AnnualReport 2004 2005

AnnualReport 2004 2005 Also available on the CRM’s website www.crm.umontreal.ca

c Centre de recherches mathématiques Université de Montréal, 2006 ISBN 2-921120-42-9

Centre de recherches mathématiques Université de Montréal C.P. 6128, succ. Centre-ville Montréal, QC H3C 3J7 Canada CENTRE DE RECHERCHES MATHÉMATIQUES

Presenting the Annual Report 2004 – 2005 5

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

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

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

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

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

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

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

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

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

Preprints and Research Reports 89

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

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

3 CENTRE DE RECHERCHES MATHÉMATIQUES

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

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

Mission of the CRM 105

4 Presenting the Annual Report 2004 – 2005 CENTRE DE RECHERCHES MATHÉMATIQUES

HIS year the quan- our activities in addition to the 1,459 registered Ttity and impact participants in our international workshops and of the CRM’s diverse conferences. activities are more The Centre’s scientific programming is struc- impressive than ever. tured into a thematic program, a general pro- In the year covered by gram, a multidisciplinary/industrial program this report, the CRM and an educational program. In addition there organized a most pro- are the eight research laboratories in which most ductive thematic year of the research work takes place. Our publication on the “Mathematics and postdoctoral fellowship programs complete of Stochastic and Mul- the outline of our activities. Here is a brief de- tiscale Modeling” put scription of each: together by Anne Bourlioux and Paul Tupper assisted by a high-level international team. The Thematic program The thematic program is CRM also organized numerous international the principal activity organized by the Centre in conferences and workshops, including the ma- the accomplishment of its national mandate sup- jor “Workshop on Computational Biology in the ported by NSERC. In general, themes alternate Post Genomics Era,” held at CRM and initiated between subjects in pure mathematics and in by the three Canadian mathematics institutes in applied mathematics, usually where mathemat- collaboration with NRC. This workshop brought ics borders with other sciences where they have together, for the first time in Canada, univer- considerable impact. In 2004-2005, the theme sity researchers with NRC scientists. Thanks chosen was in the applications of mathematics in to the prestigious NSERC Leadership Support “Stochastic and Multiscale Modeling.” It was a Initiatives program CRM hosted an “Informal splendid program lead masterfully by Bourlioux Semester in Symplectic Topology.” Another no- and Tupper. Let the numbers speak for them- table event was the three-week “Short Pro- selves: the program drew over 400 participants gram on Riemannian Geometry” organized by from around the world, several longterm vis- Vestislav Apostolov. The CRM also assisted with itors and postdoctoral researchers. It included the registrations logistics of the “Quatrième col- several workshops, mini courses and two Aisen- loque francophone sur les sondages,” a major stadt Chair lecture series given by Andrew J. international colloquium. In fact, in the single Majda (Courant Inst.) and Thomas Y. Hou (Cal- 2004 – 2005 year, CRM organized 29 events of tech). which 25 were held on its premises! This consists General program This program is comprised of four more activities than were offered the pre- of the non-thematic events organized by CRM. vious year, which was already extremely busy. The Séminaire de Mathématiques Supérieures In 2004 – 2005, CRM organized a record number (a NATO ASI) dealt with “Morse Theoretic advanced training schools, including the SMS Methods in Non-linear Analysis and Symplectic (a NATO ASI), the Spring School on “Mini- Topology” and drew 80 participants from about invasive Procedures in Medicine and Surgery: twenty countries and some 40 local participants. Mathematical and Numerical Challenges,” a We have already mentioned the Fall 2004 “In- “Summer School on Riemannian Geometry,” the formal Semester in Symplectic Topology” that “Summer School on Stochastic Calculus for Ap- had about 40 foreign participants, which greatly plications: Theory and Numerics,” and cred- benefited local students and postdoctoral fel- ited advanced courses such as the one given by lows. Following this semester, the Institute for Claude LeBris on “Multiscale Systems.” In all, Advanced Study in Princeton held a special 1,459 participants from the four corners of the workshop that largely echoed the semester. The world were officially registered in these events. general program included the Summer 2004 To all this, we must also add the seminar se- short program on Riemannian geometry and the ries organized by the centre’s eight research lab- workshop on K-Theory that inspired the Fields oratories (five of which were held in the CRM’s Institute’s forthcoming thematic semester of Fall seminar rooms), the special lectures given by the 2006; as well as the financing (in collaboration Aisenstadt Chair holders, by CRM prize win- with the two other Canadian institutes) of ac- ners (CRM – Fields, Aisenstadt, and CRM – SSC tivities organized by AARMS in the Atlantic prizes) and those in our two weekly Colloquium provinces. In addition, it includes the four an- series (one each in mathematics and statistics). nual prizes awarded by CRM and the two col- This represents a few thousand participants in loquium series in mathematics and statistics or-

6 PRESENTINGTHEANNUALREPORT 2004 – 2005 ganized jointly with ISM. These Colloquiums in and several workshops, in addition to those or- which a world-renowned researcher addresses a ganized by CRM, including for instance, the large audience are particularly important for the “Workshop on Spectral Theory of Schrödinger training of graduate students. These activities Operators,” the “Workshop on Dynamics in are mainly supported by NSERC and FQRNT Statistical Mechanics,” the “Analysis Day,” the grants. “Workshop on Low-dimensional Topology,” the Multidisciplinary and Industrial Program Even “Workshop on Bayesian Inference and Func- though the development of mathematics is at the tional Brain Mapping,” the “Montreal Scientific heart of the Centre’s preoccupations, we have Computing Days,” and several others. Thanks to a very wide definition of these and an open- the laboratories and the devoted members of the ness to its applications in other scientific fields. Centre’s Scientific Advisory Committee, more CRM is the host institution of the Québec net- than ever the CRM’s programs achieve world- work in computation and mathematical mod- class standing. eling (ncm2). While NSERC financing of the Publications The CRM has a vigorous publish- network ended recently, ncm2 still incorporates ing program with some fifteen new and forth- the Bell University Laboratories and serves to coming titles. Both the American Mathematical launch collaborative efforts. CRM is also a main Society and Springer have a CRM series. Among partner of the Mathematics of Information Tech- the new titles of the year, of note are a mono- nology and Complex Systems (MITACS), a fed- graph by V. Guillemin (MIT) and R. Sjamaar erally funded Network of Centres of Excellence. (Cornell) and another by A.J. Majda (Courant The industrial program organized by CRM in Institute), as well as proceedings edited by 2004 – 2005 was quite full with nine workshops, J. Hurtubise (McGill) and E. Markman (Mas- summer schools and special advanced courses. sachusetts) on “Algebraic Structures and Mod- These activities included the launch of a CRM – uli Spaces,” by V. Apostolov (UQÀM), A. Dancer CRIAQ – MITACS collaboration in January 2005 (Oxford), N. Hitchin (Oxford) and M. Wang (Mc- put together by CRM and held at the Office for Master) on “Perspectives on Riemannian Geom- Advanced Research of Bombardier Aerospace; etry.” See the complete list in this annual re- as well as the first major workshop bringing to- port. To which we should add the nice collection gether university and NRC researchers involved from the NATO ASI/Séminaire de Mathémati- in computational biology, and the “Workshop ques Supérieures published by Springer but en- on Latent Variable Models and Survey Data for tirely edited by CRM. Social and Health Sciences Research” funded Postdoctoral program Jointly with ISM, the jointly with the American institute, SAMSI (Sta- CRM manages a world-renowned postdoctoral tistical and Mathematical Sciences Institute), and fellowship program. In addition, postdoctoral the NSERC-funded National Program on Com- fellowships are offered in our thematic program plex Data Structures. CRM also continued its ini- as well as by the Centre’s research laboratories. tiatives in brain imaging with INSERM and the In all, 92 postdoctoral fellows were supervised Institut universitaire de gériatrie de Montréal. by CRM members during at least part of the Research Laboratories In its transformation 2004 – 2005 year. Of these, 30 fellows were partly from a FCAR-funded research centre to a funded by the CRM and at least 6 came with FQRNT-funded regroupement stratégique, CRM their own fellowship funding; many of these considerably expanded its membership base and were associated with the thematic year. To this created eight research laboratories to bring these number, we could add a dozen postdoctoral fel- members together, thus increasing substantially lows funded in part by MITACS research teams. its funding base at FQRNT and partner univer- sities. The laboratories, which only completed their second year of existence in 2004 – 2005, or- François Lalonde ganized no less than a dozen weekly seminars Director

7 Thematic Program THEMATIC PROGRAM

HE core of each year’s scientific program at the CRM is its thematic program. The Scientific Ad- Tvisory 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 are presented in the language in which they were submitted.

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

Organizers: Anne Bourlioux (Montréal), Weinan The fields of application where these issues E (Princeton), Jean-Pierre Fouque (NC State), arise, and which were discussed during the Thomas Y. Hou (Caltech), Claude Le Bris theme year, include climate modeling, front (ENPC), Andrew J. Majda (Courant Inst.), Ron- propagation, molecular dynamics, materials sci- nie Sircar (Princeton), Panagiotis T. Souganidis ence, financial engineering, and rheological flu- (UT Austin), Andrew Stuart (Warwick), Paul F. ids. Tupper (McGill), Eric Vanden-Eijnden (Courant Despite the diversity of applications, the chal- Inst.) lenges in these areas have much in common. The 2004 – 2005 thematic year was dedicated to A fundamental question is: How can one utilize the applied mathematical tools (modeling, anal- knowledge about the dynamics of a system so as ysis, computation) needed to study multiscale to design a useful mathematical model that accu- systems which arise in a variety of areas in sci- rately captures its global behaviour? One particu- ence and engineering. These systems present larly promising approach is based on stochastic many novel challenges for applied mathemati- models: this was the topic of the Summer School cians. The central difficulty is how to account for and was also a recurring theme throughout the the wide range of scales and the large number various workshops. These offered opportunities of degrees of freedom in such systems. In partic- for interaction between applied mathematicians ular, it is necessary to find an appropriate cou- specializing in modeling and numerical simula- pling between the mathematically distinct mod- tion and scientists and engineers in the various els used for the different scales in such a system. fields of applications.

9 CENTRE DE RECHERCHES MATHÉMATIQUES

Retrospective of the Thematic Year zons. Le travail du mathématicien appliqué, à l’in- terface de plusieurs communautés, prend toute son « L’année thématique 2004-2005 sur la modélisation importance dans ces nouveaux types de modélisation mathématique multiéchelle et stochastique est main- où des connaissances pluri-disciplinaires sont néces- tenant derrière nous, et c’est l’heure des bilans et re- saires pour progresser. merciements. Une des missions essentielles du CRM La variété des techniques mathématiques nécessaires est la formation à la recherche des étudiants et sta- à l’étude de ces modèles (théorie de l’homogénéisa- giaires postdoctoraux, et l’année thématique a foi- tion, théorie des larges déviations, théorie ergodique, sonné d’occasions en ce sens, en particulier l’École schémas symplectiques,. . .) ainsi que des domaines de d’été, pilotée par Eric Vanden-Eijnden, et le cours la physique concernés (mécanique statistique, modé- ISM avancé sous la houlette de Claude Le Bris – deux lisation de la turbulence, dynamique moléculaire, cli- activités à but pédagogique, certes, mais sans compro- matologie,. . .) constituait en soi un attrait majeur de mis sur la qualité. Avec un contenu à un niveau d’ex- cette année thématique pour un postdoctorant cher- cellence ils ont réussi à secouer et enthousiasmer les chant à ouvrir ses horizons. La conférence organisée participants, novices ou non. par T.Y. Hou donnait un bon exemple de la variété Ce bilan est donc une occasion très appropriée de des domaines où la modélisation multiéchelle est uti- donner la parole à l’un des participants juniors : ci- lisée, et de la diversité des techniques mathématiques dessous, le compte-rendu scientifique des activités de et numériques nécessaires à l’analyse de ces modèles. l’année du point de vue très personnel de Tony Le- Les modèles aléatoires jouent un rôle particulier dans lièvre, qui vient de réintégrer son laboratoire au CER- ces modèles en plein développement, non pas tant par MICS au terme de son année postdoctorale fort pro- le fait que la meilleure description de la matière à ductive à Montréal. l’échelle la plus microscopique (mécanique quantique) L’heure est aussi aux remerciements : aux organisa- soit intrinsèquement aléatoire, mais plutôt parce que teurs d’ateliers C. Le Bris, P. Tupper, P. Souganidis, le passage d’une échelle microscopique à une échelle R. Sircar et J.-P. Fouque, Weinan E et E. Vanden- macroscopique consiste à éliminer des degrés de li- Eijnden, en particulier aux deux conférenciers Ai- berté ou à considérer des asymptotiques dans les senstadt Andrew Majda et Tom Hou, très généreux échelles en temps ou en espace, d’où naît l’aléatoire. dans leurs interactions avec les chercheurs locaux ; et, L’atelier organisé par A.J. Majda ainsi que ses cours finalement, au personnel du CRM pour l’accueil at- de la Chaire Aisenstadt illustraient particulièrement tentif qu’il a réservé aux nombreux participants. Les ces aspects pour des applications à la modélisation cli- commentaires enthousiastes ont abondé pour souli- matique, où l’on cherche justement à bâtir, à partir de gner à quel point l’organisation locale soignée a fa- modèles précis et très complets mais en très grande vorisé de façon essentielle la qualité des interactions dimension, des modèles approximés plus simples qui scientifiques. » conservent des propriétés statistiques proches du mo- Anne Bourlioux dèle initial, avec pour objectif de comprendre les phé- nomènes déterminants pour le climat. Les étapes es- Retrospective of the Year by Tony Leli`evre sentielles sont alors la détection des degrés de liberté les plus importants, puis la dérivation d’équations « Les modèles multiéchelles s’attachent à décrire la équivalentes sur ces degrés de liberté, en utilisant des réalité, en faisant appel à plusieurs échelles de des- relations de fermeture appropriées. Ceci requiert des criptions : par exemple, dans le domaine de la méca- outils liés à la théorie de l’homogénéisation ou en- nique des solides, on cherche à comprendre les liens core à la mécanique statistique. Les modèles aléatoires entre les phénomènes à l’échelle de l’atome et les com- étaient également au cœur de la conférence consacrée portements de la matière à l’échelle macroscopique. aux mathématiques financières, organisée par R. Sir- Ces techniques d’intégration multiéchelle font appel car et J.-P. Fouque. à des technologies scientifiques récentes, dans des do- L’étude numérique et théorique des couplages de mo- maines très variés. dèles est un autre aspect que ces modélisations mul- Les différents cours et ateliers tout au long de l’année tiéchelles ont en commun. En particulier, le cou- ont mis en lumière un domaine où les mathématiciens plage de modèles aléatoires et déterministes soulève appliqués jouent un rôle primordial entre les physi- des questions numériques intéressantes liées aux rela- ciens créateurs de modèle, les mathématiciens moti- tions entre les différentes erreurs de discrétisation (en vés par des questions plus théoriques et les numéri- temps, en espace, erreur statistique pour les modèles ciens soucieux de construire des algorithmes adap- Monte Carlo). La conférence organisée par A. Bour- tés au modèle. Une des qualités de ces ateliers était lioux et P. Souganidis sur les modèles de combustion d’ailleurs de réunir des chercheurs de tous ces hori- illustrait particulièrement les questions soulevées par

10 THEMATIC PROGRAM les interactions entre modèles stochastiques (décri- riques pertinentes, sur des modèles simplifiés (com- vant l’écoulement advectif aléatoire) et modèles dé- portement d’une chaîne de ressort unidimensionnel terministes (décrivant la chimie de la combustion). par exemple) : Quelle notion de minimum (local Le couplage de modèles peut aussi se faire à des in- ou global) de l’énergie mécanique faut-il consi- terfaces, une zone étant décrite plus finement qu’une dérer ? Quelle est la bonne dynamique ? autre. C’est le problème du passage de l’informa- Je voudrais terminer ce compte-rendu très informel tion aux interfaces qui est alors soulevé. Ce thème et personnel en remerciant Anne Bourlioux pour était notamment au centre de la conférence organi- l’organisation de cette année thématique et nos nom- sée par Weinan E et E. Vanden-Eijnden sur la mo- breuses randonnées, les membres de l’administration délisation multiéchelle dans les solides, où une des du CRM pour leur accueil, Michel Delfour pour questions récurrentes concernait le choix des condi- son support financier, Stéphane Dellacherie pour nos tions aux limites entre les modèles de dynamique mo- longues discussions scientifiques ou autres, et Eric léculaire essentiellement discrets, et les modèles de Vanden-Eijnden avec qui j’ai commencé une collabo- mécanique des milieux continus. Ce domaine est un ration fructueuse au cours de cette année. » exemple où il reste encore beaucoup de questions théo- Tony Lelièvre

