-sion one resonant diffeomorphism or resonant sad-dle, Centre de recherches mathématiques, CRM-3167, September 2004.

Saidi, A., Consistent testing for independence oftwo partially nonstationary vector ARMA time se-ries, Centre de recherches mathématiques, CRM-3173, November 2004.

Schlomiuk, D., Vulpe, N., Integrals and phase por-traits of planar quadratic differential systems of in-variant lines of at least five total multiplicity, Cen-tre de recherches mathématiques, CRM-3181,March 2005.

Schlomiuk, D., Vulpe, N., The full study of pla-nar quadratic differential systems possessing exactlyone line of singularities, finite or infinite, Centrede recherches mathématiques, CRM-3183, April2005.

Yoshikawa, M., Gong, Y., Ashino, R., Vaillan-court, R., Case study on SVD multiresolution analy-sis, Centre de recherches mathématiques, CRM-3179, January 2005.

Zhao, M., Ghidaoui, M. S., Kolyshkin, A. A.,Vaillancourt, R., On the stability of oscillatorypipe flows, Centre de recherches mathématiques,CRM-3168, October 2004.

For other preprints by CRM members see page 90.

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Scientific Personnel

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CENTRE DE RECHERCHES MATHÉMATIQUES

CRM Members in 2004-2005

IN contrast with most other mathematics institutes around the world, the CRM can count on thesolid foundation of regular, associate and invited members. Regular members are all professors at

partner institutions: Université de Montréal, Concordia University, McGill University, UQÀM, Uni-versité Laval, Université de Sherbrooke and the University of Ottawa. Other members are researchersattached to the CRM in 2004–2005 as part of exchange agreements with neighbouring universities andindustry or are long-term visitors from Canadian and foreign institutions. The presence at the CRMof such an active group of researchers has brought many benefits to the Centre. In particular, theCRM’s national program is greatly facilitated by having on hand a large reserve of willing organiz-ers, who have even contributed financially to the organization of activities. The largest partnershipis with the Université de Montréal, which gives the equivalent of five fulltime teaching positions inrelease time to the CRM. Release agreements with the other Montréal area universities provide forthe equivalent of two more full-time positions. Facilities are also provided to researchers attached tojunior colleges. Several members are attached to the CRM through industrial agreements.

Regular Members

Syed Twareque Ali, Concordia

Vestislav Apostolov, UQÀM

Paul Arminjon, Montréal

André D. Bandrauk, Sherbrooke

Line Baribeau, Laval

Peter Bartello, McGill

Robert Bédard, UQÀM

Jacques Bélair, Montréal

Habib Benali, INSERM

Yoshua Bengio, Montréal

Anne Bergeron, UQÀM

François Bergeron, UQÀM

Marco Bertola, Concordia

Yves Bourgault, Ottawa

Anne Bourlioux, Montréal

Steven Boyer, UQÀM

Gilles Brassard, Montréal

Abraham Broer, Montréal

Robert C. Brunet, Montréal

David Bryant, McGill

Vašek Chvátal, Concordia

Francis H. Clarke, Lyon I

Olivier Collin, UQÀM

Claude Crépeau, McGill

Miklós Csurös, Montréal

Chris Cummins, Concordia

Galia Dafni, Concordia

Henri Darmon, McGill

Chantal David, ConcordiaMichel C. Delfour, MontréalEusebius J. Doedel, ConcordiaRachida Dssouli, ConcordiaNadia El-Mabrouk, MontréalMarlène Frigon, MontréalMartin J. Gander, Gèneve and McGillPaul M. Gauthier, MontréalEyal Z. Goren, McGillBernard Goulard, MontréalAndrew Granville, MontréalAlfred Michel Grundland, UQTRGena Hahn, MontréalRichard L. Hall, ConcordiaMichael Hallett, McGillJohn Harnad, MontréalAntony R. Humphries, McGillJacques Hurtubise, McGillVéronique Hussin, MontréalAdrian Iovita, ConcordiaDmitry Jakobson, McGillVojkan Jaksic, McGillNiky Kamran, McGillOlga Kharlampovich, McGillHershy Kisilevsky, ConcordiaPaul Koosis, McGillDmitry Korotkin, Concordia

Gilbert Labelle, UQÀMJacques Labelle, UQÀMFrançois Lalonde, Montréal

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SCIENTIFIC PERSONNEL

Robert P. Langlands, Institute for AdvancedStudy

Christian Léger, Montréal

Pierre Leroux, UQÀM

Frédéric Lesage, Polytechnique Montréal

Sabin Lessard, Montréal

Jean LeTourneux, Montréal

Claude Levesque, Laval

Jean-Marc Lina, ETS

Brenda MacGibbon, UQÀM

François Major, Montréal

Vladimir Makarenkov, UQÀM

Michael Makkai, McGill

Patrice Marcotte, Montréal

Javad Mashreghi, Laval

Sherwin A. Maslowe, McGill

Pierre Mathieu, Laval

John McKay, Concordia

Alexei G. Miasnikov, McGill

Nilima Nigam, McGill

Jirí Patera, Montréal

Iosif Polterovich, Montréal

Thomas J. Ransford, Laval

Christophe Reutenauer, UQÀM

Ivo G. Rosenberg, Montréal

Christiane Rousseau, Montréal

Roch Roy, Montréal

Peter Russell, McGill

Gert Sabidussi, Montréal

Yvan Saint-Aubin, Montréal

David Sankoff, Ottawa

Dana Schlomiuk, Montréal

E.J.P. Georg Schmidt, McGill

Alexander Shnirelman, Concordia

Ron J. Stern, Concordia

John A. Toth, McGill

Luc Vinet, McGill

Pavel Winternitz, Montréal

Daniel T. Wise, McGill

Keith J. Worsley, McGill

Associate Members

Liliane Beaulieu, Vieux-Montréal

Nantel Bergeron, York

Robert Conte, CEA Saclay

Stéphane Durand, Édouard-Montpetit

Richard Fournier, Dawson and Montréal

Decio Levi, Roma Tre

Fahima Nekka, Montréal

Yannis N. Petridis, CUNY-Lehman College

Elisa Shahbazian, Lockheed Martin

Francisco Thaine, Concordia

Pierre Valin, Défense Canada-Valcartier

Carolyne M. Van Vliet, Miami

Jean-Paul Zolésio, INRIA Sophia-Antipolis

Invited Members

Jean-François Angers, Montréal

Octav Cornea, Montréal

Louis G. Doray, Montréal

Pierre Duchesne, Montréal

Charles Dugas, Montréal

Jun Li, Montréal

François Perron, Montréal

Damien Roy, Ottawa

Abdellah Sebbar, Ottawa

Postdoctoral Fellows

Each year the CRM plays host to a great number of postdoctoral fellows. The sources for their fundinginclude the NSERC and FQRNT postdoctoral programs, the NATO international program adminis-tered by NSERC, the CRM (usually with the ISM), the CRM’s research laboratories, and individualresearch grants from CRM members. The list below includes postdoctoral fellows in residence at the

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CENTRE DE RECHERCHES MATHÉMATIQUES

CRM and those co-funded by the CRM. Some of the fellows were in residence at the CRM for onlypart of the year. The affiliation is that where their doctoral degree was obtained.