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

The CRM was honoured to have as Aisenstadt N. Frenkiel Award from the Division of Fluid chairholders, during the 2004 – 2005 theme year Dynamics, American Physical Society in 1998, Mathematics of Stochastic and Multiscale Mod- the Feng Kang Prize in Scientific Computing in eling, Professors Thomas Yizhao Hou of Califor- 1997, and was a Sloan Foundation Research Fel- nia Institute of Technology et Andrew J. Majda low from 1990 to 1992. He was also an invited of Courant Institute. plenary speaker at the International Congress on Industrial and Applied Mathematics in Sydney Thomas Yizhao Hou in 2003, an invited speaker of the International Congress of Mathematicians in Berlin in 1998, Thomas Yizhao Hou is and founding Editor-in-Chief of a SIAM inter- the Charles Lee Pow- disciplinary journal on Multiscale Modeling and ell Professor of Ap- Simulation. plied and Computa- tional Mathematics at Andrew J. Majda Caltech, and one of the leading experts in ap- Andrew J. Majda is plied and numerical the Morse Professor of analysis for vortex dy- Arts and Sciences at namics and multiscale the Courant Institute problems. In his twenty-year research career his of New York Univer- research interests have been centered around de- sity. He was born in veloping analytical tools and effective numerical East Chicago, Indiana methods for vortex dynamics, interfacial flows, on January 30, 1949. He and multiscale problems. received a B.Sc. degree from Purdue Univer- He was born in Guangzhou, China, and studied sity in 1970 and a Ph.D. degree from Stanford at the South China University of Technology be- University in 1973. fore undertaking his Ph.D. at UCLA. Upon ob- taining it in 1987, he joined the Courant Insti- Majda’s primary research interests are modern tute as a postdoctoral fellow and then became applied mathematics in the broadest possible a faculty member in 1989. He moved to the sense merging asymptotic methods, numerical applied mathematics department at Caltech in methods, physical reasoning and rigorous math- 1993, and is currently the executive officer in ematical analysis. the department of applied and computational He is well known for both his theoretical contri- mathematics. He was awarded the Morningside butions to partial differential equations and his Gold Medal in Applied Mathematics in 2004, the applied contributions to diverse areas such as SIAM Wilkinson Prize in Numerical Analysis scattering theory, shock waves, combustion, in- and Scientificc Computing in 2001, the François

11 CENTRE DE RECHERCHES MATHÉMATIQUES compressible flow, vortex motion, turbulent dif- the Courant Lecture Note Series of the American fusion, and atmosphere ocean science. Mathematical Society. Majda is a member of the National Academy of Sciences and has received numerous honours Aisenstadt Chair and awards including the National Academy of Science Prize in Applied Mathematics, the John The Aisenstadt Chair was endowed by Mont- von Neumann Prize of the Society of Indus- réal philanthropist Dr. André Aisenstadt. Under trial and Applied Mathematics, and the Gibbs its auspices, one or more distinguished mathe- Prize of the American Mathematical Society. He maticians are invited each year for a period of has been awarded the Medal of the Collège de at least one week, ideally one or two months. France and is a Fellow of the Japan Society for During their stay the lecturers present a series the Promotion of Science. He received an hon- of lectures on a specialized subject. They are orary doctorate from his undergraduate alma also invited to prepare a monograph (see the mater, Purdue University in 2000. Publications chapter in this report for a list of these publications). At the request of Dr. Aisen- He began his scientific career as a Courant In- stadt, the first of their lectures should be acces- structor at the Courant Institute from 1973 – sible to a wide audience. Previous holders of the 1975. Prior to returning to the Courant Insti- Aisenstadt Chair are: Marc Kac, Eduardo Zaran- tute in 1994, he held professorships at Princeton tonello, Robert Hermann, Marcos Moshinsky, University (1984-1994), the University of Califor- Sybren de Groot, Donald Knuth, Jacques-Louis nia, Berkeley (1978 – 1984), and the University of Lions, R. Tyrell Rockafellar, Yuval Ne0eman, California, Los Angeles (1976 – 1978). In the past Gian-Carlo Rota, Laurent Schwartz, Gérard De- several years at the Courant Institute, Majda has breu, Philip Holmes, Ronald Graham, Robert created the Center for Atmosphere Ocean Sci- Langlands, Yuri Manin, Jerrold Marsden, Dan ence with a multidisciplinary faculty to promote Voiculescu, James Arthur, Eugene B. Dynkin, cross-disciplinary research with modern applied David P. Ruelle, Robert Bryant, Blaine Law- mathematics in climate modeling and predic- son, Yves Meyer, Ioannis Karatzas, László Babai, tion. Efim I. Zelmanov, Peter Hall, David Cox, Frans Majda has recently published with Andrea Oort, Joel S. Feldman, Roman Jackiw, Duong H. Bertozzi, Vorticity and Incompressible Flow (Cam- Phong, Michael S. Waterman, Arthur T. Win- bridge University Press). Also, Majda’s lecture free, Edward Frenkel, Laurent Lafforgue, George notes, Introduction to PDE’s and Waves for the At- Lusztig, László Lovász, Endre Szemerédi , Peter mosphere and Ocean, was recently published in Sarnak, and Shing-Tung Yau.

Activities Held During the Thematic Year

Summer School Wiener processes, stochastic differential equa- Stochastic Calculus for Applications: The- tions, as well as more elaborate ideas such as the ory and Numerics Girsanov transformation and path integrals. The August 9 – 20, 2004, CRM material was presented at a semi-rigorous level organized jointly with MITACS by relying only on the standard tools of basic probability, linear algebra, and advanced calcu- Organizers: Anne Bourlioux (Montréal), Eric lus. Both theoretical and numerical aspects were Vanden-Eijnden (Courant Inst.) covered and illustrated via examples. Principal Lecturer: E. Vanden-Eijnden (Courant The purpose of the summer school was to serve Inst.) as an introduction for graduate students and Supervisor of exercise sessions: I. Fatkullin postdoctoral fellows to one of the main mathe- (Caltech) matical tools at the centre of the thematic year Invited Lecturers: P. Tupper (McGill), organized by the CRM in 2004 – 2005 so that they B. Khouider (Victoria), C. Le Bris (ENPC), could benefit to the maximum from the special- I. Fatkullin (Caltech) ized workshops to be held subsequently. This Number of participants: 51 mission was accomplished with success thanks The aim of the summer school was to cover to a combination of daily theoretical courses, the essentials of stochastic calculus, including four invited lectures on applications represen- fundamental concepts such as Markov chains, tative of some of the themes to be covered in

12 THEMATIC PROGRAM the workshops of the thematic program, and L’atelier a réuni environ 25 participants venus by daily, supervised exercise sessions. An in- assister aux 18 conférences présentées et à teresting fact was the great diversity of partici- une communication courte. La confrontation pants: students, postdocs and researchers from de compétences aussi diverses a été largement mathematics, physics, pharmacy, chemistry, en- appréciée par les participants, et les longues gineering, etc., not only from diverse Montreal plages de discussion ménagées dans l’emploi universities and research centers, but also from du temps ont rendu possibles de nombreux elsewhere in Canada, from the United States échanges dont certains seront certainement le and from Europe. Participation was assiduous germe d’interactions scientifiques à plus long throughout the two weeks — many participants terme. commented on how positive the experience was from all points-of-view: i.e., excellence of the Workshop content and of the organization. The organiz- Front Propagation and Nonlinear Stochas- ers received several queries asking if the activity tic PDE’s for Combustion and Other Ap- would be repeated in the future. plications January 26 – 29, 2005, CRM Workshop organized jointly with MITACS Multiscale Rheological Models for Fluids Organizers: November 14 – 17, 2004, CRM Anne Bourlioux (Montréal), Panagi- otis T. Souganidis (UT Austin) Organizer: Claude Le Bris (ENPC) Speakers: J. Bell (Lawrence Berkeley National Speakers: A. Bonito (EPFL), É. Cancès (ENPC), Lab.), K. Bushe (UBC), C. Devaud (Water- P. Constantin (Chicago), A. Debussche (ENS- loo), Ö.L. Gülder (Toronto), F. Hamel (Aix- Cachan Bretagne), M. Grmela (École Polytech- Marseille III), S. Heinze (MPI MIS), M. Her- nique Montréal), Z.-F. Huang (McGill), B. Jour- rmann (Stanford), D. Hillhorst (Paris XI), A. dain (EPNC), C. Le Bris (EPNC), T. Lelièvre Kiselev (UW Madison), J. Nolen (UT Austin), (Montréal), C. Liu (Penn State), A. Lozinski A. Novikov (Penn State), J.-M. Roquejoffre (EPFL), N. Masmoudi (Courant Inst.), F. Otto (Toulouse III), A. Stevens (MPI MIS), V. Volpert (Bonn), R.G. Owens (Montréal), J. Ramírez (Lyon I), A. Zlatos (UW Madison) (Politécnica Madrid), P.T. Underhill (MIT), Q. Number of participants: 22 Wang (Florida State), P. Zhang (Beijing) The development of efficient large-scale mod- Number of participants: 25 els for the numerical simulation of turbulent La modélisation multiéchelle du comportement premixed flames requires a good understand- non newtonien des fluides complexes peut être ing of the mathematical principles governing abordée par l’établissement de lois constitu- the dynamics of self-propagating fronts. One tives, mais de telles lois sont souvent difficiles à of the most challenging issues is the analysis dériver et à valider. Une stratégie alternative est of the complex interactions, at small scales, be- de faire appel à la théorie cinétique pour simuler tween advection, reaction and diffusion, includ- le comportement des microstructures présentes ing stochastic effects due to the media or the ad- dans le fluide (chaînes de polymères, particules vective flow randomness. en suspension, etc.) et de coupler cette descrip- This workshop, offered an opportunity for inter- tion microscopique avec une description macro- actions between mathematicians at the forefront scopique du fluide par les équations de la mé- of this area and scientists involved in the de- canique du continuum. sign of models and numerical methods for var- Un large spectre de questions reliées à la ious applications, in particular, turbulent com- rhéologie des fluides complexes a été abordé: bustion. les aspects de modélisation (Owens, Wang, On the theoretical side, exchanges were quite Grmela, Underhill, Huang), les aspects de sim- intense with several speakers presenting very ulation numérique (Ramírez, Bonito, Lozin- recent results on predictions of flame propaga- ski), les aspects d’analyse mathématique et tion and extinction in response to flows, notably numérique (Constantin, Otto, Cancès, Liu, Mas- those in a network of vortices; various estima- moudi, Zhang). Certaines conférences ont été tors for PDEs, comparison principles for their dédiées aux modèles faisant intervenir des équa- solutions, and probabilistic methods were fea- tions de nature stochastique (Debussche, Jour- tured. Participants appreciated and found just dain, Lelièvre, Le Bris). as instructive presentations offering a different

13 CENTRE DE RECHERCHES MATHÉMATIQUES but complementary perspective to theoretical ef- The workshop was genuinely interdisciplinary forts to understand flame fronts. For example, and new synergy between mathematics and the presentation by A. Stevens highlighted the these applications emerged throughout the interesting and potentially very promising the- meeting. One prominent example was the theme oretical connection between models of combus- of multiscale cloud modeling where the mathe- tion fronts and those in biology with a niche matical talks by Khouider, Katsoulakis, and Ma- of, so far, little studied mathematical problems. jda had serendipity with the disciplinary lec- Presentations of a more numerical and experi- tures by Grabowski, Craig and Vallis. The young mental nature also led to discussions going both scientists in attendance were able to observe this ways: an improved awareness for mathemati- vibrant scientific activity. cians of the complexity and richness of the spec- Another exciting development was the new tacular results obtained during physical and nu- mathematical theory for new types of break- merical experiments, but also very frank discus- ing waves and their impact on mean flows de- sions, for instance on the mathematical valid- veloped by Bühler in his lecture after the gen- ity of certain approximations widely used in nu- eral overview of Shepherd. Another interesting merical models. point of interaction was the mathematical tech- Workshop niques for stochastic mode reduction presented Representing Unresolved Degrees of Free- by Franzke and Timofeyev in contrast to the ob- dom for the Atmosphere and Ocean servational lecture of Branstator and the inter- esting lecture of Delsole on instantaneous op- March 2 – 5, 2005, CRM timal bases for turbulence. Finally, Turkington Organizer: Andrew J. Majda (Courant Inst.) and Bowman gave interesting novel methods for Speakers: P. Bartello (McGill), J. Bowman parametrizing turbulent flow at large scales and (Alberta), G. Branstator (NCAR), O. Büh- in the integral range. ler (Courant Inst.), L. Campbell (Carleton), G. Craig (DLR Oberpfaffenhofen), T. DelSole Workshop (George Mason), C. Franzke (Courant Inst.), Extracting Macroscopic Information from W. Grabowski (NCAR), D.M. Holland (Courant Molecular Dynamics Inst.), M. Katsoulakis (UMass Amherst), B. April 7 – 9, 2005, CRM Khouider (Victoria), P.J. Kushner (Toronto), A. Monahan (Victoria), T.G. Shepherd (Toronto), Organizer: Paul F. Tupper (McGill), Andrew D. Straub (McGill), I. Timofeyev (Houston), Stuart (Warwick) B. Turkington (UMass Amherst), G.K. Vallis Speakers: G. Ciccotti (Roma “La Sapienza”), C. (GFDL) Dellago (Wien), A. Dinner (Chicago), W. Hoover, Number of participants: 49 B. Leimkuhler (Leicester), J.H. Maddocks (ETH A central problem in attempts to understand Zürich), C. Schuette (FU Berlin), R.D. Skeel (Pur- and predict the evolution of atmospheric or due), M.E. Tuckerman (New York), E. Vanden- oceanic flows is how best to represent the un- Eijnden (Courant Inst.), A.F. Voter (Los Alamos), resolved scales in these flows. In the jargon S. Wiggins (Bristol) of dynamic meteorology or physical oceanog- Number of participants: 31 raphy this is called the parameterization prob- Models used in molecular dynamics are high- lem, while in the jargon of turbulence it is called dimensional dynamical systems (or stochastic the closure problem. The most pertinent areas dynamical systems) with multiple time-scales. A of analysis and applied mathematics are ho- major challenge for computational mathematics mogenization theory, probability and non-linear is the extraction of accurate macroscopic infor- stochastic PDEs. The purpose of this workshop mation at minimal cost. This workshop concen- was to explore two complementary issues that trated on two topics: arise in the context of the parameterization prob- lem: • the analysis and development of standard 1. the extent to which modern techniques in ap- time-stepping algorithms in the context of plied mathematics can be brought to bear on molecular dynamics, with the purpose of the its formulation and partial solution; and indirect calculation of macroscopic informa- 2. the extent to which problems in the represen- tion; tation of atmospheric and oceanic flows cre- • the design of new algorithms aimed at extract- ate fertile new areas of mathematical inquiry. ing macroscopic information directly.

14 THEMATIC PROGRAM

During the workshop some particular areas of cleation and reconstruction of stepped surfaces, focus emerged: Transition path sampling (Blue and the behaviour of nano-materials in general. moon, the string method), determining reaction Most participants were experts in the field. The coordinates (theory and practice), stochastic vs workshop was run in such a way that it pro- deterministic mechanics for molecular simula- moted in-depth, frank and sometimes heated tion (e.g., Langevin or dynamical thermostats), discussions. automatic extractions of information from huge, Several problems, such as issues of boundary high-dimensional data sets and fast dynamics conditions, dislocation dynamics and their role (“Voter” dynamics). in plastic deformation, rare events, systematic The workshop was widely considered a success. coarse-graining procedures were discussed in Because the talks were each an hour long, speak- depth. Most participants enjoyed this style of ers were able to take their time to develop their workshop and expressed interest to have more material in a clear fashion. Because we limited of such workshops in the future. the number of speakers to 12, there was am- ple time between the talks for discussion. Many participants explicitly thanked the organizers for Workshop this relaxed schedule, saying that it was a re- Integrative Multiscale Modeling and Simu- freshing change from the usual format for such lation in Materials Science, Fluids and En- workshops. vironmental Science May 11 – 13, 2005, CRM Moreover, since the speakers included mathe- maticians, physicists, and chemists, there was Organizer: Thomas Y. Hou (Caltech) a wide variety of perspectives on the differ- Speakers: J.E. Aarnes (SINTEF ICT), A. ent problems addressed. The most valuable out- Bourlioux (Montréal), C.J. Budd (Bath), R.E. come was probably the emergence of unfore- Caflisch (UCLA), S. Chen (Johns Hopkins), A.J. seen parallels between different researchers’ ap- Chorin (UC Berkeley), P. Constantin (Chicago), proaches to the analysis of molecular dynamics L.J. Durlofsky (Stanford), Y. Efendiev (Texas data. A&M), B. Engquist (PSCI), A.C. Fannjiang (UC Davis), R. Ghanem (Southern California), J. Workshop Glimm (SUNY Stony Brook), Y.G. Kevrekidis Multiscale Modeling of Solids (Princeton), R. Kuske (UBC), C. Liu (Penn State), April 28 – 30, 2005, CRM W.K. Liu (Northwestern), M. Luskin (Min- nesota), L.R. Petzold (UCSB), H. Tchelepi (Stan- Organizer: Weinan E (Princeton), Eric Vanden- ford), M.F. Wheeler (UT Austin), J. Xin (UT Eijnden (Courant Inst.) Austin), S. Yip (MIT), D. Zhang (Los Alamos) Speakers: N. Bernstein (US Naval Research Number of participants: 44 Lab.), W. Cai (Stanford), W.A. Curtin (Brown), There were 22 invited speakers from various dis- E. Kaxiras (Harvard), A.J. Lew (Stanford), X. Li ciplines. They are all leading experts in their (IMA), W. K. Liu (Northwestern), G. Lu (Cal- fields. The workshop also attracted participants ifornia State), M. Marder (UT Austin), R. E. from academia and industry. It generated very Miller (Carleton), A. Needleman (Brown), H. lively and stimulating discussions during the Park (Vanderbilt), M.G. Reznikoff (Bonn), R.E. lectures, and the coffee breaks. People from dif- Rudd (Lawrence Livermore National Lab.), M. ferent backgrounds found common research in- Tang (Lawrence Livermore National Lab.), Y. Xi- terests through the interactions of the workshop. ang (Hong Kong University of Science & Tech- We also identified a number of key challenges nology) that remain to be resolved in the future. These Number of participants: 33 challenges include the multiscale analysis and This was a very successful workshop. It is quite computational methods for problems without different from most other workshops on mul- scale separation where global information be- tiscale modeling, since it was quite focused. comes important, stochastic modeling and how This workshop concentrated on energetic and ki- to quantify the uncertainty effect due to the netic issues associated with defects, cross-slip, presence of random noise in modeling, bridging grain boundary migration, and phase bound- the gap between fundamental multiscale anal- ary dynamics in solids. The objective was to de- ysis for model problems and the engineering velop mathematical models for complex multi- applications and the dynamic non-linear inter- scale phenomena such as crystal plasticity, nu- action across different length scales. Every in-

15 CENTRE DE RECHERCHES MATHÉMATIQUES vited speaker gave a first-rate lecture. This in- (Imperial College London), T. Bielecki (IIT), cludes both the senior established leaders in A. Cadenillas (Alberta), R. J. Elliott (Calgary), the field and the younger generation of rising J. Fan (Princeton), P. Glasserman (Columbia), stars. In many cases, the topic of one lecture U. Haussmann (UBC), E. Hillebrand (LSU), U. complemented another lecture. As a result, the Horst (UBC), S. Howison (Oxford), M. Jeanblanc workshop generated a lot of interactions among (Évry-Val d’Essone), I. Karatzas (Columbia), S. the participants. We can see that mathemati- Kou (Columbia), D. Kramkov (Carnegie Mel- cians talked to engineers, and engineers learned lon), D. Pelletier (NC State), É. Renault (North from mathematicians. For example, the lecture Carolina), P. J. Schönbucher (ETH Zürich), K. by Wing-Kam Liu on applying the immersed Solna (UC Irvine), N. Touzi (CREST), L. Wu boundary method to biological nanofilm depo- (Baruch College), T. Zariphopoulou (UT Austin) sition inspired discussion with Bjorn Engquist, Number of participants: 93 who has done work on improving the accuracy The theme of this workshop was emerging direc- of immersed boundary methods. The lecture of tions in financial mathematics, with emphasis on Shiyi Chen on multiscale simulation of fluid- stochastic modeling of market uncertainties, the- solids interaction also inspired a lot of discus- oretical and numerical approximations to pric- sions on during the lecture regarding its poten- ing, hedging and portfolio optimization control tial applications to engineering problems and problems, and data estimation issues. The goal some of its limitations. The lectures by Durlof- was to bring together researchers in a variety sky, Efendiev, and Arnes gave an admirable of disciplines (mathematics, engineering, oper- overview on the topic of upscaling of flow in ations research and economics, for example) to porous media, covering both the state-of-the-art emphasize different techniques and approaches. methodology and the frontier applications in the industry. Sidney Yip gave an outstanding talk The meeting was very successful in bringing to- on the dynamic aspect of multiscale modeling in gether experts from the various fields of finan- materials science applications. Linda Petzold’s cial mathematics, statistics and econometrics. It lecture is an excellent example how an effective gave an opportunity to graduate students to be multiscale algorithm can make a difference in bi- exposed to a range of interesting and exciting ological applications. Glimm’s talk showed the research problems and also an opportunity to importance of high resolution schemes in cap- postdocs to show their work in twenty-minute turing the small scale interfacial instability while talks. The format was extremely successful and a less accurate method may completely miss most likely it will be adopted by others: we had these important fine scale details. Finally, Con- fourty-five minute long talks (including ques- stantin’s lecture provided the fundamental the- tions) and fifteen-minute breaks during talks for ory for some non-Newtonian models for com- coffee and further discussions. plex fluids. The workshop brought forward exciting new Many participants told the organizer how much developments in (among others): utility- they had enjoyed the workshop. In some sense, indifference pricing, numerical solution of non- we have integrated successfully the different as- linear partial differential equations, credit risk, pects of multiscale problems and started a very multiscale techniques for volatility modeling (in healthy and constructive dialogue among ex- credit, equity and fixed income), estimation of perts from different disciplines. If we continue volatility and its time-scales and even the occur- this type of cross-disciplinary interactions, we rence of the Riemann-Zeta function in finance! will be able to make significant advances of the The organizers are delighted to have had the op- field. portunity to put together such a workshop at CRM, and many of the participants have con- Workshop tacted us afterwards to express their gratitude Stochastic Modeling in Financial Mathe- also. matics June 1 – 5, 2005, CRM organized jointly with SAMSI and partially Advanced Course funded by MITACS Multiscale Systems: Modeling and Simula- tion Organizers: Ronnie Sircar (Princeton), Jean- Fall 2004, CRM Pierre Fouque (NC State) Speakers: R. Almgren (Toronto), D. Becherer Professor: Claude Le Bris (ENPC)

16 THEMATIC PROGRAM

This course was an introduction to the study Scientific point-of-views: of multiscale problems from the applied mathe- matician’s point of view. Various strategies were • Physics described and analyzed, each of them explained • Mathematical Analysis; in the framework of a specific application. • Numerical Analysis; • Programming. Examples of applications:: • Solid Mechanics This is a very active research area. The course • Laminated Materials; aimed at establishing the mathematical basis • Molecular Chemistry; of this discipline so that the student will be • Polymeric Fluids Dynamics; equipped to explore various multiscale research • Chemical Reactions Kinetics. areas.

Past Thematic Programs

The Centre de recherches mathématiques has 1996 – 1997 Combinatorics and Group Theory organized thematic activities every year since 1995 – 1996 Applied and Numerical Analysis 1993. Before that, starting in 1987, special 1994 – 1995 Geometry and Topology semesters and concentration periods were com- 1993 – 1994 Dynamical Systems and Applica- bined with thematic years. tions Here follows a list of thematic activities orga- 1992 Probability and Stochastic Control nized by CRM since 1987: (Special Semester) 1991 – 1992 Automorphic Forms in Number 2003 – 2004 Geometric and Spectral Analysis Theory 2002 – 2003 Math in Computer Science 1991 Operator Algebras (Special Semester) 2001 – 2002 Groups and Geometry 1990 Nonlinear PDE’s and Applications (Focal 2000 – 2001 Mathematical Methods in Biology Period) and Medicine 1988 Shimura Varieties (Special Semester) 1999 – 2000 Mathematical Physics 1987 Quantum Field Theory (Special Semester) 1998 – 1999 Number Theory and Arithmetic Ge- 1987 – 1988 Fractals: Theory and application ometry 1987 Structural Rigidity (Special Semester) 1997 – 1998 Statistics

17 General Program GENERAL PROGRAM

HE CRM’s general program funds a wide variety of scientific events, both on-site and elsewhere Tin 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 mathematical sciences 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 Geometry cally, the simplest structures are those of con- June 28 – July 16, 2004, CRM stant curvature, and his five lectures covered both the asymptotically flat and the hyperbolic Organizers: Vestislav Apostolov (UQÀM), An- (or conformally-compact) cases. He described a drew Dancer (Oxford), Nigel Hitchin (Oxford), large class of examples of such metrics, and then McKenzie Wang (Hamilton) focused on general questions of existence and Short courses instructors: Michael Anderson uniqueness. He explained through his talks the (SUNY Stony Brook), Karsten Grove (Mary- so-called Anti-de Sitter/Conformal Field The- land), Nigel Hitchin (Oxford) ory correspondence in physics, and gave a num- Invited speakers: M. Anderson (SUNY Stony ber of results on the structure of the map from Brook), O. Biquard (Strasbourg), R. Bielawski the space of Einstein conformally-compact met- (Glasgow), C. Boyer (New Mexico), R. Bryant rics to the conformal structures on the bound- (Duke), D. Calderbank (Edinburgh), J. Chen ary. These lectures were masterful in their grasp (UBC), X. Chen (UW Madison), A. Dancer of both the physical theories and the rigorous (Oxford), M. Dunajski (Cambridge), P. Gaudu- mathematical results related to them. chon (École Polytechnique Palaiseau), A. Fraser Karsten Grove gave a four-lecture mini-course (UBC), K. Grove (Maryland), M. Herzlich (Mont- on comparison geometry, from a fairly new and pellier II), N. Hitchin (Oxford), C. LeBrun original point of view. The comparison geome- (SUNY Stony Brook), N.C. Leung (Minnesota), J. try has its roots in global Riemannian geometry, Lohkamp (Augsburg), C. Margerin (École Poly- where it took off in the 1930s through the works technique Palaiseau), M. Min-Oo (Hamilton), A. of Hopf, Morse, Schoenberg, Myers and Synge. Nabutovsky (Toronto), D. Page (Alberta), G. Pa- The real breakthrough came in the 1950s with padopulos (Cambridge), H. Pedersen (Odense), the pioneering works of Rauch, Alexandrov, To- P. Petersen (UCLA), C. Pope (Texas A&M), R. ponogov and Bishop. Since then, the simple idea Rotman (Toronto), K. Shankar (Oklahoma), X. of comparing the geometry of an arbitrary Rie- Wang (MIT), B. Wilking (Münster), W. Ziller mannian manifold with the geometry of con- (Pennsylvania) stant curvature spaces has had a tremendous Number of participants: 90 evolution. First in conjunction with Morse the- This three-week program, held during the sum- ory and convexity, then with Gromov-Hausdorff mer of 2004 at the Centre de recherches mathé- topology on spaces of Riemannian manifolds, matiques, focused on the study of Riemannian and the geometry of singular spaces, and most metrics whose curvature satisfies constraints recently in the presence of symmetries. All these (the so-called special geometries). The relation aspects were beautifully presented through the between curvature and topology has been of in- lectures which had a great success. terest since the beginning of differential geome- What is special about 6, 7 and 8 dimensions? try and, more recently, metrics with special cur- Why do we study Calabi-Yau threefolds, G2 and vature properties have come to the fore in phys- Spin(7) manifolds? These were the questions ad- ical problems related to string theory. These sub- dressed in Nigel Hitchin’s introductory lectures jects were the leitmotivs of the program that was to these special geometries of great interest in attended by over 90 participants. string theory. Based on the fundamental prin- The program opened with a week of introduc- ciple to look at the geometry of open orbits of tory short courses designed for graduate stu- Lie groups, he presented a truly elegant and dents and postdoctoral fellows. original approach to the subject. The orthogo- nal groups SO(n, n) also appear in this setting Michael Anderson gave a comprehensive survey through their spin representations, and this pro- on Einstein metrics on open manifolds, which vided an entrance into the exciting world of gen- have a certain structure at infinity. Asymptoti- eralized geometry. His lectures were beautifully

19 CENTRE DE RECHERCHES MATHÉMATIQUES orchestrated with many examples and construc- ings of infinitely many topological types of cer- tions on moduli spaces. tain 3-dimensional hyperbolic manifolds. The audience during this first week was quite Wolfgang Ziller related the existence of positive eclectic, ranging from physicists to geometers sectional curvature metrics on the total space of to topologists. All three lecturers did wonder- fiber bundles with the recent constructions of ful tutorial work during the office hours they Einstein self-dual orbifolds, due to N. Hitchin, kindly provided to the participants. There were D. Calderbank and M. Singer. Burkhard Wilking many fruitful discussions across boundaries, then presented a classification of the positively and these led in particular to an informal lecture curved compact manifolds of cohomogeneity by Michael Anderson on the celebrated recent one, a result that he, K. Grove and W. Ziller work of Perelman, aiming at a complete resolu- have recently obtained, and he discussed in de- tion of Thurston’s geometrisation conjecture. tail the still open case of a smooth 3-Sasakian 7- The last two weeks of the program included 43 manifold constructed out of Hitchin’s Einstein one-hour specialized talks, elaborating in partic- self-dual orbifolds. Ingi Petursson and Ailana ular on the subjects introduced during the first Fraser talked about their exciting results on com- week. pact Riemannian manifolds of (almost) positive isotropic curvature. Einstein metrics, positive sectional curvature, obstruction theory for positive scalar curvature Joachim Lohkamp presented the complete proof were the main topics during the second week of of the positive mass theorem that he and U. the program. Christ have recently found. Marc Herzlich then defined an analogous asymptotic invariant in Michael Anderson presented his new construc- the case of asymptotically hyperbolic metrics, tion of compact Einstein metrics, by using a called “hyperbolic mass,” and proved the “pos- generalization of Thurston’s theory of hyper- itive mass property” in this case. Margarita bolic Dehn surgery and gluing techniques. His Kraus talked about inequalities which bound the construction provides the first known families Riemannian curvature tensor with the asymp- of 4-dimensional compact Einstein manifolds totic “mass invariant” of an asymptotically flat which are neither Kählerian nor locally sym- Lorentzian manifold. Hélène Davaux found a metric. Christoph Böhm gave a comprehensive new upper estimate of the scalar curvature of a overview of general existence results for homo- compact spin manifold in terms of the spectrum geneous Einstein metrics, including many new of the Laplacian of the universal covering, thus examples. Charles Boyer lectured on his recent providing a new obstruction to the existence of a works with K. Galicki and J. Kollár that pro- positive constant scalar curvature metrics. duce an abundance of new Einstein metrics on compact manifolds of dimension 2n + 1, includ- There were also two talks on upper curva- ing exotic spheres. Don Page explained how an ture bounds during this second week, given by Euclidean version of the general Kerr-de Sitter Regina Rotman and Krishnan Shankar. Alexan- metric leads to the construction of amazingly ex- dre Nabutovsky gave an excellent overview of plicit Einstein metrics on Sn−2-bundles over S2. variational methods in Riemannian Geometry, David Calderbank lectured on his recent works and Niky Kamran surveyed some long time be- with H. Pedersen and M. Singer that classify haviour results for solutions of geometric hy- both locally and globally self-dual Einstein man- perbolic equations arising in the Lorenzian Kerr ifolds and orbifolds that admit an isometric ac- space-time. tion of a 2-torus. Andrew Dancer presented a The third week of the program was mostly fo- classification for superpotentials that have been cused around the geometry of metrics with spe- used to reduce the Einstein equations to sub- cial holonomy, Kähler and Hermitian metrics systems. Olivier Biquard explained the relation with special curvature, and holomorphic meth- between 3-dimensional CR geometry and Ein- ods in Riemannian geometry. stein geometry, and defined a new eta invariant Roger Bielawski lectured on his recent works on for CR manifolds coming from this correspon- invariant Kähler metrics with prescribed Ricci dence. David Duchemin presented his work curvature, on the complexification of a symmet- on quaternionic-Kähler fillings of quaternionic- ric space of compact type. Paul Gauduchon gave contact structures in dimension 7. Gordon Craig a new description of all Kähler metrics with van- explained his gluing construction of Einstein fill- ishing Bochner curvature, thus providing an al- ternative approach to R. Bryant’s classification

20 GENERAL PROGRAM of these manifolds. Gideon Maschler presented Following Hitchin’s ideas, Marco Gualtieri intro- his recent works with A. Derdzinski that clas- duced the notion of generalized Kähler geome- sify, both locally and globally, all Einstein man- try and explained how these structures naturally ifolds which are conformally Kähler. Christina appear on 4-manifolds and in connection with Tønnesen-Friedman presented an abundance of twisted K-theory classes of even dimensional Lie new explicit examples of extremal Kähler met- groups. rics on toric bundles. Yann Rollin talked about Thus, in three very intensive weeks, the program his very important recent work with M. Singer succeeded in tying together most of the new re- that relates existence of scalar-flat Kähler metrics sults in the subject and a variety of new projects and stability of parabolic vector bundles. Maur- were born. The participants affirmed frequently izio Parton and Ruxandra Moraru talked about and spontaneously that the program was a great reduction and instanton moduli spaces over cer- success. tain hyper-Hermitian manifolds. The lecture notes of the short courses given dur- Gueo Grantcharov, Ana Fino and Helge Joer- ing the first week of the program, as well as gensen explained their classification results of a number of other contributions will be pub- certain homogeneous spaces with special holon- lished as a joint CRM – AMS volume. We wish to omy properties. Bogdan Alexandrov discussed acknowledge the National Science Foundation some fuzzy threads in the literature concern- (NSF) for their contribution. ing the notion of weak holonomy. Stefan Ivanov presented a proof of a Goldberg-type conjec- S´eminaire de math´ematiques sup´erieures – ture concerning Einstein G2-manifolds. Georges NATO ASI 2004 Papadopoulos introduced the notion of spino- Morse Theoretic Methods in Non-Linear rial cohomology and explained how it can be Analysis and Symplectic Topology applied to study manifolds with special holon- June 21-July 2, 2004, Université de Montréal omy. Min-Oo talked about calibrated geome- This Seminar was held with financial support try in spaces with special holonomy G2 and from the NATO, the CRM, the Vice-rectorat à la Spin(7), and its relevance to string theory. He recherche, the Faculté des Sciences and the Dé- discussed various explicit constructions recently partement de mathématiques et de statistique of found by physicists. His lecture was later fol- Université de Montréal lowed by a talk by his collaborator, Spiro Ka- rigiannis, on calibrated cycles in certain bun- Organizers: Octavian Cornea (Montréal), Paul I. dle constructions of metrics with holonomy G2. Biran (Tel Aviv) There were two other talks on calibration the- Speakers: A. Abbondandolo (Scuola Nor- ory associated to special Lagrangian manifolds, male Superiore di Pisa), P. Biran (Tel Aviv), given by Marianty Ionel and Adrian Butscher. R. Cohen (Stanford), O. Cornea (Montréal), Wei-Dong Ruan discussed convergence and de- M. Farber (Durham), K. Fukaya (Kyoto), H. generation of complete Kähler – Einstein hyper- Hofer (Courant Inst.), M. Izydorek (Politech- surfaces in complex tori. nika Gda´nska), Y.-G. Oh (UW Madison), L. Robert Bryant lectured on complete Riemannian Polterovich (Tel Aviv), M. Schwarz (Leipzig), metrics for which the Ricci tensor is a Hessian C. Vitebo (École Polytechnique Palaiseau) of a function. This class of manifolds naturally Number of participants : 65 appears in the study of Ricci flow on manifolds. The talks at this meeting centered on Morse the- Claude LeBrun gave a very beautiful new proof oretical techniques which can be used to solve of all the classical results concerning compact difficult analytic problems as well as problems surfaces with closed geodesics, by using a in symplectic topology and in robotics. The key twistor-theoretic approach to reduce these prob- tool in modern symplectic topology is Floer ho- lems to certain rigidity properties of complex- mology techniques, and this has constituted a re- analytic surfaces. Maciej Dunajski demonstrated curring theme for the lectures given at the SMS. how the twistor-approach can be applied to var- In the first week Helmut Hofer talked about the ious nonlinear integrable equations arising in foundations of symplectic field theory, one of mathematical physics to find solutions via sim- the major new “machines” in symplectic topol- ple algebro-geometric operations on families of ogy whose development has been pursued by rational curves. Hofer, Eliashberg and Givental for a number of years now. The origins of symplectic field the- ory lie in Floer’s machinery but it goes much be-