Alain Bourget, McMaster University

Abdellatif Bourhim, Université Mohammed V

Guillaume Bourque, University of SouthernCalifornia

Peter S. Campbell, University of Alberta

Raquel Casesnoves, Université de Montréal

Stéphane Dellacherie, Université de Paris VII

Mostafa Gabbouhy, Université Ibn Tofaïl

David T. Gay, University of California atBerkeley

Yoshitaka Hachimori, University of Tokyo

Harald Andres Helfgott, Princeton University

Alexander Ivrii, Stanford University

Sergei Krutelevich, Yale University

Marcelo Lanzilotta Mernies, StanfordUniversity

Tony Lelièvre, École nationale des ponts etchaussées

Jun Li, Université de Montréal

Peter McNamara, Massachusetts Institute ofTechnology

Marco Merkli, University of Toronto

Man Yue Mo, Oxford University

Ramin Mohammadalikhani, University ofToronto

Chadi Nour, Université de Lyon I

Ambrus Pal, Columbia University

Yan Pautrat, Université de Grenoble I

Bélà Gabor Pusztai, University of Szeged

Mario Roy, Universität Göttingen

Anupam Saikia, University of Cambridge

Mohamed Noureddine Senhadji, Universitéd’Oran

Libor Snobl, Czech Technical Institute

Shannon Lee Starr, University of California atDavis

Phi Long Thanh (Nguyen), ColumbiaUniversity

Ye Tian, Columbia University

Stephan Tillmann, University of Melbourne

Michèle Suzanne Titcombe, University ofBritish Columbia

José Manuel Urquiza, Université de Paris VI

Dimiter Vassilev, Purdue University

Ismet Yurdusen, Middle East TechnicalUniversity

Alexander Zhalij, Institute of Mathematics, Kiev

Long-term Visitors

Each year the CRM hosts a large number of visitors. The majority come to the Centre to participatein scientific activities organized or co-organized by the CRM. In the year 2004-2005, 348 such partici-pants registered for workshops of the thematic program, 728 in activities of the general program and324 in those of the industrial and multidisciplinary program. The following list includes only visitorswho were in residence for at least four weeks:

Huzihiro Araki, Kyoto

Harry W. Braden, Edinburgh

Laurent Bruneau, Warsaw

Pierre Charollois, Bordeaux I

Monica-Gabriela Cojocaru, Queen’s

Robert Conte, CEA Saclay

Stephan De Bièvre, Lille I

Jan Derezinski, Warsaw

Alain Desgagné, Drake

Amine El Gradechi, Artois

Ibrahim Fatkullin, Caltech

Alexander Fedotov, ITEP Moscou

Mark Fels, Utah State

André Garon, Polytechnique Montréal

Michael Gekhtman, Notre Dame

Rajendra Gurjar, Tata Institute

Bernard Helffer, Paris Sud

Thomas Yizhao Hou, Caltech

Alexander Its, IUPU Indianapolis

Yael Karshon, Toronto

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SCIENTIFIC PERSONNEL

Ely Kerman, Illinois at Urbana-Champaign

Boualem Khouider, Victoria

Frédéric Klopp, Paris XIII

Alexey Kokotov, Concordia (LTA)

Pierre Lafaye de Micheaux, Grenoble II

Yoram Last, Hebrew

Claude Le Bris, ENPC

Claude LeBrun, SUNY Stony Brook

Decio Levi, Roma Tre

Michael Levitin, Heriot-Watt

Andrew J. Majda, Courant Inst.

Kayo Masuda, Himeji Institute of Technology

Masayoshi Miyanishi, Kwansei Gakuin

Nikolai Nadirashvili, Chicago

Soghra Nobakhtian, Isfahan

Renata Otahalova, Silesia

Lubomir Pekar, Faculty Hospital Motol

Claude-Alain Pillet, Toulon

Mohamad Reza Pouryayevali, Isfahan

Igor Rivin, Temple

Stephan Ruscheweyh, Würzburg

Pavle Saksida, Ljubljana

Gerald Schmieder, Oldenburg

Artur Sergyeyev, Silesia

Jean-Claude Sikorav, ENS Lyon

Panagiotis Souganidis, Texas A&M

Piergiulio Tempesta, SISSA Trieste

Loïc Teyssier, Strasbourg

Marc Thiriet, INRIA Rocquencourt

Zora Thomova, SUNY Syracuse

Jiri Tolar, Czech Technical Institute

Eric Vanden-Eijnden, Courant Inst.

Nicolae Vulpe, Academy of Sciences, Moldova

Eduardo Santillan Zeron, Cinvestav-IPN

Jean-Paul Zolésio, INRIA Sophia-Antipolis

Short-term Visitors

Visitors who were in residence for less than four weeks:

Casim Abbas, Michigan State

Michael T. Anderson, SUNY Stony Brook

Silvia Anjos, Instituto Superior Technico

Meenaxi Bhattacharjee, Würzburg

Michel Bernadou, Pôle universitaire Léonard deVinci

Anne-Laure Biolley, Toronto

Olivier Biquard, Strasbourg

Frédéric Bourgeois, UL Bruxelles

Charles P. Boyer, New Mexico

Robert Bryant, Duke

Leonid Chekhov, Steklov Mathematical Institute

Andrew Dancer, Oxford

Hassan Doosti, Mashhad

C. Eilbeck, Celera Genomics

Yakov Eliashberg, Stanford

Misha Entov, Institut Weizmann

Alexandre Ern, ENPC

Catalin Fetita, Institut National desTélécommunications

Felix Finster, Regensburg

Eric Friedlander, NorthwersternLine Garnero, Hôpital de la Salpêtrière

Paul Gauduchon, École PolytechniquePalaiseau

Jean-Pierre Gazeau, Paris VIIPeter Gibson, TorontoVictor Ginzburg, UC Santa CruzPeter Glynn, StanfordDaniel R. Grayson, Illinois at