21 CENTRE DE RECHERCHES MATHÉMATIQUES yond that, and both in applications in complex- Mini-Workshop on Computational Aspects ity. Hofer’s lectures were therefore extremely of Dynamical Systems timely. Matthias Schwarz presented his recent July 19, 2004, Concordia University proof for a result of Viterbo relating the Floer ho- organized by the Applied Mathematics Labora- mology of the cotangent bundle and the string tory topology of the zero section of this bundle. This notion of string topology has been recently in- Organizer: Eusebius Doedel (Concordia) troduced by Chas and Sullivan with a purely Speakers: A. Vanderbauwhede (Gand), B. topological motivation, and the fact that it fits Krauskopf (Bristol), H. Osinga (Bristol), P. Tup- perfectly with the quantum product in Floer’s per (McGill). theory is quite remakable. Michael Farber dis- The aim of this mini-workshop was to bring cussed applications to robotics. Paul Biran de- together theory and application of numerical scribed efficient methods to use Floer homology techniques for dynamical systems. New devel- in the monotone case to prove results concern- opments were demonstrated with case studies ing the topological structure of Lagrangian sub- of dynamical systems arising in applications. manifolds. Leonid Polterovich showed how to Problems considered included the continuation relate this symplectic topology to dynamics and and bifurcation of periodic orbits in symmet- geometric group theory methods. Octav Cornea ric Hamiltonian systems, and the computation presented higher order Floer type invariants and of invariant manifolds, including unstable man- applications. ifolds in delay equations with application to a This was an intense first week with lectures laser with optical delay, and computation of one- of the highest order of interest for specialists dimensional unstable manifolds when the equi- as well as for beginners in the field. Some of librium loses its hyperbolicity or the manifold is the topics discussed (in particular by Hofer, a strong unstable manifold. The problem of justi- Schwarz, Cornea and Polterovich) were pre- fying long-time large-scale simulations of molec- sented publicly for the first time at the SMS – ular systems was also considered through a con- NATO ASI. The second week continued as cept of weak ergodicity. strongly: Claude Viterbo talked about gener- ating functions techniques, Alberto Abbondan- dolo discussed Morse theory in Hilbert spaces, Conference on Fixed Point Theory and its Kenji Fukaya talked about a new version of his Applications in Honour of Andrzej Granas A machinery (developed with Oh and Ono) August 16 – 20, 2004, CRM organized by the Mathematical Analysis Labo- and∞ applications, some of which overlapped with applications obtained by different meth- ratory, a collaboration with the Département de ods by Cornea jointly with Lalonde and men- mathématiques et de statistique of Université de tioned in the first week. Marek Izydorek lec- Montréal tured on his approach to the infinite dimensional Conley index and Yong-Geun Oh presented his Organizer: Marlène Frigon (Montréal) recent spectral invariant techniques and chain Principal speakers: V. Benci (Pisa), B. Bojarski level Floer methods. Finally, Ralph Cohen de- (Polish Academy of Sciences), H. Brezis (Rut- scribed his topological approach to string topol- gers), R. Brown (UCLA), B. Cornet (Paris I), E. ogy and its potential implications for symplectic Fadell (Wisconsin), J. Jaworowski (Indiana), J.W. topology. Lee (Oregon State), F.-C. Liu (Inst. Sinica, Tai- wan), A. Marino (Pisa), J. Mawhin (Louvain), Obviously, as it follows from the description S.B. Nadler Jr. (West Virginia), R. Nussbaum above, many of the talks of different speakers (Rutgers), H. Steinlein Munich) were strongly interrelated (for example, Hofer’s Number of participants: 50 talks and those of Cornea, those of Schwarz with those of Cohen, those of Oh and those of La Conférence sur la théorie des points fixes et Viterbo). This contributed to the overall quality ses applications a réuni à Montréal du 16 au 20 and strength of the SMS – NATO ASI itself. août 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 principaux de la Conférence étaient la théorie des points fixes et ses applications à l’analyse non linéaire, aux équations différentielles et aux systèmes dy-

22 GENERAL PROGRAM namiques. Notamment, les sujets suivants ont but this was not to be. Suslin predicts, however, été traités : la théorie du degré topologique sur that this proof will be properly written up within des espaces de Banach ou sur des variétés et la a year. The Bloch–Kato conjecture has sensa- théorie du degré équivariant, les théorèmes de tional calculational consequences; these include point fixe et de point périodique, la théorie de the Lichtenbaum–Quillen conjecture which says Nielsen et celle de Perron-Frobenius, les applica- that K-theory can be computed from étale coho- tions KKM et les théorèmes de type minimax, les mology. méthodes variationnelles appliquées à des pro- blèmes d’équations aux dérivées partielles. Informal Semester on Symplectic Topology Fall 2004, CRM Workshop on Algebraic K-Theory Organizers: October 2 – 6, 2004, CRM Octav Cornea (Montréal), François Lalonde (Montréal) Organizers: Eric Friedlander (Northwestern), Speakers: M. Entov (Haifa), J.-Y. Welschinger Dan Grayson (Urbana-Champaign), Rick Jar- (ENS Lyon), F. Bourgeois (Université Libre de dine (Western Ontario), Manfred Kolster (Mc- Bruxelles), J.-Y. Welschinger (ENS Lyon), M. Pin- Master) sonnault (Toronto), P. Seidel (Chicago), S. Anjos Speakers: P. Balmer (ETH Zürich), G. Carlsson (IST Lisbonne), D. McDuff (SUNY Stony Brook), (Stanford), J.-L. Colliot-Thélène (Paris-Sud 11), A.-L. Biolley (Toronto), Y. Ruan (UW Madison), T. Geisser (USC), A. Goncharov (Brown), J. C. Liu (Harvard), K. Wehrheim (Princeton), R. Hornbostel (Regensburg), M. Karoubi (Paris Hind (Notre Dame), V. Ginzburg (UC Santa VII), M. Levine (Northeastern), I. Madsen Cruz),Y. Eliashberg (Stanford), E. Kerman (U (Aarhus), F. Morel (Munich LMU), O. Röndigs of I Urbana-Champaign), Y. Karshon (Toronto), (Bielefeld), M. Schlichting (LSU), R. Sujatha (Tata C. Abbas (Michigan State), A. Teleman (Aix- Institute), A. Suslin (Northwestern), B. Totaro Marseille 1). (Cambridge), M. Walker (Nebraska), K. Zain- This was an informal thematic semester, held in oulline (Bielefeld) addition to the official theme year on Multi-scale Number of participants : 49 Stochastic Modelling. With two major thematic The meeting reflected some of the major devel- programs going on at the same time in Fall 2004 opments of the past year in the subject, particu- at the CRM, one can easily imagine the inten- larly in motivic homotopy theory. These include sity of activities and febrility during that period. Levine’s proof of the Voevodsky slice conjecture, The informal Semester on Symplectic Topology Morel’s proof of the unstable connectivity theo- was a Canadian Leadership Initiative funded by rem for motivic homotopy types (which was de- NSERC; it was the natural sequel to the events scribed in his talk as a type of Hurewicz the- in symplectic topology that had started with the orem), and the identification by Röndigs and NATO Advanced Study Institute in the Summer Ostvaer of Voevodsky’s triangulated category of 2004. Our purpose was to invite a number of of motives with the stable category of mod- researchers in the field who have made recent ules over the cycle-theoretic Eilenberg–MacLane remarkable contributions to the subject and we spectrum. Levine’s theorem uses a homotopy asked them to discuss their work in an infor- theoretic approach to the Chow moving lemma, mal, flexible, workshop setting. We encouraged which was discussed during his talk. The Levine them to be present at the CRM for periods from and the Röndigs–Ostvaer results together sub- a week up to a month and, in particular, during stantially demystify the relation between the a concentration period in the first two weeks of motivic stable category and motivic cohomol- November. This created to an excellent working ogy, while Morel’s work points the way to ex- atmosphere and it was very useful to post-docs, plicit calculations of motivic homotopy groups. students and established researchers alike. Suslin displayed a spectral sequence for the mo- Some of the lecturers have given one lecture of tivic cohomology of an arbitrary Severi-Brauer one hour and some others two or more some- variety which is built from a decomposition of times longer talks. The maximum has been at- the motive associated to its Cechˇ resolution. tained by Welschinger who gave three lectures It had been expected that the proof of the Bloch- of an average length of two hours each. Kato conjecture relating Galois cohomology to Also present and active in the discussions were the Milnor K-theory of a field would be com- Jean-Claude Sikorav (ENS Lyon) as well as pletely written up by the time of this conference, Shengda Hu (Montréal), Alex Ivrii (Montréal)

23 CENTRE DE RECHERCHES MATHÉMATIQUES and the two organizers. A number of students Montreal Scientific Computing Days also participated sporadically: Clement Hyvrier, February 26 – 27, 2005, CRM Remi Leclercq as well as Baptiste Chantraine. organized by the Applied Mathematics Labora- Eliashberg’s, Kharshon’s and Seidel’s talks were tory organized jointly with CIRGET’s seminar. Organizers: Tony Humphries (McGill), Nilima Scientific description Nigam (McGill), Robert Owens (Montréal) A number of talks focused on “hot” topics in Invited speakers: J. Gopalakrishnan (Florida), J. symplectic topology: examples are the work S. Hesthaven (Brown) on real Gromov-Witten invariants in the pres- Number of participants: 101 ence of symmetry with the two different points of view of Welschinger and ChiuChu Liu. In The second edition of this annual event, was Welschinger’s case, the symmetry is the real in- once again a great success, this year attracting volution on complex manifolds with fixed locus 101 participants, mostly from Québec and On- equal to a Lagrangian submanifold. Really, what tario, up from 78 participants last year. The ob- Welschinger is doing is to construct enumerative jective of this conference is to encourage scien- invariants similar to the Gromow – Witten ones, tific exchange within the scientific computing in a way that requires careful gluing of moduliu community in Québec and further afield. The spaces according to rules that are dictated by a two-day program included two short courses of- new concept, the “mass.” In Liu’s case, the sym- fered by international experts, at a level accessi- metry was given by a S1-action whose effect was ble to advanced graduate students. to collapse the boundary of a moduli space so Jay Gopalakrishnan gave two long lectures on that new invariants could be defined. Multigrid methods, a class of numerical tech- The emerging theory of polyfolds, a whole new niques to solve linear systems arising from dis- theory that would give the right framework to cretization of PDEs using a hierarchy of dis- deal with lots of elliptic moduli spaces (i.e., cretization grids. These methods can often com- spaces of solutions to certain underdetermined pute an approximate solution up to a given pre- partial differential equations on curved spaces of cision at asymptotically optimal computational arbitrary dimensions), due to Hofer – Wisocky – cost. The optimal complexity of multigrid has Zehnder were patiently explained by Katrin brought within the reach of simulation many sci- Wehrheim. Applications of symplectic field the- entific problems previously thought to be of in- ory and contact homology were discussed in tractable size. The first lecture covered the fun- the talks of Bourgeois, Hind, Eliashberg as well damental theory and mechanics of multigrid as in those of Kerman and Ginzburg who de- methods, showing how it leads to optimal algo- scribed their novel way to detect periodic or- rithms, and illustrating it on simple examples. bits of Hamiltonian flows by using a Floer the- The second lecture considered more compli- oretic construction which takes into account pe- cated applications, highlighting examples from riodic orbits belonging to distinct homotopy electromagnetics, and investigated the modifica- classes (the so-called “Floer Branched Homol- tions needed to successfully apply the multigrid ogy”). We also heard about more topological paradigm. The interplay between convergence points of view concerning the space of Hamil- theory of discretizations and convergence analy- tonian diffeomorphisms as in the talks of An- sis of multigrid was emphasized, especially how jos, McDuff, and Pinsonnault. Andrei Teleman one has led to improvements in the other. and Paul Seidel both discussed topics closer Jan Hesthaven gave two long lectures on Dis- to algebro-geometric problems relevant in sym- continuous Galerkin methods for solving time- plectic topology. dependent PDEs. These discontinuous finite el- The main support for this semester was pro- ement methods, although proposed first more vided by a LSI NSERC grant (whose coordi- than three decades ago, have recently received nator is Steven Boyer). The CRM provided of- considerable attention due to a number of very fice spaces and computer capabilities as well attractive properties, e.g., solid theoretical foun- as a seminar room and other administrative dation, ability to work with high-order and assistance. We were also helped by Ms. Di- adaptive grids, support for unstructured grids ane Bélanger, the administrative assistant to the and very high performance on parallel comput- Mathematics Canada Research Chairs at Univer- ers. The first lecture covered the fundamental sité de Montréal who kindly took care of the ho- theory of these methods, discussing some key tel reservations. theoretical results, illustrated by illuminating ex-

24 GENERAL PROGRAM amples. The second lecture focused on more ap- tion d’images. Plusieurs méthodes d’estimation plied aspects and how to develop and imple- et de calculs ont été présentées. ment these methods for a variety of problems Charles Bouman (Purdue) a fait le point sur les and applications. nouveaux imageurs optiques qui soulèvent au- Both lecturers gave superb and well appreci- jourd’hui autant d’intérêt sur le plan des possi- ated presentations, and also made comprehen- bilités de « voir » l’activité cérébrale que de défis sive notes available, Hesthaven even supplied au niveau des méthodologies de reconstruction a suite of software routines for implementing tomographique. La tomographie bayésienne a the Discontinuous Galerkin method. There were fait l’objet de l’exposé d’Ali Mohammad-Djafari also 15 twenty-minute contributed talks, many (Supélec), spécialiste reconnu des questions de by postdoctoral fellows and graduate students, reconstruction à partir de données partielles et who were especially encouraged to participate, incomplètes. L’exposé de Keith Worsley (McGill) and a pizza and poster session on Saturday donnait un point de vue critique sur l’approche evening. bayésienne en la remettant dans une perspec- tive d’étude de groupe pour l’inférence robuste de l’activation cérébrale. Cet exposé complé- Workshop on Bayesian Inference and Func- tait fort bien les deux présentations fouillées de tional Brain Mapping Christophe Phillips (Liège) qui a su remettre en March 31 – April 2, 2005, CRM perspective les outils méthodologiques dans le organized by PhysNum and the Statistics Labo- contexte appliqué de l’imagerie cérébrale qui ratory peut, aujourd’hui, profiter de la fusion de plu- sieurs types d’information. L’atelier a également Organizers: J.-F. Angers (Montréal), J.-M. Lina donné l’occasion à de jeunes chercheurs de pré- (ETS) senter leurs propres travaux. Christophe Grova Speakers: A. Mohammad-Djafari (Supélec), C. (McGill) a ainsi présenté une méthodologie Bouman (Purdue), C. Phillips (Liège), K. Wors- d’évaluation pour comparer les performances ley. (McGill), C. Grova (McGill), J. Daunizeau des estimateurs. Jean Daunizeau (Montréal) a (Montréal) donné une solution au problème de fusion mul- Number of participants: 30 timodale qui permet de prendre en compte dif- En choisissant d’ancrer l’analyse bayésienne férentes sources d’information et François Des- dans le contexte de l’imagerie en neuroscience, trempes (Montréal) a présenté un estimateur les organisateurs avaient comme objectif de sus- bayésien pour les modèles de champs de Mar- citer l’intérêt des jeunes chercheurs quant aux kov cachés qui sont largement utilisés en image- avenues de recherche qui s’offrent aujourd’hui rie mathématique. dans ce domaine extrêmement dynamique des Le format de cet atelier a permis d’établir un biosciences. Les thèmes suivants ont été abor- bon échange entre les différents conférenciers et dés : les participants. Plusieurs étudiants ont pu aussi • reconstruction d’images selon une approche présenter leurs travaux et en discuter avec les bayésienne ; chercheurs plus expérimentés dans ce domaine. • application des modèles de chaînes de Mar- kov cachées à la modélisation des couleurs ; Workshop on Analysis and Computation of • aspect calculatoire des problèmes inverses en Lattice, Delay and Functional Differential imagerie biomédicale ; Equations • comparaison entre différentes méthodes de April 25, 2005, McGill University fusion d’information ; organized by the Applied Mathematics Labora- • comparaison entre différents paradigmes tory d’estimation ; • sélection de modèles pour les données en Organizer: Tony Humphries (McGill) imagerie par résonance magnétique fonction- Invited speakers: D. Breda (Universita degli nelle ; Studi di Udine), D. Pelinovsky (McMaster), P.-L. • estimation à la source pour les électroencépha- Buono (UOIT), B. Moore (McGill), T. Humphries logrammes. (McGill), R. Wilds (McGill) Number of participants: 18 Ces sujets couvraient différents aspects des pro- This workshop focused on recent developments blèmes souvent rencontrés lors de la reconstruc- in the analysis and computation of lattice, de-

25 CENTRE DE RECHERCHES MATHÉMATIQUES lay and functional differential equations, with Topics in Low-Dimensional Topology particular emphasis on advanced-retarded dif- May 16 – 17, 2005, UQÀM ferential delay equations which define travel- organized by CIRGET ling wave solutions to lattice differential equa- tions, and related problems. It brought together Organizers: Steven Boyer (UQÀM), Olivier researchers with theoretical, computational and Collin (UQÀM) applications interests. Topics covered included Number of participants: 15 determining stability of solutions via pseu- Fifteen mathematicians and students partici- dospectral approximation of characteristic val- pated in this two-day workshop held at UQÀM. ues, bifurcations of travelling wave solutions Five of the six talks focused on the topology in discrete NLS lattices, and unfolding of lo- and geometry of 3-manifolds and one other on cal bifurcations in equations modelling biolog- 4-dimensional topology. The two main themes ical phenomena. Also covered were travelling were applications of geometric methods in 3- waves and propagation failure in problems with manifolds and the contact topology in dimen- inhomogeneous diffusion, as well as numerical sion 3. computation of travelling waves in lattice differ- ential equations including model problems and The speakers and their titles were: problem truncation. • Joseph Masters (SUNY Buffalo), Quasi- Analysis Day Fuchsian surfaces in hyperbolic knot-manifolds April 29, 2005, CRM • Baptiste Chantraine, (UQÀM), Isotopies lengen- organized by the Mathematical Analysis Labo- driennes et cobordismes lagrangiens ratory • Xingru Zhang, (SUNY Buffalo), Virtual fibring of Montesinos link complements Organizers: Thomas Ransford (Laval), Chris- • David Gay, (UQÀM), Constructing singular Lef- tiane Rousseau (Montréal), Alina Stancu (Mont- schetz pencils and fibrations réal), Galia Dafni (Concordia), Dmitry Jakobson • Olga Plamenevskaya, (MIT), Khovanov homol- (McGill) ogy, Heegaard Floer invariants, and contact struc- Speakers: T. Kaczynski (Sherbrooke), A. Koko- tures tov (Concordia), F. Nazarov (Michigan State) • Michel Boileau, (Toulouse 3), Finiteness of 3- Number of participants: 27 manifolds and non-zero degree mappings. Le laboratoire a commencé ses activités seule- ment en 2003-2004. Le programme scientifique de l’année 2003-2004 a été remarquable tant Analytic Number Theory Conference par sa qualité que par les rapprochements qu’il May 19 – 21, Université Laval a permis entre des membres qui se connais- organized by CICMA saient peu. Ce laboratoire est celui qui a le plus de membres. Ses membres sont dispersés dans Organizers: Jean-Marie De Koninck (Laval), toutes les universités québécoises, ce qui force Claude Levesque (Laval) différents sous-groupes à travailler en paral- Speakers: C. Ballot (Caen), W. Banks (Missouri), lèle. Pour remédier à ce problème, nous avons J. Friedlander (Toronto), V. Garcia (Puerto Rico), commencé en 2004-2005 la tradition d’une jour- A. Granville (Montréal), H. Kadiri (Montréal) , S. née d’analyse à laquelle seront conviés tous les Louboutin (Luminy), F. Luca (Morelia), R. Murty membres. À court terme il n’y a pas lieu de faire (Kingston), C. Pomerance (Dartmouth), L. Sza- venir beaucoup de conférenciers de l’extérieur lay (Ouest-Hongrie) mais plutôt de laisser la parole aux membres. Le Number of participants: 43 format incluait des conférences d’une heure et La conférence portait sur une grande variété des conférences d’une demi-heure, en évitant les de thèmes en théorie analytique des nombres, conférences en parallèle. dont les fonctions arithmétiques, les séries de Dirichlet, les courbes elliptiques, la méthode du crible, les sommes de diviseurs, les problèmes du type Waring, les fonctions zêta de Dede- kind, les équations de Pell simultanées, le théo- rème de Polya-Vinogradov, les petits intervalles contenant des premiers en progression arithmé- tique. Le principal objectif de cette rencontre

26 GENERAL PROGRAM

était la mise en commun de différents résultats par François Brisebois de Statistique Canada et d’actualité en théorie analytique des nombres. portait sur l’analyse de données sur la santé, re- cueillies à l’aide d’enquêtes à plans complexes Quatri`eme colloque francophone sur les alors que le deuxième, était animé par Olivier sondages Sautory de INSEE-CEPE et portait sur les pro- May 24 – 27, 2005, Université Laval cédures SAS d’échantillonnage et d’analyse de Official Meeting of the Société Française de données d’enquête. Le colloque comme tel a dé- Statistique (SFdS), supported by the Statistics buté le mercredi 25 mai au matin par un ex- Laboratory posé sur le rôle des méthodologistes dans la ges- tion de la qualité par Gordon Brackstone, pré- Chair of the scientific committee: Louis-Paul sident de l’association internationale des statis- Rivest (Laval) ticiens d’enquêtes, une section de l’Institut inter- Chair of the organizing committee: Louise national de la statistique. Une centaine de com- Bourque (ISQ) munications y ont été présentées, 70 libres et 30 Speakers: J. Domingo-Ferrer (Rovira i Cir- sur invitation. La plénière de clôture, où M. et gili de Tarragone, Catalogne), J. Baulne (ISQ), Mme Mizrahi de l’ARgSES dressaient un histo- L. Des Groseillers (ISQ), E. Gagnon (ISQ), P. rique des enquêtes de santé en France, s’est ter- St-Cyr (Statistics Canada), R. Orok (Statistics minée le vendredi 27 mai à 17h00. Canada), P. Collomb (INED), M.-C. Tremblay (Environment Canada), S. Cotter (Office fédéral Plusieurs séances ont porté sur des dévelop- de la statistique, Suisse), P. Gauthier (Statis- pements de statistique théoriques motivés par tics Canada), F. Dupont (INSEE), E. Graf (Of- l’analyse de données d’enquête. Le bootstrap, fice fédéral de la statistique, Suisse), E. Rancourt le lissage et l’utilisation de modèles statistiques (Statistics Canada), M. Thompson (Waterloo), A. pour les données d’enquête y ont été abordés. Saïdi (Statistics Canada), C. Boudreau (Medi- Les enquêtes de santé ont également fait l’objet cal College of Wisconsin), N. Lavigne (Statis- de nombreuses communications ; on y a traité du tics Canada), R. Morrison (Statistics Canada), choix du mode de collecte, et de la pondération S. Giroux (Statistics Canada), M.-E. Tremblay des données, entre autres. La plénière de clôture (ISQ), N. Plante (ISQ) R. Courtemanche (ISQ), D. présentait un historique des enquêtes de santé Joye (SIDOS), R. Silberman (LASMAS-CNRS), L. en France. Des thèmes propres à la statistique Bourque (ISQ), R. Barnabé (Statistics Canada), officielle tels la gestion de la qualité, le recense- A. Davison (EPFL), C. Sårndal, J.-D. Opsomer ment, l’utilisation de données administratives et (Iowa State), J.-F. Beaumont (Statistics Canada), le respect de la confidentialité des informations P. Bernard (Montréal), D. Lievesley (UNESCO) fournies par les répondants ont été traités dans Number of participants: 240 de nombreuses sessions. Une séance sur l’accès, par les chercheurs, aux micros données confi- L’organisation du Colloque de Québec a été as- dentielles dans les pays francophones s’est ter- surée par l’Institut de la statistique du Qué- minée par une visite du laboratoire CIQSS-Laval bec (ISQ) et l’Université Laval, en collaboration où les chercheurs de l’université Laval ont accès avec Statistique Canada, l’Association des statis- aux données d’enquête de l’Institut de la statis- ticiennes et statisticiens du Québec (ASSQ), la tique du Québec et de Statistique Canada. Société statistique du Canada (SSC), le Centre de recherches mathématiques et l’Association inter- Les organisateurs ont reçu de nombreux té- nationale des statisticiens d’enquête (de l’Insti- moignages d’appréciation tant pour les aspects tut international de statistique). scientifiques qu’organisationnels du colloque. En effet, le programme scientifique chargé et fort Plus de 240 participants, venant de l’Europe et relevé était accompagné d’un programme social des Amériques, ont participé à ce colloque qui fort intéressant. Quant aux conférences présen- a duré quatre jours. Deux ateliers portant sur tées dans le cadre du colloque, elles se retrouve- des méthodes statistiques spécifiques à l’analyse ront dans les actes qui seront publiés chez Du- de données d’enquête complexes ont été présen- nod en 2006, assurant ainsi une pérennité à la re- tés le mardi 24 mai. Environ 75 participants ont cherche qui y a été présentée. pris part à ces ateliers. Le premier était animé

27 CENTRE DE RECHERCHES MATHÉMATIQUES

CRM-ISM Colloquium Series

The CRM, together with the Institut des sci- January 7, 2005: Vladimir Remeslennikov ences mathématiques (the Québec university (UQÀM) et Ilya Kazatchkov (Omsk) graduate mathematics consortium), runs two Free Partially Commutative Groups Montréal colloquium series, one in mathematics December 10, 2004: Vladimir Korepin (SUNY and another in statistics (the latter jointly with Stony Brook) GERAD). These series offer during the academic Quantum Correlations and Number Theory year survey talks by distinguished mathemati- cians and statisticians on topics of current inter- December 3, 2004: Yuri Gurevich (Microsoft) est. What is an Algorithm? November 26, 2004: Bruce Reed (McGill) CRM – ISM Mathematics Colloquium Routed Routing and Graph Minors

Coordinators: Octavian Cornea (Montréal), November 19, 2004: Alejandro Adem (UBC) Dmitry Jakobson (McGill). Periodic Complexes and Group Actions April 22, 2005: Isadore Singer (MIT) November 5, 2004: Claude Le Bris (ENPC) The Geometry of Twisted K-Theory Flots généralisés de solutions pour des équations dif- férentielles déterministes et stochastiques à coeffi- April 15, 2005: Kaleem Siddiqi (McGill) cients irréguliers Medial Integrals for Shape Analysis October 22, 2004: Jean-Pierre Gazeau (Paris VII) April 8, 2005: Fabio Bagarello (Palermo) États cohérents et quantification de systèmes simples Relations between Multi-Resolution Analysis and Quantum Mechanics: Applications to the Fractional October 15, 2004: Stephanos Venakides (Duke) Quantum Hall Effect The Nonlinear Analogues of the Fourier Transform, Steepest Descent and Eikonal Analysis April 1, 2005: Mark Haiman (UC Berkeley) Macdonald Polynomials October 8, 2004: Ronald Fintushel (Michigan State) March 18, 2005: Alexander Its (IUPUI, Indianop- Lagrangian Tori in 4-Manifolds olis) On the Asymptotic Analysis of Toeplitz Determi- October 1, 2004: John Harnad (Concordia) nants via the Riemann – Hilbert Method Random Matrices, Orthogonal Polynomials and In- tegrable Systems March 11, 2005: Krystyna Kuperberg (Auburn) Wild and 2-Wild Trajectories September 24, 2004: Paul Schupp (Illinois, Ur- bana Champaign) March 4, 2005: Matt Gursky (Notre Dame) The Uniform Membership Problem, Foldings and Some Fully Nonlinear Equations in Geometry Polynomial Time February 18, 2005: Askold Khovanskii (Toronto) September 17, 2004: Pengfei Guan (McGill) Insolvability of Equations in Finite Terms Convexity of Solutions of Geometric Nonlinear Par- February 11, 2005: Steven Lu (UQÀM) tial Differential Equations Positivity Theorems and the Structure of Compact Complex Manifolds CRM – ISM – GERAD Statistics Collo- quium February 4, 2005: Stephan De Bièvre (Lille I) Chaos quantique: au-delà du théorème de Coordinators: Christian Léger (Montréal) main- Schnirelman coordinator, Pierre Duchesne (Montréal), Brenda January 28, 2005: David Bryant (McGill) MacGibbon (UQÀM), Arush Sen (Concordia), How can a Mathematician Cope with Phylogenetic Russ Steele (McGill). Uncertainty? April 8, 2005: Hira Koul (Michigan State) January 21, 2005: Jozef Dodziuk (CUNY) Goodness-of-Fit Testing in Interval Censoring Case 1 Elliptic Difference Operators on Graphs March 18, 2005: Jeffrey S. Rosenthal (Toronto) January 14, 2005: Haynes Miller (MIT) Adaptive MCMC: A Java Applet’s Perspective Elliptic Moduli in Algebraic Topology

28 GENERAL PROGRAM

March 11, 2005: Ricardas Zitikis, (Western On- On the Minimax Optimality of Block Thresholded tario) Wavelet Estimators with Long Memory Data Comparing Points in Multi-Dimensional Spaces, Novembere 12, 2004: Donald Dawson (Carleton Even When They Are Random et McGill) March 4, 2005: Debbie Dupuis (HEC) 2004 CRM-Fields Prize Ozone Concentrations: a Robust Analysis of Multi- Stochastic Dynamics of Evolving Populations variate Extremes November 5, 2004: Christopher Field (Dal- February 25, 2005: Changbao Wu (Waterloo) housie) Empirical Likelihood Approach to Calibration with Robustness Issues in Models for Molecular Evolution Survey Data October 29, 2004: Corinne Berzin (Grenoble II) February 18, 2005: Edward L. Ionides (Michi- Théorèmes centraux limites pour des fonctionnelles gan) non linéaires de processus gaussiens et applications Infectious Diseases: Data Analysis via Continuous October 22, 2004: Randy Sitter (Simon Fraser) Time Population Models 2004 CRM-SSC Prize February 11, 2005: Angelo J. Canty (Toronto) Resampling in Complex Surveys Finding Differentially Expressed Genes from October 15, 2004: Qihe Tang (Concordia) Affymetrix Microarray Data Asymptotic Ruin Probabilities in the Presence of February 4, 2005: Richard Cook (Waterloo) Stochastic Returns on Investments Some Robust Methods for Studies Involving Recur- October 8, 2004: Adrian Raftery (Washington) rent Events La prévision météorologique probabiliste January 25, 2005: Hao Yu (Western Ontario) October 1, 2004: Xin Gao (York) Residual Processes of GARCH Models and Their Ap- A Unified Nonparametric Approach for Unbalanced plications Factorial Design December 3, 2004: Subhash Kochar (ISI) September 24, 2004: David Haziza (Statistique Dependence Orderings for Order Statistics and Canada) Records Approche par modèle de non-réponse pour l’inférence November 26, 2004: Weidong Tian (Waterloo) en présence de données imputées Stochastic Volatility Models: A Large Deviation Ap- September 17, 2004: Steven X. Wang (York) proach Weighted Likelihood Estimation November 19, 2004: Linyuan Li (New Hamp- shire)

29 Multidisciplinary and Industrial Program MULTIDISCIPLINARY AND INDUSTRIAL PROGRAM

HE main vehicles for the CRM’s efforts in this area are the research networks to which it belongs. TPrincipally, MITACS, a national network focusing on the mathematics of information technology and complex systems, and the National Program on Complex Data Structures (NPCDS). The reports are presented in the language in which they were submitted.