Urbana-ChampaignKarsten Grove, MarylandAlexander Gutfraind, WaterlooGergely Harcos, UT AustinKevin Hare, WaterlooSamvel Haroutiunian, Yerevan State UniversityRichard Hind, Notre DameNigel J. Hitchin, OxfordRick Jardine, Western OntarioGeorge Kesidis, Penn StateManfred Kolster, McMasterVladimir E. Korepin, SUNY Stony BrookOlivier Lafitte, Paris XIII

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CENTRE DE RECHERCHES MATHÉMATIQUES

Michael Lamoureux, Calgary

Jibin Li, Kunning University of Science andTechnology

Chiu-Chu Liu, Harvard

Joachim Lohkamp, Augsburg

Grégoire Malandain, INRIA

Gary Margrave, Calgary

Dusa McDuff, SUNY Stony Brook

Arian Novruzi, Ottawa

Tom Osborn, Manitoba

Charles Peskin, Courant Inst.

Martin Pinsonnault, Fields Inst.

Alexandru-Anton Popa, Princeton

Emma Previato, Boston

Sophia Rabe-Hesketh, UC Berkeley

Yongbin Ruan, UW Madison

Simon Salamon, Imperial College London

Paul Seidel, Chicago

Anders Skrondal, London School of Economics

Raj Srinivasan, Saskatchewan

Andrei Teleman, Aix-Marseille I

Mary E. Thompson, Waterloo

Alexander Turbiner, UNAM

Ravi Vakil, Stanford

Stephanos Venakides, Duke

McKenzie Y. Wang, McMaster

Katrin Wehrheim, ETH Zürich

Jean-Yves Welschinger, ENS Lyon

Hongmei Zhu, York

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Preprints and Research Reports

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CENTRE DE RECHERCHES MATHÉMATIQUES

THE quality of the CRM members’ research can be measured by the abundance of their scientificpublications. Here follows a list of research reports, preprints and articles submitted during 2004–

2005.

Aberkane, A., Brlek, S., Sequences with com-plexity given by that of Thue-Morse, DiscreteMathematics, submitted.

Ali, S. T., Bagarello, F., Some physical appear-ances of vector coherent states and CS relatedto degenerate Hamiltonians, Journal of Math-ematical Physics, 46 (May 2005), 053518.

Anjos, S., Lalonde, F., The homotopy type of thespace of symplectic balls in S2XS2 above thecritical value, arXiv:math.SG/0406129, July2004.

Apostolov, V., Calderbank, M. J., Gauduchon,P.,Tonnesen-Friedman, C. W., Hamiltonian2-forms in Kaehler geometry III: Compact ex-amples, math.DG/0501516, January 2005.

Apostolov, V., Tonnesen-Friedman, C. W., Aremark on Kähler metrics of constant scalarcurvature on ruled complex surfaces, The Bul-letin of the London Mathematical Society,to appear.

Arminjon, P., Touma, R., Central finite volumemethods with constrained transport divergencefor ideal MHD, Journal of ComputationalPhysics, 204:2 (May 2005), 737–759.

Arminjon, P., Touma, R., Central schemes withconstrained transport divergence treatment fortwo-dimensional ideal MHD, SIAM Journalon Scientific Computing, submitted.

Asgharian, M., Wolfson, D. B., Zhang, X.,Checking stationarity of incidence rate usingprevalent cohort survival data, Statistics inMedicine, submitted.

Asgharian, M., Wolfson, D. B., Zhang, X.,A simple criterion for the stationarity of theincidence rate from prevalent cohort studies,Statistics in Medicine, submitted.

Aval, J., Bergeron, F., Bergeron, N., Diago-nal Temperley-Lieb invariants and harmonics,arXiv:math.CO/0411568, November 2004.

Azambre, D., Bergeron, M., Mullins, J., SOCLEproject : UML to UCFG compilation : Compos-ability and source code generation, NationalDefense of Canada, 2004.

Bandrauk, A., Chelkowski, S., Nguyen, H. S.,Attosecond control of electrons in molecules,

International Journal of Quantum Chem-istry, submitted.

Bandrauk, A., Nguyen, H. S., Attosecondmolecular spectroscopy, Canadian Journal ofChemistry, submitted.

Baron, M., Bell, M. G., Bookman, A., Jerome,D., Kamiska, E., Lupton, T., Pope, J., Steele,R., Reliability and validity of ophthalmoscopiccapillaroscopy in systemic sclerosis, Journal ofExperimental Rheumatology (2005), sub-mitted.

Bengio, Y., Delalleau, O., Le Roux, N.,The curse of dimensionality for local kernelmachines, Département d’informatique etrecherche opérationnelle, Technical Reportno. 1258, March 2005.

Bengio, Y., Larochelle, H., Implantation etanalyse d’un modèle graphique à entraîne-ment supervisé, semi-supervisé et non su-pervisé pour la désambiguïsation sémantique,Département d’informatique et rechercheopérationnelle, Technical Report no. 1252,2004.

Bengio, Y., Monperrus, M., Discovering sharedstructure in manifold learning, Départe-ment d’informatique et recherche opéra-tionnelle, Technical Report no. 1250, July2004.

Bergeron, A., Stoye, J., On the similarity of setsof permutations and its applications to genomecomparison, Journal of Computational Biol-ogy, submitted.

Bergeron, F., Biagioli, R., Tensorial square of thehyperoctahedral group coinvariant space, sub-mitted.

Bergeron, F., McNamara, P., Some positivedifferences of products of Schur functions,arXiv:math.CO/0412289, December 2004.

Bergeron, M., Mullins, J., SOCLE project : UMLand OCL Semantics in ASM, National De-fense of Canada, 2004.

Bergeron, N., Gao, Y., Hu, N., Drinfel’d doublesand Lusztig’s symmetries of two-parameterquantum groups, arXiv:math.RT/0505614,May 2005.

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SCIENTIFIC PERSONNEL

Bergeron, N., Hohlweg, C., Colouredpeak algebras and Hopf algebras,arXiv:math.AC/0505612, May 2005.

Bergeron, N., Reutenauer, C., Rosas, M. H.,Zabrocki, M., Invariants and coinvariantsof the symmetric group in noncommutingvariables, arXiv:math.CO/0502082, Febru-ary 2005.

Bergeron-Brlek, A., Brlek, S., Labelle, J., Irra-tionality of

√3 — A geometric proof, Mathe-

matics Magazine, submitted.

Bertola, M., Eynard, B., Harnad, J., Semi-classical orthogonal polynomials, matrix mod-els and isomonodromic tau functions, Centrede recherches mathématiques, CRM-3169,October 2004,; arXiv:nlin.SI/0410043.

Bertola, M., Gekhtman, M., Biorthogonal Lau-rent polynomials, Töplitz determinants, mini-mal Toda orbits and isomonodromic tau func-tions, Centre de recherches mathémati-ques, CRM-3182, March 2005.

Bertolini, M., Darmon, H., The rationality ofStark-Heegner points over genus fields of realquadratic fields, submitted.

Beuter, A., Lambert, B., MacGibbon, B., Quan-tifying postural tremor changes in workers ex-posed to low levels of manganese, Journal ofNeuroscience Methods, submitted.

Blomer, V., Granville, A., Estimates for the rep-resentation numbers of binary quadratic forms,Duke Mathematical Journal, submitted.

Bouchard, M., Carrier, G., Brunet, R. C.,Noisel, N., Labarre, G., Dumas, P., We-ber, J. P., Biological monitoring of exposure toorganophosphorus insecticides in horticulturalgreenhouse workers, Science of Total Envi-ronment, submitted.

Bourlioux, A., Khouider, B., A rigorous asymp-totic perspective on the large scale simulationsof turbulent premixed flame fronts, MultiscaleModelling and Simulations, submitted.

Brassard, G., Broadbent, A., Tapp, A., Quan-tum pseudo-telepathy, Foundations ofPhysics, to appear.

Brassard, G., Broadbent, A., Tapp, A., Re-casting Mermin’s multi-player game into theframework of pseudo-telepathy, Quantum In-formation and Computation, to appear.

Brassard, G., Méthot, A. A., Tapp, A., Min-imum entangled state dimension required

for pseudo-telepathy, Quantum Informationand Computation, to appear.

Brlek, S., Melançon, G., Paquin, G., Propertiesof the extremal intinite smooth words, Jour-nal of Automata, Languages and Combi-natorics, submitted.

Brlek, S., Pergola, E., Roques, O., Non UniformRandom Generation of Generalized MotzkinPaths, Acta Informatica, submitted.

Bumagin, I., Kharlampovich, O., Mias-nikov, A. G., Isomorphism problem forfinitely generated fully residually free groups,arXiv:math.GR/0502496, February 2005.

Caffarelli, L. A., Guan, P., Ma, X.-N., A generalconvexity principle for fully nonlinear ellipticequations .

Chelkowski, S., Bandrauk, A., Apolonski, A.,Phase-dependent asymmetries in strong-fieldionization, Physical Reviews A, submitted.

Chelkowski, S., Bandrauk, A., Corkum, P.,Control of nuclear processes with super intenselaser fields, Physics Reviews Letters, sub-mitted.

Chen, Y., Dinwoodie, I. H., MacGibbon,B., Sampling for conditional inference oncase/control data, Journal of the Royal Sta-tistical Society B, submitted.

Clarke, F. H., Continuity of solutions to a basicproblem in the calculus of variations, Annalidella Scuola Normale Superiore de Pisa,submitted.

Coleman, R., Iovita, A., Hidden structures oncurves, submitted.

Colin, F., Frigon, M., Systems of singular Pois-son equations in unbounded domains, Ad-vances in Differential Equations, 2005:9(September 2005), 1035–1052.

Cornea, O., Lalonde, F., A universal Floertheory, localization and applications, Centrede recherches mathématiques, CRM-3172,2004.

David, C., Fearnley, J., Kisilevsky, H., Vanish-ing of L-functions of elliptic curves over num-ber fields, arXiv:math.NT/0406012, June2004.

De Koninck, J.-M., Doyon, N., Esthetic numbersand game theory, submitted.

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CENTRE DE RECHERCHES MATHÉMATIQUES

De Koninck, J.-M., Doyon, N., Kátai, I., Count-ing the number of twin Niven numbers, sub-mitted.

De Koninck, J.-M., Kátai, I., Subbarao, M. V.,A consequence of a theorem of Filaseta, sub-mitted.

Desrosiers, P., Lapointe, L., Mathieu, P., Sym-metric functions in superspace, Advances inMathematics, to appear.

Doray, L. G., Luong, A., Najem, E. H., Ef-ficiency of some estimators for a generalizedPoisson autoregressive process of order 1, Jour-nal of Statistical Computation and Simula-tion, submitted.

Dryanov, D., Fournier, R., On a discrete variantof Bernstein’s polynomial inequality, Centrede recherches mathématiques, CRM-3178,January 2005.

Duchesne, P., Testing for serial correlation for un-known form in cointegrated time series models,GERAD, G-2004-76, October 2004.

El Boukili, A., Madrane, A., Vaillancourt,R., Multifrontal solution of sparse unsym-metric matrices arising from semiconductorequations, Centre de recherches mathéma-tiques, CRM-3125, June 2004.

Fortin, J.-F., Jacob, P., Mathieu, P., SM(2,4κ;)fermionic characters and restricted jagged par-titions, Journal of Physics A, 38 (February2005), 1699–1709.

Fortin, M., Reutenauer, C., A note on compres-sion spaces, submitted.

Frenette-Charron, J.-B., Pelletier, M., Danyluk,J., Chauve, C., Sarhan, F., The plant Lipocalingene family, submitted.

Frigon, M., Montoki, E., Multiplicity results forsystems of second order differential equations,Nonlinear Studies, submitted.

Gagarin, A., Labelle, G., Leroux, P.,Charactererization and enumeration oftoroidal K3,3-subdivision-free graphs,arXiv:math.CO/0411356, November 2004.

Gauthier, G., Rémillard, B., Turcotte, D., Pric-ing variance options in a GARCH setting,GERAD, G-2004-57, July 2004.