Activities of the Multidisciplinary and Industrial Program

Workshop on Stochastic Networks ical theory for stochastic networks. A large por- July 16 – 26, 2004, CRM tion of the talks related to various challenges that are arising in the wireless networks set- Organizers: Peter Glynn (Stanford), George Ke- ting, where key issues include the spatial vari- sidis (Penn State), Donald A. Dawson (McGill), ation, bandwidth limitations, and the need to Raj Srinivasan (Saskatchewan) generate distributed control policies. The format Number of participants: 90 of the conference, in which only four one hour In July 2004, within the framework of its Mul- talks were scheduled over each of the six days tidisciplinary and Industrial Program, the CRM (with the exception of the Wednesday session, hosted a workshop on Stochastic Networks in which only three talks were scheduled), lent with three different activities. The Madison-style itself to an environment in which participants Stochastic Network Conference (SNC) included were able to pursue significant technical interac- two satellite workshops. The two-day workshop tions. In spite of the lack of opportunity to give on Economics of Communication Networks pre- full contributed talks, the meeting attracted a ceded the SNC, while the three-day Call Cen- significant number of attendees, in large part be- tre Workshop (CCW), partially funded by the cause it provided an opportunity for unhurried Wharton Financial Institutions Center, was at technical exchanges amongst all participants. the tail end of the SNC. It should be noted that Alcatel provided finan- cial support to the meeting, in recognition of Workshop on Economics of Communication the relevance of the research agenda to its core Networks mission. A number of industrial participants at- Organizer: George Kesidis (Penn State) tended the meeting. In addition, one of the ma- jor journals in the area, Queuing systems: Theory This workshop attracted some of the major fig- and applications, contacted the organizer subse- ures who are working on increasingly important quent to the meeting to request that a special economic issues related to the theory of commu- invited issue, consisting of papers based on the nication networking. In particular, two very in- talks given at the meeting, be put together. This teresting talks on the role of economic incentives special issue is being pursued, and publication for emerging peer-to-peer networks drew a great is expected late in 2005. This journal’s interest in deal of discussion during the breaks. Lively dis- pursuing such a special issue is a clear testimony cussions also broke out during several talks and to the quality of the talks offered as part of the participants expressed the value of the clarifica- Stochastic Networks Conference. tion of issues that was achieved in this some- times confusing area where a diversity of issues need to be considered simultaneously. For exam- Call Center Workshop ple, Organizer: Raj Srinivasan (Saskastchewan) • the roles and mathematical definitions of “fairness” and how they might be interpreted To recognize the recent flurry of research ac- as regulation in a communication network tivities in the call center area, the last day of that is run more according to free market dy- the SNC was designated as a joint activity with namics than in current practice; the CCW. There were four talks on that day • how security, pricing & billing, and quality-of- of the SNC, most of them being concentrated service may be interrelated. on staffing large call centres using fluid models. This joint activity was very well received by the Stochastic Networks Conference eighty-two people in attendance. The CCW con- Organizer: Peter Glynn (Stanford) tinued for another two days with twelve talks. There were twenty-eight to forty-two people in This meeting attracted the major figures who are attendance for the two-day activity. The talks contributing to the development of a mathemat- covered a wide range of topics including queu-

31 CENTRE DE RECHERCHES MATHÉMATIQUES ing network with time varying rates, statisti- velopment, design, and testing; to establish fu- cal analysis of call centres, workforce planning ture biomedical research priorities; and finally, and profit maximization, revenue management to create new opportunities for research col- through cross-selling and managing learning laborations between industry, government and and turnover in employee staffing. The work- academia. shop also included a tutorial on call centers. During this workshop, industrial, academic One of the highlight of the talks was the pre- and governmental organizations discussed and sentation from Chantal Gagné, the General Man- identified keys research areas in the field of (but ager of Bell Canada Holdings, who discussed not limited to): several challenges involved in the management Drug development/design/testing of call centers at Bell Canada. In particular, she emphasized the difficulties facing the industry • design issues; in forecasting call volume over the eighteen • use of signaling networks to aid in intelligent months planning horizon and training work drug design; force during that period. Active participation • in vitro drug testing; from the audience resulted in lively and pro- • diabetes drug design; ductive discussions. Besides the annual two-day • analysis, interpretation and integration of Call Center Forum run by the Wharton Finan- biomedical data. cial Institutions Centre for their industrial partic- ipants, the CCW hosted by CRM is the first ma- Medical devices jor workshop on call centres. Based on the feed- • techniques/devices for arrhythmia detection back we have received from the participants, this and treatment; workshop was a very successful one. • analysis of medical imaging (mri, cat scan, pet, etc.); MITACS Biomedical Workshop • devices for the treatment of diabetes, e.g., pro- January 19 – 20, 2005, CRM grammable implanted pumps; • organised by MITACS analysis of gene chip data; • analysis, interpretation and integration of Organizers: Leon Glass (McGill), Michael biomedical data. Mackey (McGill), Jack Tuszynski (Alberta), David Ritscher (Medtronic), Jeffrey Saltzman Furthermore, issues concerning public health (Merck), Colin Hill (Gene Network Sciences), were raised. For instance: device manufactur- Alain Vinet (Montréal), Gerda de Vries (Alberta), ers, drug companies, large data collections from Kevin Hall (National Institutes of Health), Jian- huge sets, lack of incentive from drug or device hong Wu (York), Thomas Hillen (Alberta) manufacturers to develop studies addressing is- Speakers: R. McInnes (Institute of Genetics), S. sues. Bull (Toronto), A. Atoyan (Montréal), L. Greller Participants had the opportunity to share their (Biosystemix), M. Weiner (Biophan Technolo- academic interests and propose new collabora- gies), J. Tuszynski (Alberta), J. Saltzman (Merck), tions. Also, various biomedical internship possi- C. Hill (Gene Network Sciences), K. Worsley bilities were proposed. (McGill) Number of participants: 47 Launching of Aeronautics Cooperation CRM – CRIAQ – MITACS A number of MITACS research projects are cur- January 20, 2005, Dorval rently involved in biomedical research with sci- entists and partners drawn from across Canada. On January 2005, at the initiative of CRM and Our experience from both research projects and with the help of CIRANO’s Director, the first networking activities demonstrates that there is exploratory day between mathematicians and considerable interest in this area among both in- the Canadian Aeronautical Industry was held dustry and government organizations. at the Bombardier offices in Dorval. Presenta- The main objectives of the workshop were: to tions were given by the Advanced Research Di- bring together individuals from industry, gov- rector at Bombardier, Bombardier researchers, ernment and academia who are interested in Pratt & Whitney representatives, MITACS Direc- biomedical research; to share experiences from tor and CEO, CRIAQ’s president, and CRM di- industry and government participants on key is- rector. Also present were Michel Delfour from sues relating to medical devices and drug de- CRM and Neil Stewart from DIRO (Montréal).

32 MULTIDISCIPLINARY AND INDUSTRIAL PROGRAM

This event was held in preparation to the The topics discussed in the plenary session were: Toronto MITACS meeting on Aeronautics. funding agencies, universities and the chal- lenges of interdisciplinary research and the sci- entific collaborations between mathematicians Workshop on Computational Biology in the and biologists. During the first session, the main Post-Genomics Era themes were: the challenge of interdisciplinary March 19 – 20, 2005, CRM research, what NSERC is doing and should do, the MITACS model and the US model. Scientific committee: Sandrine Dudoit (UC Berkeley), Avner Friedman (Ohio State), Michael Hallet, (McGill), Leah Keshet (UBC), Mark Lewis (Alberta), Normand Mousseau (Mont- Workshop on Latent Variable Models and réal), John Nash (CNRC-ISB), Enrico Purisima Survey Data for Social and Health Sciences (CNRC-IRB), Jamie Stafford (Toronto) and Raj- Research mund L. Somorjai (CNRC-IBD) May 4 – 6, 2005, CRM Steering committee: Barbara Lee Keyfitz (di- NPCDS activity rector, Fields), Ivar Ekeland (director, PIMS), sponsored by the CRM, the NPCDS, the SAMSI François Lalonde, (director, CRM), William and Statistics Canada Cowley (Senior Program Officer, NRC), Isabelle Blain (Vice-President, CRSNG) Organizers: Mary Thompson (Waterloo), Chris Number of participants: 64 Skinner (Southampton), Paul Biemer (UNC Chapel Hill), Jamie Stafford (Toronto), Milo- The origin of the workshop is the result of long- rad Kovacevic (Statistics Canada), Randy Sitter term discussions between NRC and the mathe- (Simon Fraser), David Bellhouse (Western On- matics institutes, CRM, Fields and PIMS. tario), Roland Thomas (Carleton) Firstly, the workshop was intended to explore Speakers: H.Ariizumi (Wilfrid Laurier), T. As- possible joint research activities between the parouhov (Muthen & Muthen), K.A. Bollen NRC labs and industry on the one hand and (UNC Chapel Hill), Brault, A. Carle (U.S. Cen- researchers in the Canadian universities, espe- sus Bureau), K. Chantala (UNC Chapel Hill), cially those who have developed specific mathe- S. Christ (UNC Chapel Hill), A. Cyr (Statis- matical expertise, on the other hand, on the gen- tics Canada), A. Davies (Statistics Canada), M. eral subject of computational biology (taken in Kovacevic (Statistics Canada), B. Meekins (Bu- a broad sense). Thus the workshop provided an reau of Labor Statistics), B. Muthén (UCLA), opportunity to seek possible common research J. Olsen (Brigham Young), M. Paterson (Sher- interests and complementary methods or points brooke), S. Rabe-Hesketh (UC Berkeley), J.N.K. of view between the two milieux. The ultimate Rao (Carleton), G. Roberts (Statistics Canada), A. goal was to see whether or not there is a gen- Sacker (University College London), C. Skinner uine interest in interacting at a scientific level (Southampton), A. Skrondal (London School of The workshop provided an opportunity to learn Economics), R.D. Wiggins (City University Lon- about foreign experiences, especially in the US don) and in France, where there have been efforts to Number of participants: 65 launch initiatives that have led to the emergence This workshop was part of the contribution of of a genuine “computational community.” the National Program on Complex Data Struc- A further purpose of the workshop was to tures (NPCDS) to the theme year on Latent Vari- broaden the scientific interaction between bi- able Models in the Social Sciences (LVMSS) of ologists and mathematicians, to address biolo- the Statistical and Applied Mathematical Sci- gists’ concern that their models are so simplis- ences Institute (SAMSI) in North Carolina. tic that they will not be challenging to math- The program began with a tutorial by Anders ematics; whether mathematics can provide ap- Skrondal and Sophia Rabe-Hesketh based on proaches to seemingly intractable problems of their recent book, Generalized latent variable mod- biology, and to provide direction to mathemati- elling (Chapman and Hall/CRC). The tutorial cians about new domains that will need study. covered a great deal of ground, including a thor- The main scientific themes of the workshop ough introduction to the author’s framework for were: biomedical data analysis, computational latent variable models, and a variety of interest- structural biology, proteomics and protein mod- ing applications. It was very valuable for both eling and genomics analysis. experts and novices.

33 CENTRE DE RECHERCHES MATHÉMATIQUES

The difficulties in adapting latent variable meth- (École Polytechnique), R. Lohner (George Ma- ods to complex survey data are perhaps best son), G. Malandain (INRIA Sophia Antipolis), appreciated in the context of multi-level mod- M. S. Olufsen (NC State), R. Owens (Montréal), J. els, and Chris Skinner provided an excellent Peirò (Imperial College London), M. Sorine (IN- overview of progress to date in this area. Papers RIA Rocquencourt), D. Steinman (Robarts Re- by Chantala and Suchindran and by Kovacevic search Institute, London, ON), M. Thiriet (IN- and Huang provided further insights into the RIA Rocquencourt), J. Urquiza (Montréal), K. performance of currently available techniques. Worsley (McGill), J.-P. Zolésio (INRIA, Sophia- Bengt Muthén and Tihomir Asparouhov intro- Antipolis) duced Mplus and demonstrated its efficiency Number of participants: 58, including 18 stu- and flexibility for latent variable models. The dents. software is being developed in conjunction with The object of this combined Spring School and leading edge research in social science method- Workshop was to bring together experts of in- ology, and the complex survey project will make ternational stature on several facets of mini- it even more useful. The discussions of the appli- invasive procedures in medicine and surgery cation papers were also greatly enhanced by the and to identify the underlying mathematical and contributions of the Mplus team. computing challenges. The main themes of the The workshop provided an opportunity for a workshop were: review of the accomplishments of the SAMSI • Biology and mechanics of blood flows; theme year on latent variable models, by its • brain imaging and functions; leader, Ken Bollen. • cardiac pump; One gratifying feature of the workshop was the • fluid-structure interactions; high quality of the presentations, and of the • image-based computations; analyses put forward. It is very good for statisti- • imaging, meshing and computing; cians and social scientists each to see something • image processing; of the best of what the other has to offer. • immersed boundaries; • medical devices; • Spring School and Workshop on Mini- mathematical modeling and computer simu- invasive Procedures in Medicine and lation of the circulation and the hearth; • Surgery: Mathematical and Numerical particle flows; • Challenges wall transport. May 16 – 27, 2005, CRM This ambitious project resulted from a sustained sponsored by CRM, MITACS and INRIA and productive collaboration between Marc Scientific committee and organizers: Michel Thiriet (INRIA, France), André Garon (École Delfour (Montréal), André Fortin (Laval), André Polytechnique, Canada) and Michel Delfour Garon (École Polytechnique Montréal), Charles (CRM and DMS, Canada). The importance of Peskin (Courant Inst.), Marc Thiriet (INRIA Roc- such exchanges between France and Canada quencourt) was recognized two years ago by INRIA which Main speakers of the School: Charles Peskin conferred the status of associated group to the (Courant Inst.), Marc Thiriet (INRIA Rocquen- researchers. court) The initiative of holding a Spring School in the Speakers and animators of mini-workshops of days preceding the Workshop proved to be a the School: Miguel Fernandez (INRIA Rocquen- great success; student participation was excel- court), Julie Grant (École Polytechnique Mont- lent and exchanges were useful and animated. réal), Gérard Plante (Institut de Pharmacolo- We had the privilege to have two exceptional gie de Sherbrooke), Grégoire Malandain (INRIA principal speakers whose 12 talks were comple- Sophia-Antipolis), Catalin Fetita (Institut Na- mentary. Charles Peskin (Courant Institute, New tional des Télécommunications) York) is one of the pioneers in the field of mathe- Invited speakers: Y. Bourgault (Ottawa), G.W. matical modeling and in the simulation of flows Burgreen (Mississippi State), L. Cohen (Paris- and the heart. He his also the father of “im- Dauphine), M. Delfour (Montréal), C.R. Ethier mersed boundaries” and of the first valve sim- (Toronto Western Research Institute), C. Fetita ulations. Marc Thiriet (member of CNRS, Labo- (Institut National des Télécommunications), A. ratoire Jacques-Louis Lions, Université Pierre et Fogelson (Utah), A. Fortin (Laval), A. Garon Marie Curie), and principal investigator respon-

34 MULTIDISCIPLINARY AND INDUSTRIAL PROGRAM sible for the REO project at INRIA, Rocquen- ond one on “Molecule transport in vessel walls court, France), is a pneumologist by training as and blood flows.” Finally, Grégoire Malandain well as a mechanical engineer specializing in flu- (INRIA Sophia-Antipolis, Projet Epidaure) and ids. He was a tremendous driving force during Catalin Fetita (Institut National des Télécom- the school, thanks to, in particular, an extraor- munications, Projets Artemis) lead the one on dinarily encyclopedic book of more than 300 “Medical image processing: from vessel wall ex- pages titled “Biology and mechanics of blood tration to surface mesh production.” flows” which was given in pre-publication to The main workshop of the second week brought all participants. This work will be published by together world-renowned specialists around Springer. The theme of his lectures was “From nine of the major themes of the activity. It was input data (biologic, medical, physical, rheolog- a privileged meeting ground for the American, ical) to blood flow numerical simulations.” Canadian and French team, in a very casual These two series of principal lectures of the Québécois ambiance. The participation was sus- school were completed by three afternoons tained until the very last session on Friday. Stu- of thematic mini-workshops. Miguel Fernan- dents interested to give a talk gave their presen- dez (INRIA, Rocquencourt, Projet REO) ani- tations on Wednesday afternoon and at the end mated the one on “Numerical simulations of of the other days. the fluid-structure coupling in physiological ves- Finally, the organizers would like to tank CRM, sels.” Dr. Gérard Plante (Institut de Pharma- INRIA and MITACS for their financial assis- cologie de Sherbrooke) and Julie Grant (École tance. Polytechnique, Montréal) conducted the sec-

35 CRM Prizes CRMPRIZES

CRM – Fields Prize 2005 awarded to David W. Boyd

David Boyd, this tures. His service to the Canadian mathemati- year’s recipient, is cal community includes terms as vice-president one of Canada’s of the Canadian Mathematical Society, chair of leading number the NSERC Mathematics grant selection com- theorists. He has mittee, and Acting Director of the Pacific Insti- made seminal con- tute for the Mathematical Sciences. The recipi- tributions to ana- ent outlines the main themes of his research in lytic number theory, Le Bulletin du CRM, vol. 11, no 1, pp. 14 – 15. noteworthy among which are his ex- The CRM – Fields Prize plorations of the deep connections The Centre de recherches mathématiques and between the Mahler The Fields Institute established the CRM-Fields measure of polynomials and special values of prize in 1994 to recognize exceptional research in their associated L-functions. the mathematical sciences. The recipient is cho- sen by a selection committee made up of mem- Professor Boyd received his B.Sc. from Carleton bers of the Advisory Committee of the CRM and University in 1963, and his M.A. and Ph.D. from the Scientific Advisory Panel of the Fields Insti- the University of Toronto in 1964 and 1966. He tute. has taught at the University of Alberta and the California Institute of Technology, and has been Previous recipients of the prize are H.S.M. (Don- at UBC since 1971 where he is currently Full Pro- ald) Coxeter (1995), George A. Elliott (1996), fessor. He is a winner of the E.W.R. Steacie Prize, James Arthur (1997), Robert V. Moody (1998), a Fellow of the Royal Society of Canada, and has Stephen A. Cook (1999), Israel Michael Sigal won both the Canadian Mathematical Society’s (2000), William T. Tutte (2001), John B. Friedlan- Coxeter – James and Jeffery – Williams Prize lec- der (2002), Edwin Perkins (2003), John McKay (2003), and Donald A. Dawson (2004).

Andr´eAisenstadt Prize 2005 awarded to Ravi Vakil

The 2005 André- clusions is that all Schubert problems are enu- Aisenstadt Prize merative over the real numbers. This has been a was awarded to major goal in the area of real enumerative geom- Ravi Vakil of Stan- etry for at least two decades, and Dr. Vakil has ford University. Af- given a complete solution. ter completing his The exceptional work of Ravi Vakil was recog- B.Sc. and M.Sc. at nized by several prizes and honors, including the University of a NSF Career Fellowship, a Sloan Research Fel- Toronto in 1992, lowship, a Centennial Fellowship and a G. de Dr. Vakil obtained B. Robinson Prize. The Prize was awarded to his Ph.D. from Har- Dr. Ravi Vakil at a ceremony held on April 29, vard University in 2005 at the CRM. The recipient’s research de- 1997 under the su- scription can be found in Le Bulletin du CRM, vol. pervision of Joe Harris. Dr. Vakil then spent a 11, no 1, pp. 2 – 3. year as a postdoctoral fellow at Princeton Uni- versity, and three years at MIT as a C.L.E. Moore The Andr´eAisenstadt Prize Instructor, before becoming an Assistant Profes- sor at Stanford in 2001. Created in 1991, the André-Aisenstadt Mathe- Dr. Vakil works in algebraic geometry, investi- matics Prize is intended to recognize and re- gating the enumerative geometry of projective ward research achievements in pure and applied algebraic curves. His most spectacular work has mathematics by talented young Canadian math- been done in the last years, in his study of degen- ematicians. This prize consists of a $3,000 award erations in a Grassmannian, to solve several old and a medal. The recipient is chosen by CRM’s problems in Schubert calculus. One of his con- advisory committee. At the time of considera-

37 CENTRE DE RECHERCHES MATHÉMATIQUES tion, candidates must be Canadian citizens or (1995), Adrian S. Lewis (1996), Lisa Jeffrey permanent residents of Canada, and no more (1997), Henri Darmon (1997), Boris Khesin than seven years from their Ph.D. (1998), John Toth (1999), Changfeng Gui (2000), The previous recipients of the André-Aisensadt Eckhard Meinrenken (2001), Jinyi Chen (2002), Prize are: Niky Kamran (1992), Ian Putnam Alexander Brudnyi (2003), and Vinayak Vatsal (1993), Michael Ward (1995), Nigel Higson (2004).