Ghidaoui, M. S., Kolyshkin, A. A., Vail-lancourt, R., Transient turbulent flow in apipe, Centre de recherches mathématiques,CRM-3176, January 2005.

Goulard, B., Lina, J.-M., St-Jean, P., Stationarymultiscale graphical models, Applied Proba-bility, to appear.

Goupil, A., Chauve, C., Combinatorial operatorsfor Kronecker powers of representations of Sn,arXiv:math.RT/0503307, March 2005.

Gouyou-Beauchamp, D., Leroux, P., Enumera-tion of symmetry classes of convex polyominoeson the honeycomb lattice, Theoretical Com-puter Science, to appear.

Granville, A., Cycle lengths in a permutation aretypically Poisson distributed, submitted.

Granville, A., Prime divisors are Poisson dis-tributed, submitted.

Granville, A., Kurlberg, P., Poisson statistics viathe Chinese remainder theorem, Journal fürdie Reine und Angewandte Mathematik,submitted.

Granville, A., Martin, G., Prime numberraces, American Mathematical Monthly, ac-cepted.

Granville, A., Soundararajan, K., Large char-acter sums: Pretentious characters and thePolya–Vinogradov theorem, Journal of theAmerican Mathematical Society, submit-ted.

Granville, A., Soundararajan, K., Extreme val-ues of |ζ(1 + it)|, Journal of the RamanujanMathematical Society, submitted.

Granville, A., Soundararajan, K., An uncer-tainty principle for arithmetic sequences, An-nals of Mathematics, submitted.

Grundland, A. M., Snobl, L., Description ofsurfaces associated with Grassmannian sigmamodels on Minkowski space, Journal of Math-ematical Physics, 46:8 (2005), 3508–3520.

Grundland, A. M., Snobl, L., Description of sur-faces associated with CPN−1 sigma models onMinkowski space, arXiv:math.DG/0405513.

Grundland, A. M., Snobl, L., Description ofsurfaces associated with Grassmannian sigmamodels on Minkowski space, Journal of Math-ematical Physics, 46:8 (2005), 3508–3520.

Grundland, A. M., Strasburger, A., Za-krzewski, W. J. M., Surfaces immersed insu(N+1) Lie algebras obtained from the CPNsigma models, Centre de recherches mathé-matiques, CRM-3180, February 2005.

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SCIENTIFIC PERSONNEL

Guan, P., Lin, C.-S., Ma, X.-N., The Christoffel–Minkowski problem. II. Weingarten curvatureequations, submitted.

Guan, P., Lin, C.-S., Ma, X.-N., The existenceproblem for curvature measures .

Guan, P., Lin, C.-S., Wang, G., On quotientequations in conformal geometry, submitted.

Guan, P., Ma, X.-N., Zhou, F., The Christoffel–Minkowski problem. III. Existence and convex-ity of admissible solutions, submitted.

Guan, P., Wang, G., Conformal deformations ofthe smallest eigenvalue of the Ricci tensor,Max Planck Institute for Mathematics inthe Sciences, 43/2005, May 2005.

Guignon, V., Chauve, C., Hamel, S., Distanced’édition entre “tige-boucles”, submitted.

Gurjar, R., Masuda, K., Miyanishi, M., Rus-sell, P., Affine lines on affine surfaces and theMakar–Limanov Invariant, submitted.

Hahn, G., Composing directed hypergraphs, Jour-nal of Combinatorial Theory. Series B, sub-mitted.

Hanley, J. A., MacGibbon, B., Creating non-parametric bootstrap samples using Poissonfrequencies, Computer Methods and Pro-grams in Biomedicine, submitted.

Iovita, A., Pollack, R., On Iwasawa theory ofelliptic curves over Q at primes of supersin-gular reduction over Zp-extensions of num-ber fields, Journal für die Reine und Ange-wandte Mathematik accepted.

Iovita, A., Stevens, G., On p-adic families ofmodular forms, submitted.

Jakobson, D., Levitin, M., Nadirashvili, N.,Polterovich, I., Spectral problems with mixedDirichlet–Neumann boundary conditions:Isospectrality and beyond, Journal of Com-putational and Applied Mathematics, toappear.

Jakobson, D., Polterovich, I., Estimates from be-low for the spectral function and for the re-mainder in local Weyl’s law, submitted.

Jaksic, V., Last, Y., Simplicity of singular spec-trum in Anderson type Hamiltonians, submit-ted.

Kokotov, A., Korotkin, D., Tau-functions onspaces of Abelian and quadratic differentialsand determinants of Laplacians in Strebel met-

rics of finite volume, Journal of DifferentialGeometry, submitted.

Kokotov, A., Korotkin, D., Isomonodromic tau-function of Hurwitz Frobenius manifolds andits applications, International MathematicsResearch Notices, submitted.

Korotkin, D., On some integrable system arisingin differential geometry and general relativity,Annales des sciences mathématiques duQuébec, submitted.

Labelle, G., Leroux, P., Gagarin, A., Struc-ture and labelled enumeration of K3,3-subdivision-free projective-planar graphs,arXiv:math.CO/0406140, June 2004.

Labute, J., Lemire, N., Minac, J., Swallow, J.,Cohomological Dimension and Schreier’s for-mula in Galois cohomology, Bulletin of theLondon Mathematical Society, submitted.

Labute, J., Lemire, N., Minac, J., Swallow, J.,Demuskin groups, Galois Modules, and the el-ementary type conjecture, to appear.

Lapalme, E., Lina, J.-M., Mattout, J., Sourcesclustering and entropic inference in MEG,IEEE Transactions on Biomedical Engi-neering, submitted.

Léger, C., MacGibbon, B., On the bootstrap incube root asymptotics, Canadian Journal ofStatistics, accepted.

Lepage, T., Lawi, S., Tupper, P., Bryant, D.,Continuous and tractable models for the varia-tion of evolutionary rates, Mathematical Bio-sciences, 199:2 (February 2006), 216–233.

Lu, S., Dethloff, G., Logarithmic surfaces an hy-perbolicity, arXiv:math.AG/0406287, June2004.

Mélard, G., Roy, R., Saidi, A., Exact maxi-mum likelihood estimation of structured orunit root multivariate time series models, Cen-tre de recherches mathématiques, CRM-3129, June 2004.

M’Lan, C.-E., Joseph, L., Wolfson, D. B.,Bayesian sample size determination for casecontrol studies, Journal of American Statis-tical Association, submitted.

Ngan, K., Straub, D. N., Bartello, P., Aspect ra-tio effects in quasi-2D turbulence, Physics ofFluids, submitted.

Nguyen-Ba, T., Kolyshkin, A. A., Vaillan-court, R., Hermite-Birkhoff differential equa-

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CENTRE DE RECHERCHES MATHÉMATIQUES

tion solvers, Centre de recherches mathé-matiques, CRM-3175, Décember 2004.

Ollivier, Y., Wise, D. T., Kazhdan groupswith infinite outer automorphism group,arXiv:math.GR/0409203, September 2004.

Ratnarajah, T., Vaillancourt, R., Quadraticforms on complex random matrices and chan-nel capacity, Centre de recherches mathé-matiques, CRM-3126, June 2004.

Ratnarajah, T., Vaillancourt, R., Alvo, M., Com-plex random matrices and Rician channel ca-pacity, Centre de recherches mathémati-ques, CRM-3174, October 2004.

Rochon, D., A bicomplex Riemann zeta function,Tokyo Jounal of Mathematics, submitted.

Rousseau, C., Divergent series: past, present, fu-ture. . . , American Mathematical Monthly,submitted.

Rousseau, C., Christopher, C., Modulus of an-alytic classification for the generic unfold-ing of a codimension one resonant diffeomor-phism or resonant saddle, Centre de recher-ches mathématiques, CRM-3167, Septem-ber 2004.

Russell, P., Koras, M., Contractible surfaces witha quotient singularity, submitted.

Saidi, A., Consistent testing for independenceof two partially nonstationary vector ARMAtime series, Centre de recherches mathéma-tiques, CRM-3173, November 2004.

Sauer, N. W., Rosenberg, I. G., Interval cardi-nality in the lattice of clones, submitted.

Schlomiuk, D., Vulpe, N., Planar quadratic vec-tor fields with invariant lines of total multiplic-ity at least five, submitted.

Schlomiuk, D., Vulpe, N., Integrals and phaseportraits of planar quadratic differential sys-tems of invariant lines of at least five total mul-tiplicity, Centre de recherches mathémati-ques, CRM-3181, March 2005.

Schlomiuk, D., Vulpe, N., The full study of pla-nar quadratic differential systems possessingexactly one line of singularities, finite or infi-nite, Centre de recherches mathématiques,CRM-3183, April 2005.

Waite, M. L., Bartello, P., Stratified turbulencegenerated by internal gravity waves, Journalof Fluid Mechanics, submitted.

Waite, M. L., Bartello, P., The transition fromgeostrophic to stratified turbulence, Journal ofFluid Mechanics, submitted.

Walsh, T. R. S., Enumeration of unrooted maps inthe plane, Technical report, UQÀM, TechnicalReport no. 2005-01, February 2005.

Winternitz, P., Levi, D., Continuoussymmetries of difference equations,arXiv:nlinSI/0502004, to appear.

Yoshikawa, M., Gong, Y., Ashino, R., Vaillan-court, R., Case study on SVD multiresolutionanalysis, Centre de recherches mathémati-ques, CRM-3179, January 2005.

Zhao, M., Ghidaoui, M. S., Kolyshkin, A. A.,Vaillancourt, R., On the stability of oscillatorypipe flows, Centre de recherches mathéma-tiques, CRM-3168, October 2004.

Zlobec, I., Steele, R., Nigam, N., Compton, C.,A predictive model of rectal tumor response topre-operative radiotherapy using classificationand regression tree (CART) methods, ClinicalCancer Research (2005), submitted.

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Committees Heading the CRM

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CENTRE DE RECHERCHES MATHÉMATIQUES

Bureau de direction

THE Bureau consists of members from the Université de Montréal (eight to eleven members) andfrom the outside (two to five members). The rector of the Université de Montréal and the Dean

of its Arts and Sciences faculty are represented on the Bureau. The Bureau adopts the policies of theCentre, recommends the nomination and the promotion of researchers and the appointment of regu-lar and associate members, advises the Director on the preparation of the budget and the Universitéde Montréal on the choice of the Director.

Yoshua BengioUniversité de Montréal

François BergeronUniversité du Québec à Montréal

Alain Caillé, Vice-Rector, ResearchUniversité de Montréal

Joseph Hubert, DeanArts and Sciences FacultyUniversité de Montréal

Hershy KisilevskyConcordia University

François LalondeUniversité de Montréal

Christian LégerUniversité de Montréal

Christiane RousseauUniversité de Montréal

Peter RussellMcGill University

Yvan Saint-AubinUniversité de Montréal

Chantal David (Concordia University) and Jean LeTourneux (Université de Montréal), both DeputyDirectors of the CRM, were invited members.

Scientific Advisory Committee

THE Scientific Advisory Committee is constituted of distinguished researchers from Canada andabroad. Its members are either mathematicians or scientists with close ties to the mathematical

sciences. The Advisory Committee is informed periodically of the activities of the Centre through theDirector. The Committee transmits recommendations about the general scientific orientation of theCRM and gives advice about proposeded scientific activities.

Jerry Bona is a Pro-fessor at the Depart-ment of Mathemat-ics, Statistics andComputer Scienceat The University ofIllinois at Chicago.He received a B.Sc.degree from Wash-ington University inSaint Louis (1966)and a Ph.D. fromHarvard University

(1971). His research experience is vast. His re-search interests include fluid mechanics, par-tial differential equations, computational math-ematics and the associated numerical analysis,oceanography, coastal engineering and mathe-matical economics. He is an Elected Fellow ofthe American Association for the Advancementof Science and a member of the editorial board

of twenty-five scientific journals and of severalacademic committees and panels. Jerry Bona is aco-organizer of the Mathematicians and Educa-tional Reform Network.

Jean-Pierre Bour-guignon receivedan engineering de-gree from ÉcolePolytechnique and aPh.D. in mathemat-ics. A differentialgeometer by train-ing, he has beeninterested by themathematical as-pects of physical theories: Dirac operators andspins, and general relativity. His areas of spe-cialty are the geometrical estimation of eigen-values of Laplace-Beltrami operators, Kähleriangeometry and, more recently, Finslerian geom-etry. Jean-Pierre Bourguignon directs advanced

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SCIENTIFIC PERSONNEL

research classes at CNRS. He is the Director ofInstitut des hautes études scientifiques (IHES) atBures-sur-Yvette and Professor of Mathematicsat École Polytechnique. From 1990 to 1992, heserved as President of the Société mathématiquede France and from 1995 to 1998 of the EuropeanMathematical Society. He is a member of severalscientific advisory committees in Europe. Since1996, he is a member of Academia Europaeaand since 2002 a foreign associate of the SpanishRoyal Academy.