CAP – CRM Prize 2005 awarded to Robert C. Myers

The Canadian Asso- His 1999 paper on the dielectric effect for branes, ciation of Physicists known in the community as the Myers effect, has (CAP) and the Centre been highly influential. Guided by duality, he de recherches mathé- constructed a consistent action for branes mov- matiques (CRM) were ing in a background field, and thereby discov- very pleased to an- ered the Myers effect which describes how in the nounce that the 2005 presence of background fields, a stack of branes CAP – CRM Prize in will become polarized and spread out. This deep Theoretical and Math- insight has in turn inspired a number of im- ematical Physics was portant contributions by some of the leading re- awarded to Professor searchers in string theory and quantum gravity. Robert C. Myers of the His very recent work also include significant and Perimeter Institute in Waterloo for his outstand- exciting contributions in a number of different ing contributions to theoretical physics, ranging areas. With his collaborators, Robert Myers has from aspects in gravitational physics to founda- found new constructions of cosmic strings that tional aspects of string theory. can have a profound consequences in finding ex- After a B.Sc. in Applied Physics in Waterloo in perimental support for string theory. This work 1982, Robert Myers went to Princeton Univer- is one of the few genuine “stringy” predictions sity where he completed a M.Sc. (1983) and a that have come out of string theory, and opens Ph.D. (1986) under the supervision of Profes- up the exciting possibility of testing string the- sor M.J. Perry. He then held a postdoctoral po- ory by making astronomical observations. sition at the Institute for Theoretical Physics of The high quality of the research of Professor My- the University of Santa Barbara, and he joined ers has been recognized by several prestigious McGill University in 1989, where he became a research awards, such as the CAP’s Herzberg Full Professor in 2000. Since 2001, he is a Long- Medal, and the first award in the Gravity Re- Term Researcher at the new Perimeter Institute search Foundation Essay Contest (that he won for Theoretical Physics, and also holds a cross- twice). The 2005 CAP – CRM Prize was awarded appointment as a Full Professor in the Physics to Professor Myers at the Annual Congress of the Department at the University of Waterloo. CAP held in June 2005 at Vancouver. Robert Myers has played a pivotal role in the development of string theory and is one of its The CAP – CRM Prize most broad and creative researchers. We high- light here some of his contributions, which have The Centre de recherches mathématiques (CRM) had a tremendous impact in theoretical physics. and the Canadian Association of Physicists His work in the 1980s (some in collaboration (CAP) created in 1995 on the occasion of the 50th with M. Perry) generalized the standard four- anniversary of the CAP, a joint prize in recog- dimensional rotating black hole solution in gen- nition of exceptional achievements in theoretical eral relativity to higher dimensions. These met- and mathematical physics. The prize consists of rics have been the starting point for a number of a $2,000 award and a medal. recent constructions of brane solutions in string Previous winners were Werner Israel (1995), theory. His work on non-critical string theory William G. Unruh (1996), Ian Affleck (1997), J. shed profound new insights into the dimension- Richard Bond (1998), David J. Rowe (1999), Gor- ality of space-time in string theory, by showing don W. Semenoff (2000), André-Marie Tremblay that the string theory made sense in dimensions (2001), Pavel Winternitz (2002), Matthew Chop- other than the critical dimension originally envi- tuik (2003) and JiˇríPatera (2004). sioned. 38 CRMPRIZES

CRM – SSC Prize 2005 awarded to Jiahua Chen

The CRM – SSC Jiahua Chen has also made important profes- Prize in Statistics sional contributions as Associate Editor of the has been awarded Canadian Journal of Statistics and of Quality Tech- this year to Dr. Ji- nology and Quantitative Management, and as a ahua Chen (Profes- member of the Statistical Sciences Grant Selec- sor, Department of tion Committee of the Natural Sciences and En- Statistics and Actu- gineering Research Council. He has been dedi- arial Science, Uni- cated in his service to his department, in par- versity of Waterloo) ticular as Associate Chair for Graduate Stud- for his outstanding ies. He was elected President of the Interna- contributions to the tional Chinese Statistical Association in 2005. statistical sciences. This prize announcement was made at Univer- Within 15 years of sity of Saskatchewan in Saskatoon, site of this his Ph.D. he has made major sustained contri- year’s Annual SSC Meeting. The recipient out- butions to three areas: design of experiments, lines the main themes of his research in Le Bul- inference for mixtures and survey methodology. letin du CRM, vol. 11 no 1, pp. 12 – 13. Professor Chen blends powerful mathematical ability with keen insight into what is important The CRM – SSC Prize statistically. His work combines deep theory and practical methodology for dealing with difficult The Statistical Society of Canada, founded in issues. 1977, is dedicated to the promotion of excellence Apart from his three main research areas, Jiahua in statistical research and practice. This presti- Chen has made notable contributions to many gious award, jointly sponsored by the SSC and other areas including fish surveys, empirical the Centre de recherches mathématiques (CRM), likelihood, fractal images, genetics and robust is given each year to a Canadian statistician in estimation. Professor Chen applies strong tech- recognition of outstanding contributions to the nical and mathematical skill with a remarkable discipline during the recipient’s first 15 years af- aptitude for handling important and practical ter earning a doctorate. Jiahau Chen is the sev- problems. He has published extensively in the enth recipient of the CRM – SSC Prize. Journal of the Royal Statistical Society, Biometrika, Previous winners of the award were Chris- the Journal of the American Statistical Associa- tian Genest (1999), Robert J. Tibshirani (2000), tion, the Annals of Statistics, Biometrics, Statistica Colleen D. Cutler (2001), Larry A. Wasserman Sinica, the Canadian Journal of Statistics and other (2002), Charmaine B. Dean (2003) and Randy Sit- influential journals. ter (2004).

39 CRM Partnership CRMPARTNERSHIP

HE CRM is strongly committed to its national mission and takes measures to ensure that the Tlargest 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 eminent Canadian scientists from various parts of the country; it is present at all important forums where the future directions of the Canadian mathematical sciences are discussed; it urges its organizers to make efforts to ensure the participation of the Canadian specialists in their activities; it organizes and supports scientific events across the country; it collaborates with Canadian institutes, societies and 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 official languages of Canada and it is highly visible on the international scene. In keeping with its national role, it coordinates its activities with the Fields Institute, PIMS, the Canadian Mathematical Society (CMS), MITACS, the Canadian Applied and Industrial Mathematics Society (CAIMS), the Statistical Society of Canada (SSC), the Canadian Association of Physicists (CAP), and other societies as well with other institute abroad.

CRM Partners

The Fields Institute (FI) and the Pacific neers (IEEE), Alcatel, and the Institute for Math- Institute for the Mathematical Sciences ematics and its Application (IMA). (PIMS) In its publishing activities, the CRM is contin- uing its partnership with the American Math- Since the early 1990s two ematical Society (AMS), in particular with its other research institutes have two series of joint publications, the CRM Mono- joined the CRM on the Cana- graph Series and the CRM Proceedings and Lecture dian scene: Toronto’s Fields Notes. It also has two series with Springer, in Institute (FI), and the Pacific statistics and in mathematical physics. The CRM Institute for Mathematical Sci- has exchange agreements with the Fields Insti- ences (PIMS). As well as coordinating their tute, PIMS, MSRI (Mathematical Sciences Re- scientific activities, the three institutes have search Institute), the Institute for Mathematics worked closely on a variety of initiatives, the and its Applications, École Normale Supérieure most important of which has been the Mathe- (France), the Isaac Newton Institute, the Institut matics of Information Technology and Complex des Hautes Études Scientifiques (IHÉS, France), Systems (MITACS). and the Banff International Research Station. Other initiatives involved these institutes, such as the Associations and Professional Societies CRM–Fields prize awarded in recognition of outstanding ac- The CRM maintains close ties with the different complishments in the mathe- professional societies in the mathematical sci- matical sciences in Canada. It ences: CMS, CAIMS, SSC, and CAP. The pres- was created in 1994 and start- ident of the CMS is an ex-officio member of ing in 2006 will become the the CRM Scientific Advisory Committee. CRM CRM–Fields–PIMS prize. The also financially supports a number of initiatives administrative responsibility for this prize will of the CMS, such as the mathematical camps, alternate each year between the three institutes. the Canadian Mathematics Education Forum, as well as the travel grant program for students International Collaboration who attended the joint Canada-France meeting in Toulouse in 2004. Together with the other in- In 2004–2005, on the international scene, the stitutes, the CRM organizes or sponsors special CRM collaborated or received financial assis- sessions at the CMS, CAIMS, and SSC meet- tance from the National Science Foundation ings. The CRM awards a prize each year jointly (NSF), the Banff International Research Station with the SSC; similarly, with CAP, it awards a (BIRS), INSERM in Paris, the Statistical and Ap- prize each year in mathematical and theoretical plied Mathematical Sciences Institute (SAMSI), physics. Moreover, the CRM hosted the 2004 An- the Institute of Electrical and Electronics Engi- nual Meeting of the SSC.

41 CENTRE DE RECHERCHES MATHÉMATIQUES

The Mathematics of Information Technol- the recently completed reallocations exercise at ogy and Complex systems (MITACS) NSERC. The program was funded by NSERC for four years for a total of $687,000. An additional MITACS began as a vi- $200,000 has been committed to the program by sion of the three Canadian the institutes. mathematical sciences insti- The National Program was conceived as a model tutes. They envisioned a pan- for a national network in the statistical sciences, Canadian network of projects in partnership with the mathematics institutes. each focused on using sophis- The broad goal of the proposal is to foster na- ticated mathematical tools for tionally coordinated projects with substantial in- modeling industrial problems teractions with the large community of scientists in key sectors of the Canadian involved in analysis of complex data sets, and economy. MITACS was officially launched on to establish a framework for national network- February 19, 1999. By March 1999, all 21 initial ing of research activities in the statistical com- research projects were underway. munity. MITACS leads Canada’s effort in the genera- The original proposal targeted the development tion, application and commercialization of new and application of statistical methods for the mathematical tools and methodologies within a analysis of data obtained from complex survey world-class research program. The network ini- sample designs and longitudinal biological, epi- tiates and fosters linkages with industrial, gov- demiological and medical studies. More specific ernmental, and not-for-profit organizations that objectives of the program include the develop- require mathematical technologies to deal with ment of collaborations between university and problems of strategic importance to Canada. MI- extra-university researchers, and the provision TACS is driving the recruiting, training, and of training for graduate students in important placement of a new generation of highly math- scientific areas through these collaborations. ematically skilled personnel that is vital to Canada’s future social and economic well being. MITACS networks academia, industry and the NPCDS Projects public sector to develop cutting edge mathemat- Statistical Methods for Complex Survey Data ical tools vital to a knowledge-based economy. Project Leader: Changbao Wu (Waterloo) The only Network of Centres of Excellence Canadian Consortium on Statistical Genomics (NCE) for the mathematical sciences, MITACS Project Leader: Rafal Kustra (Toronto) currently has 305 scientists, 611 students and 169 Data Mining with Complex Data Structures partner organizations working on 32 ongoing Project Leaders: Hugh Chipman (Acadia), Anto- projects, involving 48 Canadian universities. nio Ciampi (McGill), Theodora Kourti (McMas- To improve Canada’s international competitive- ter), Helmut Kröger (Laval) ness, MITACS research focuses on five key sec- Design and Analysis of Computer Experiments tors of the economy: for Complex Systems • biomedical and health; Project Leader: Derek Bingham (Simon Fraser) • environment and natural resources; Forests, Fires and Stochastic Modeling • information processing, risk and finance and Project Leaders: John Braun (Western Ontario), communication; Charmaine Dean (Simon Fraser), Dave Martell • networks and security. (Toronto)

MITACS Inc. is a federally incorporated not-for- profit society formed to administer the MITACS NPCDS Workshops Network of Centres of Excellence. NPCDS/SAMSI Workshop on the Design and Analysis of Computer Experiments for Com- National Program on Complex Data Struc- plex Systems tures (NPCDS) Banff, Alberta, July 13–17, 2004 Organizers: Jim Berger (Duke, SAMSI), Derek This initiative was developed in partnership Bingham (Simon Fraser), Randy Sitter (Simon with the three mathematical sciences insti- Fraser), Jamie Stafford (Toronto, NPCDS), Will tutes and the reallocations committee during Welch (UBC)

42 CRMPARTNERSHIP

Workshop on Missing Data Problems AARMS Scientific activities Fields Institute, Toronto, August 5-6, 2004 CMS/CAIMS Summer 2004 Meeting Organizers: Richard Cook, Don McLeish (Water- Dalhousie University, June 13–15, 2004 loo) Sessions organized by AARMS: • Algebraic Topology Workshop on Data Mining Methodology and Organizers: Keith Johnson (Dalhousie), Renzo Applications Piccinini (Milano) Fields Institute, Toronto, October 28-30, 2004 • Graphs, Games and the Web Organizers: Hugh Chipman (Acadia), Antonio Organizer: Richard Nowakowski (Dalhousie) Ciampi (McGill), Michael Vainder (Generation • Nonlinear Dynamics in Biology and Medicine 5) Organizer: Shigui Ruan (Dalhousie and Mi- Workshop on Latent Variable Models and Sur- ami) vey Data for Social and Health Sciences Re- • Hopf Algebras and Related Topics search Organizers: Yuri Bahturin (Memorial), Mar- CRM, May 4–6, 2005 garet Beattie (Mount Allison), Luzius Grunen- Organizers: Mary Thompson (Waterloo), Chris felder (Dalhousie), Susan Montgomery Skinner (Southampton), Paul Biemer (UNC (Southern California), Earl Taft (Rutgers) Chapel Hill), Jamie Stafford (Toronto), Milo- • 16th Canadian Symposium on Fluid rad Kovacevic (Statistics Canada), Randy Sitter Organizers: Richard Karsten (Acadia), Serpil (Simon Fraser), David Bellhouse (Western On- Kocabiyik (Memorial) tario), Roland Thomas (Carleton). A description AARMS Workshop on Symbolic Computation of this activity can be found in page 33 Dalhousie, June 16, 2004 Workshop on Forest Fires and Point Processes Organizers: Alan Coley (Dalhousie), Robert Mil- Fields Institute, Toronto, May 24–28, 2005 son (Dalhousie), Mark Fels (Utah State) Organizers: W. John Braun (UWO), David Martel International Conference on Nielsen Theory (Toronto), Rick Schoenberg (UCLA) and Related Topics Atlantic Association for Research in the Memorial University of Newfoundland, June Mathematical Sciences (AARMS) 28–July 2, 2004 Organizers: Philip Heath (Memorial), Edward Keppelmann (Nevada) AARMS was founded in March 1997 at a time when the National Network for Research in the International Conference on Nonlinear Dy- Mathematical Sciences was being discussed and namics and Evolution Equations planned. AARMS exists to encourage and ad- Memorial University of Newfoundland, July 6– vance research in all mathematical sciences, in- 10, 2004. cluding statistics and computer science, in the Organizers: Andy Foster (Memorial), Brian Slee- Atlantic region. In addition, AARMS acts as a man (Leeds), Jianhong Wu (York), Yuan Yuan regional voice in discussions of the mathemat- (Memorial), Xiaoqiang Zhao (Memorial), Xingfu ical sciences on a national level. Since its incep- Zou (Memorial) tion, AARMS has played an important role in the 2004 AARMS Summer School research activities in the Atlantic region, spon- Memorial University of Newfoundland, July 12– soring or co-sponsoring numerous meetings and August 16, 2004 workshops. In the summer of 2002, AARMS ini- Director: Edgar Goodaire (Memorial) tiated an annual Summer School for graduate students and promising undergraduates. APICS 2004: AARMS Symposium on Func- AARMS is grateful to Canada’s three mathemat- tional Analysis and Operator Algebra ical institutes, the Centre de recherches mathé- University of New Brunswick, Saint John, Octo- matiques, the Fields Institute, and the Pacific ber 17, 2004 Institute for Research in the Mathematical Sci- Organizers: Dan Kucerovsky (UNB Fredericton), ences as well as Acadia University, Dalhousie Andrew Toms (UNB Fredericton) University, Memorial University, and the Uni- East Coast Combinatorics Conference 2005 versity of New Brunswick (Fredericton) for pro- Lord Beaverbrook Hotel, Fredericton, January viding funding for its activities. 22, 2005 Organizers: David Bremner (UNB Fredericton), Hugh Tomas (UNB Fredericton)