Jean-Louis Colliot-Thélène is directeurde recherche at theCentre national dela recherche scien-tifique (CNRS) atUMR 8628 (Univer-sité de Paris-Sud,Orsay). He special-izes in algebraic ge-ometry and its links

to arithmetic. He obtained a Doctorat d’État(1978) from Paris-Orsay. He is a member of theeditorial boards of Annales scientifiques de l’ÉcoleNormale Supérieure (of which he was editor-in-chief until recently), the Journal of Number Theoryand the Journal of K-Theory. Jean-Louis Colliot-Thélène is one of the main organizers of the2005-2006 Thematic Program at MSRI (Berke-ley).

Walter Craig isCanada ResearchChair of Mathemat-ical Analysis andits Applications atthe Department ofMathematics andStatistics of McMas-ter University. Hereceived degreesfrom the Universityof California, Berke-ley (B.A., 1977) and

from the Courant Institute of Mathematical Sci-ences, New York University (M.Sc., 1979, andPh.D., 1981) and has held positions at BrownUniversity and Stanford University before join-ing McMaster. He is principally interested in lin-ear and nonlinear partial differential equations,Hamiltonian dynamical systems, fluid dynam-ics, quantum mechanics, and nonlinear func-tional analysis. He is a member of the editorialboards of SIAM: Mathematical Analysis and the

Fields Institute and a Council member of theAmerican Mathematical Society.

Peter Glynn is ThomasW. Ford Professor in theSchool of Engineering atStanford University. Hereceived his Ph.D in Op-erations Research fromStanford University in1982. He is a Fellow ofthe Institute of Mathe-matical Statistics and hisresearch interests focuson computational proba-bility, queueing theory, statistical inference forstochastic processes, and stochastic modeling.

Mark Haiman is aProfessor at the De-partment of Math-ematics of the Uni-versity of Califor-nia, Berkeley. Hereceived his de-grees from the Mas-sachusetts Instituteof Technology inComputer Scienceand Electrical Engi-neering (B.Sc., 1979) and in Mathematics (Ph.D.,1984). His research interests are in algebraiccombinatorics, algebraic geometry, representa-tion theory, and lattice theory. He is a member ofthe editorial board of Algebra universalis.

Nigel Hitchin isSavilian Professor ofGeometry at NewCollege, OxfordUniversity. He holdsa Ph.D. degree inMathematics (1972)from Wolfson Col-lege of Oxford Uni-versity. He is prin-cipally interested indifferential and algebraic geometry and its re-lationship with the equations of mathematicalphysics. Current projects include the areas of hy-perkähler geometry, special Lagrangian geome-try and mirror symmetry, geometric solutions ofPainlevé equations, magnetic monopoles, vectorbundles on algebraic curves, and the theory ofgerbes.

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CENTRE DE RECHERCHES MATHÉMATIQUES

Richard Lockhart is a Pro-fessor at the Department ofStatistics and Actuarial Sci-ence Simon Fraser Univer-sity. He received a B.Sc. inMathematics from the Univer-sity of British Columbia (1975)and degrees in Statistics fromthe University of California,Berkeley (M.A., 1976, Ph.D.,1979). A former Editor of the

Canadian Journal of Statistics , he has also servedon the Advisory Committee on Statistical Meth-ods of Statistics Canada. He was President of theStatistical Society of Canada in 1996-1997. Muchof his work is in the area of model assessment,generally in the form of goodness-of-fit.

Mitchell Luskinis a Professor ofMathematics at theUniversity of Min-nesota, a Fellow ofthe Minnesota Su-percomputing Insti-tute and a memberof the graduate fac-ulty of the Depart-

ment of Aerospace Engineering and Mechanicsof the University of Minnesota. He holds degreesin Mathematics from Yale University (B.Sc.,1973) and the University of Chicago (M.Sc., 1976,Ph.D., 1977). His research interests include nu-merical analysis, scientific computing, appliedmathematics, partial differential equations, com-putational materials science, and computationalphysics. He delivered an invited lecture at theInternational Congress of Mathematicians heldin Beijing in 2002. He is a member of the editorialboards of Dynamics and Differential Equations, theInternational Journal of Computational and Numer-ical Analysis and Applications, Communications inApplied Analysis, the International Journal of Dif-ferential Equations and Applications, and the Inter-national Journal of Pure and Applied Mathematics.

M. Ram Murty is aProfessor of Mathe-matics and Queen’sResearch Chair atQueen’s University.He holds a Ph.D. de-gree in Mathemat-ics (1980) from MIT.A specialist in alge-braic and analyticnumber theory, hisresearches focus onArtin’s conjecture,elliptic curves, modular forms, automorphicforms, Langland’s program, Selberg’s conjec-tures, and cryptography.

Carl Pomeranceis a Professor atthe Departmentof Mathematics ofDartmouth College.From 1999 to 2003,he was a memberof the technical staffof Bell Labs-LucentTechnologies. Heholds degrees fromBrown University(B.A., 1966) andfrom Harvard University (M.A., 1970, Ph.D.,1972). A number theory specialist, he has re-ceived numerous prizes and awards includingthe Levi L. Conant Prize of the American Math-ematical Society. He is one of the editors-in-chiefof Integers : The Electronic Journal of Combinato-rial Number Theory and a member of the editorialboard of the Journal of Supercomputing and theAMS Undergraduate Book Series.

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SCIENTIFIC PERSONNEL

Peter Shalen is aProfessor at the De-partment Mathe-matics, Statisticsand Computer Sci-ence at The Uni-versity of Illinoisat Chicago. He re-ceived his B.A. fromHarvard College(1966) and his Ph.D.from Harvard Uni-

versity (1972). He also spent a year as an under-graduate at École Normale Supérieure in Paris.His main research interests are 3-dimensionaltopology, hyperbolic geometry, and geometricand combinatorial group theory. He is associateeditor of the Journal of Knot Theory and its Rami-fications and was the geometric topology editorof the Transactions of the American MathematicalSociety from 1992 to 2000.

Steven Zelditch is aProfessor of Math-ematics at JohnsHopkins Univer-sity. He received hisPh.D. from the Uni-versity of California,Berkeley, in 1981. Apast member of theeditorial board ofAnnales Scientifiquesde l’École NormaleSupérieure, he is presently on the editorial boardof the American Journal of Mathematics. His re-search centers around applications of microlo-cal analysis to problems concerning: asymp-totics of eigenfunctions/eigenvalues on Rieman-nian manifolds, statistical algebraic geometry,problems of mathematical physics ranging fromquantum chaos to 2D Yang – Mills to string/Mtheory.

Alain Caillé, Vice-Principal (Research), Université de Montréal, François Lalonde, CRM Director andEddy Campbell, President of the Canadian Mathematical Society were ex-officio members of the Ad-visory Committee. François Bergeron (Université du Québec à Montréa), Chantal David (ConcordiaUniversity) and Jean LeTourneux (Université de Montréal), all Deputy Directors of the CRM, wereinvited members of the Committee.

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CRM Administrative and Support Staff

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CRM ADMINISTRATIVE AND SUPPORT STAFF

The Director’s Office

François LalondeDirector

François BergeronActing Director (Summer 2004), DeputyDirector

Chantal DavidDeputy Director, Theme Years

Jean LeTourneuxDeputy Director, Publications

Administration

Vincent MasciotraHead of Administration

Michèle GilbertAdministrative Assistant

Muriel PasqualettiAdministrative Assistant

Guillermo Martinez-ZalceResearch Laboratories AdministrativeCoordinator

Diane Brulé-De-FilippisSecretary

Josée SimardSecretary

Scientific Activities

Louis PelletierCoordinator

Josée LaferrièreAssistant

Sakina BenhimaProject Manager

Computer Services

Daniel OuimetSystems Administrator

André MontpetitOffice Systems Manager (half time)

François CassistatTechnical Assistant

Frédéric LoisierTechnical Assistant

Publications

André MontpetitTeX Expert (half time)

Louise LetendreTechnician

Communications

Suzette ParadisCommunications Officer and Webmaster

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Statement of Revenue and Expendituresfor the Fiscal Year Ending on

May 31, 2005

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STATEMENT OF REVENUE AND EXPENDITURES

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103

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CENTRE DE RECHERCHES MATHÉMATIQUES

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104

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Mission of the CRM

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CENTRE DE RECHERCHES MATHÉMATIQUES

THE Centre de recherches mathématiques(CRM) was created in 1969 by the Univer-

sité de Montréal through a special grant from theNational Research Council of Canada. It becamean NSERC national research centre in 1984. It iscurrently funded by NSERC (Natural Sciencesand Engineering Research Council), by the Gov-ernment of Québec through the FQRNT (Fondsquébécois de la recherche sur la nature et lestechnologies), by the Université de Montréal, aswell as McGill University, Université du Québecà Montréal, Concordia University, University ofOttawa, Université Laval and by private dona-tions. The mission of the CRM is to do researchin mathematics and closely related disciplinesand to provide leadership in the development ofthe mathematical sciences in Canada.

The CRM carries on its mission and nationalmandate in several ways:• its general program and its multidisciplinary

and industrial program provide funding forconferences and special events at the CRMand across the country,

• each year it invites, through the AisenstadtChair, one or more distinguished mathemati-cians, to give advanced courses as part of itsthematic program,

• it awards four prizes yearly: the CRM-Fields Prize recognizing major contributionsto mathematics, the Aisenstadt Prize givenfor outstanding work done by a young Cana-dian mathematician, the CAP-CRM Prizefor exceptional achievement in theoreticaland mathematical physics, and the CRM-SSCPrize for exceptional contributions to statisticsin early career,

• it publishes technical reports and about tenbooks per year. Some of its collections are pub-lished jointly with the AMS and with Springer,

• it has an extensive postdoctoral fellowshipprogram, with more than thirty postdoctoralfellows in place last year, funded in partner-ship with other organizations and researchers,

• it informs the community of its activitiesthrough its newsletter, Bulletin du CRM, andits web site at www.CRM.UMontreal.CA,

• it participates, with the other two Canadianinstitutes, in groundbreaking national initia-tives. One example is the MITACS project(Mathematics of Information Technology andComplex Systems). They sponsor the AnnualMeetings of the Mathematical Sciences Soci-eties (SMC, SSC, SCMAI), the developmentof the mathematical sciences in the Atlantic

provinces through AARMS, and other ac-tivities organized outside the three institute.They also participate in the National Programon Complex Data Structures jointly with theCanadian statistical community.

This national mandate is complemented by, andindeed supported by, a long-standing vocationof promoting research in the mathematical sci-ences in Québec. For instance:

• the CRM supports research through its eightresearch laboratories spanning most of the im-portant areas of the mathematical sciences,

• it supports, through partnership agreements,a group of local researchers chosen mainlyfrom departments of mathematics and statis-tics, but also computer science, physics, eco-nomics, engineering, etc.,

• it organizes series of regular seminars and lec-ture courses on different areas of the mathe-matical sciences,

• it sponsors joint activities with the ISM (In-stitut des sciences mathématiques) includingthe weekly CRM/ISM colloquium, graduatecourses offered by distinguished visitors anda program of postdoctoral fellowships,

• it works actively at developing contacts withindustry. Its joint activities with liaison and re-search centres (CIRANO, CRIM and MITACS)and research centres doing applied research(CRT, GERAD, INRS-EMT, and INSERM) ledto the creation of industrial networks. Theprevious involved, in 2004-2005, BombardierAerospace and the Brain Imaging Unit CRM-IUGM-INSERM

The CRM fulfils its national mission by involv-ing the largest possible number of Canadianmathematicians in its scientific programs, bothas participants and as organizers. It also sup-ports many events taking place outside Mont-réal and the Province of Québec. It is recognizedworldwide as one of the major institutes in themathematical sciences.

The director of the CRM is assisted by two man-agerial structures: the Bureau de direction andthe Scientific Advisory Committee. The Advi-sory Committee is a group of internationallyrenowned mathematicians from Canada andabroad, who approve scientific programs andthematic years, choose recipients of the Aisen-stadt Prize and suggest new scientific venturesto explore.

106