43 CENTRE DE RECHERCHES MATHÉMATIQUES

Quantum Gravity Workshop The following research conferences, workshops, University of New Brunswick, Fredericton, and mini conferences were made possible April 28–30, 2005 through sponsorship by CRM: Organisateurs: Arundhati Dasgupta (UNB Fred- CRM–University of Ottawa Distinguished Lec- ericton), Jack Gegenberg (UNB Fredericton), ture Series Viqar Husain (UNB Fredericton) The series features talks by prominent mathe- maticians from Canada and abroad on topics at Academic Partners the forefront of today’s mathematical research. September 10, 2004: Barbara Lee Keyfitz (Hous- All this activity rests on a solid base of cooper- ton) ation with universities in the region, in partic- Why Are Multidimensional Conservation Laws So ular the Montréal universities, and most partic- Difficult? ularly the Université de Montréal, whose sup- port for the CRM has been unfailing. The Uni- Lie Theory Workshop versité de Montréal releases five of its faculty March 5–6, 2005, members to work at the CRM each year, and the Organizers: Erhard Neher (Ottawa), Wulf Ross- support of these faculty members is an essential mann (Ottawa) asset for the CRM’s scientific activities. There is Network for Computing and Mathematical in addition a regular program of teaching release with the other Montréal universities, bringing Modeling (ncm2) the equivalent of another two positions to the The CRM is one of founding members the CRM each year. On an ad-hoc basis linked to the the Network for Computing and Mathematical theme program, the CRM has also been arrang- Modeling, ncm , a collaboration which allows ing release of research personnel from nearby 2 the network to respond to the needs of industry universities such as Laval, Sherbrooke, Queen’s in a large number of fields related to a common and Ottawa. The partnerships of the CRM with area of computing and mathematical modeling, the other research institutes in the Montréal area mostly around five major themes: risk manage- have been very profitable. ment, information processing, imaging and par- With the financial support of the Université allel computing, transport and telecommunica- de Montréal, McGill University, Université de tions, health and electronic commerce. Québec à Montréal, Concordia University, and The five centres that established the network Université Laval as well as grants from Fonds de were the CRM, the Centre de recherche en cal- recherche québécois sur la nature et les technolo- cul appliqué (CERCA), the Center for Interuni- gies (FQRNT) of Québec and of NSERC, CRM fi- versity Research and Analysis on Organizations nances the activities of the eight laboratories rep- (CIRANO), the Center for Research on Trans- resenting the most active branches of the mathe- portation (CRT), and the Group for Research in matical sciences. These laboratories are the scene Decision Analysis (GERAD). Since then, three of scientific vitality par excellence and serve to new members joined the network: the Cooper- feed the national and international scientific pro- ative Centre for Research in Mesometeorology grams of the CRM. Please refer to the chapter (CCRM), the Centre de Recherche Informatique “Research Laboratories” for reports describing de Montréal (CRIM) and the Institut National de the activities of each of these laboratory. la Recherche Scientifique-Énergie, Matériaux et Association with University of Ottawa Télécommunications (INRS-EMT).

In 2003, the Department of Mathematics and Laboratoires universitaires Bell (LUB) Statistics became a member of the Centre de The CRM is an active participant in the ncm ’s recherches mathématiques (CRM). In partner- 2 Laboratoires universitaires Bell, part of a joint ship with the University of Ottawa, the CRM project between the ncm and Bell. The labora- co-finances postdoctoral fellowships, a series 2 tories aim at creating innovations in the field of CRM–University of Ottawa conferences and of multimedia research and applications (mainly teaching releases so that University of Ottawa interactive applications aimed at the general faculty members can undertake research collab- public, electronic commerce applications and orations with colleagues in the CRM’s laborato- new generations of evolved networks) as well as ries or to participate in CRM scientific activities.

44 CRMPARTNERSHIP at promoting the training of a highly qualified, Neuro-imagerie Québec” (RNQ) under the um- international calibre workforce in these areas. brella of the Institut Universitaire de Gériatrie in Montréal. RNQ, with its 70 researchers, has re- Neuro-imaging initiative in Qu´ebec (RNQ) cently purchased some key equipment in neuro- imaging through a very large grant ($11M). One In recent years, CRM’s PhysNum laboratory of the strongest alliances of CRM within that net- has developed a strong collaborative network work is its association with the INSERM labora- with various partners in neuroimaging in the tory for brain-imaging at Jussieu–La Salpêtrière, Montréal area. This network was formalized Paris (director: Habib Benali). with the constitution of the “Regroupement

Joint Initiatives

The annual meetings of the CMS, SSC and Understanding associations: implications for the de- CAIMS, together with some of their training and sign and analysis of longitudinal surveys promotion activities, are jointly sponsored by the CRM, the Fields Institute, the PIMS and MI- Special Invited Addresses of the Sections TACS. The reports of these activities are presented in • Raymond Chambers (Southampton) the language in which they were submitted. Informative sampling and sampling information. • Daryl Pregibon (Google, Inc.) Annual Meeting of the Statistical Society Graph Mining of Canada • Richard Simon (US National Cancer Institute) May 30 to June 2, 2004, CRM, Université de Key features in the design and analysis of DNA Montréal microarray studies Organizers: Program Committee Chair, Chris- tian Genest (Laval); Local Arrangements Chair, Pierre Robillard Award Address (Best Thesis): Christian Léger (Montréal) Rachel MacKay Altman (Washington) Hidden Markov Models: Multiple Processes and The thirty-second annual Model Selection meeting of the Statistical So- ciety of Canada was hosted Canadian Journal of Statistics Award Address: by the Université de Mont- Belkacem Abdous (Laval), Kilani Ghoudi réal and the Centre de recher- (United Arab Emirates), Bruno Rémillard (HEC ches mathématiques. Over Montréal) 550 registrants participated in Nonparametric Weighted Symmetry Tests the meeting, which featured a wide range of sessions, in- CMS/CAIMS Summer 2004 Meeting cluding workshops of three SSC sections: bio- statistics, survey methods, and business and in- June 13–15, 2004, Dalhousie University dustrial statistics. Meeting Directors: Richard Wood (Dalhousie), The meeting was sponsored by the Centre de Raymond Spiteri (Dalhousie) recherches mathématiques, the Fields Institute, The CMS/CAIMS Summer 2004 Meeting was PIMS, MITACS, Hydro Québec, the Université held at Dalhousie University on June 13–15, de Montréal, Pfizer, Bell University Laborato- 2004, and welcomed 432 participants. The Pub- ries, and the Institut de la statistique du Québec. lic Lecture, entitled “Getting at the truth,” was The scientific program was extremely rich with given by Ed Barbeau on June 14 and was very 109 invited papers and 142 contributed papers. well attended. Among the invited papers, the following ad- Other special events included plenary talks de- dresses are especially noteworthy. livered by: Peter Cameron (Queen Mary), Craig Fraser (Toronto), Mark Lewis (Alberta), Alan C. Presidential Invited Address Newell (Arizona/Warwick), Peter Olver (Min- Kathryn Roeder (Carnegie Mellon) nesota), Frank T. Smith (University College Lon- Discovering haplotype blocks in the human genome don), Mikhail Zaicev (Moscow State) Gold Medal Address The Canadian Mathematical Society was Mary Thompson (Waterloo) pleased to present lectures from their research

45 CENTRE DE RECHERCHES MATHÉMATIQUES prize winners, specifically the CMS Jeffery- Nonlinear Dynamics in Biology and Medicine Williams Lecture, given by Joel Feldman (UBC), Organizer: Shigui Ruan (Dalhousie) and Leo Jonker (Queen’s), who received the first CMS Excellence in Teaching Award. The CAIMS Numerical Algorithms for Differential Equa- Research Prize Lecture was given by Robert D. tions and Dynamical Systems Russell (Simon Fraser) and the CAIMS Cecil Organizer: Tony Humphries (McGill) Graham Doctoral Dissertation Award Lecture Qualitative Behaviour and Controllability of was given by Ramadan Akila (Guelph). Partial Differential Equations A wide variety of fields of interest were repre- Organizer: Holger Teismann (Acadia) sented in the symposia topics detailed below. Most of these are fields that are well represented Topology by researchers in Atlantic Canada: Organizers: Keith Johnson (Dalhousie), Renzo Piccinini (Milano) 16th Canadian Symposium on Fluid Dynamics Topos Theory Organizers: Richard Karsten (Acadia), Serpil Ko- Organizer: Myles Tierney (Rutgers and UQÀM) cabiyik (Memorial) Applications of Invariant Theory to Differen- The NExTMAC Workshop was organized sepa- tial Geometry rately from the meeting and took place on June Organizers: Robert Milson (Dalhousie), Mark 12, 2004. Fels (Utah State) The Meeting Committee would like to acknowl- edge with much thanks the financial support Classical Analysis in honour of David Bor- of the following: Atlantic Association for Re- wein’s 80th Birthday search in the Mathematical Sciences, le Centre de Organizers: Jonathan Borwein (Dalhousie), Mike Recherches Mathématiques, the Fields Institute Overton (Courant Inst.) for Research in Mathematical Sciences, Math- Dynamical Systems ematics of Information Technology and Com- Organizer: Michael A. Radin (Rochester Institute plex Systems, Pacific Institute for the Mathemat- of Technology) ical Sciences, Acadia University, Dalhousie Uni- versity, Memorial University of Newfoundland, Financial Mathematics Mount Allison University, Saint Mary’s Univer- Organizers: Joe Campolieti (Wilfrid Laurier), sity, Maplesoft, Springer, Unisys Canada Inc. David Vaughan (Wilfrid Laurier), Yongzeng Lai, (Wilfrid Laurier) Toulouse 2004 : First Joint Canada-France Meeting of the Mathematical Sciences General Topology and Topological Algebra Organizers: Ilijas Farah (York), Vladimir Pestov July 12–15, 2004, Centre de congrès Pierre (Ottawa) Baudis, Toulouse Scientific Director: Francis Clarke (Lyon I) Graphs, Games and the Web Organizers: Anthony Bonato (Wilfrid Lau- The first Canada-France congress involved the rier), Jeannette Janssen (Dalhousie), Richard three Canadian societies: CMS, CAIMS, SSC, Nowakowski (Dalhousie) and their French counterparts: SMF, SMAI and SFdS. Four hundred and thirty delegates regis- History of Mathematics tered with a significant number of students and Organizer: Thomas Archibald (Acadia) postdoctoral fellows. Several lectures were given in French. Hopf Algebras and Related Topics Organizers: Yuri Bahturin (Memorial), Margaret The plenary lectures were given by Laurent Beattie (Mount Allison), Luzius Grunenfelder Lafforgue (IHES), Grégoire Allaire (École Poly- (Dalhousie), Susan Montgomery (Southern Cali- technique Palaiseau), Maïtine Bergounioux (Or- fornia), Earl Taft (Rutgers) léans), Jonathan Borwein (Dalhousie), David Brillinger (UC Berkeley), Walter Craig (Mc- Mathematical Education Master), Henri Darmon (McGill), Emmanuel Organizers: Richard Hoshino (Dalhousie), John Giroux (ENS-Lyon), Gabor Lugosi (Pompeu Grant McLoughlin (UNB Frederecton) Fabra), Mikhail Lyubich (Toronto), Christophe Reutenauer (UQÀM), Alain-Sol Sznitman (ETH

46 CRMPARTNERSHIP

Zürich), Murad Taqqu (Boston) and Henry cardo Biagioli (UQÀM), Peter McNamara Wolkowicz (Waterloo). Michèle Artigue (Paris (UQÀM), Christophe Reutenauer (UQÀM) VII) gave the education lecture. Approximation Theory There were 16 special sessions: Operator alge- Organizers: Richard Fournier (Dawson), Paul bras, Symplectic topology and geometry, Num- Gauthier (Montréal) ber theory, Spectral and geometric analysis, Par- tial differential equations, Dynamical systems, Arithmetic Geometry Differential Equations and Control, Variational Organizers: Eyal Goren (McGill), Adrian Iovita Analysis and optimization, Stochastic Analysis, (Concordia) Multifractals and long memory processes, the Combinatorial and Geometric Group Theory Probability/Statistics interface, Statistical analy- Organizers: Inna Bumagin (Carleton), Dani Wise, sis of functional data, Numerical analysis, Low (McGill) dimensional topology and geometrical group theory, Mathematical biology, Complex dynam- Commutative Algebra ical systems. Eric Muller (Brock) organized a Organizers: Sara Faridi (Ottawa), Sindi Sabourin panel on the popularization of mathematics. (York), Will Traves (US Naval Academy), Adam Discussions are under way for a second Canada- van Tuyl (Lakehead) France meeting to be held in the summer of 2008 Discrete Geometry in Montreal. Organizers: Karoly Bezdek (Calgary), Rob Calderbank (Princeton), Robert Connelly (Cor- CMS Winter 2004 Meeting nell), Bob Erdahl (Queen’s) December 11–13, 2004, McGill University Meeting Director: Olga Kharlampovich (McGill) Dynamical Systems and Applications Organizer: Michael A. Radin (Rochester Institute The Meeting welcomed 450 of Technology) participants. Following the Groups, Equations, Non-commutative Alge- usual format of the CMS Win- braic Geometry ter Meeting, the program in- Organizers: Olga Kharlampovich (McGill), cluded a wide variety of ses- Alexei G. Myasnikov (McGill) sions, a contributed paper session, plenary and prize lectures, and a public lecture. Most ac- Harmonic Analysis tivities and all scientific talks were held at the Organizer: Galia Dafni (Concordia) Hilton Bonaventure Hotel. The meeting began History of Mathematics with Alexei G. Myasnikov (McGill) delivering Organizers: Thomas Archibald (Acadia), Rich a public lecture entitled, “Complexity of Com- O’Lander (St. John’s), Ron Sklar (St. John’s), putations and Cryptography.” The event, held Alexei Volkov (UQÀM) at the Best Western Hotel Europa, drew a large audience and was followed by a welcoming re- Interactions between Algebra and Computer ception. Science Organizers: Olga Kharlampovich (McGill), Plenary talks were delivered by: Michael Ben- Alexei G. Myasnikov (McGill), Vladimir Shpil- nett (UBC), Persi Diaconis (Stanford), Rostislav rain (CUNY-City College) Grigorchuk (Texas A&M), François Lalonde (Montréal) and Rainer Steinwandt (Karlsruhe). Mathematical Methods in Statistics Organizers: Russell Steele (McGill), Alain Vandal The Canadian Mathematical Society was (McGill), David Wolfson (McGill) pleased to present lectures from their research prize winners, namely, the CMS Coxeter-James Mathematics for Future Teachers Prize Lecture, given by Izabella Laba (UBC), the Organizer: Leo Jonker (Queen’s) CMS Doctoral Prize Lecture, given by Nicolaas Number Theory Spronk (Waterloo) and the CMS Adrien Pouliot Organizers: Chantal David (Concordia), Andrew Prize lecture, given by Jean-Marie De Koninck Granville (Montréal) (Laval). A wide variety of fields of interest were repre- Special Structures in Differential Geometry sented in the symposia topics detailed below. Organizers: Gordon Craig (Bishop’s), Spiro Kari- Algebraic Combinatorics giannis (McMaster) Organizers: François Bergeron (UQÀM), Ric-

47 CENTRE DE RECHERCHES MATHÉMATIQUES

Universal Algebra and Complexity the following: McGill University Provost, McGill Organizers: Jennifer Hyndman (UNBC), Benoit University Dean of Science, McGill University Larose (Concordia), Denis Therien (McGill) Department of Mathematics and Statistics, Cen- tre de recherches mathématiques (CRM), CRM Contributed papers session was organized by Analysis Laboratory, Fields Institute, MITACS William G. Brown (McGill) and Pacific Institute for the Mathematical Sci- The Meeting Committee would like to acknowl- ences. edge with much thanks the financial support of

48 Mathematical Education CENTRE DE RECHERCHES MATHÉMATIQUES

N its mission to promote and stimulate research in the mathematical sciences, at all levels, the CRM Iprovides 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 math´ematiques (ISM)

Le CRM a plusieurs activités communes avec l’ISM, en particulier un programme conjoint de bourses postdoctorales, deux colloques CRM- ISM, un en mathématiques et un en statistique et l’organisation de cours avancés liés à la pro- grammation thématique. Depuis l’été 2003, le Fondé en 1991 par les départements de mathé- CRM participe également au programme de matiques et de statistique des quatre univer- bourses d’été pour les étudiants de premier cycle sités montréalaises, l’Institut des sciences ma- qui permet aux stagiaires postdoctoraux de su- thématiques est un consortium des six uni- perviser ces étudiants. versités québécoises (Concordia, Laval, McGill, l’Université de Montréal, l’UQÀMet l’Univer- CRM-ISM Postdoctoral Fellowships sité de Sherbrooke) qui offrent un programme de doctorat en mathématiques. S’appuyant sur Les bourses postdoctorales CRM-ISM offrent à l’ensemble des chercheurs universitaires qué- des jeunes chercheurs prometteurs la chance de bécois travaillant en sciences mathématiques, consacrer la majeure partie de leur temps à leurs il coordonne un grand nombre de ressources, travaux de recherche. Le processus de sélection aussi bien matérielles qu’intellectuelles, pour at- de ces boursiers est très rigoureux : en orga- teindre la masse critique qui fait de Montréal nisant un seul concours pour les six universi- et du Québec un pôle nord-américain de for- tés membres de l’ISM, l’institut reçoit un grand mation et de recherche en sciences mathéma- nombre de candidatures qui sont ensuite éva- tiques. L’Institut est financé par le ministère de luées par les 150 professeurs membres de l’Ins- l’Éducation du Québec et par les six universités titut. Il s’agit d’un concours extrêmement com- membres. pétitif où environ un candidat sur quarante est Voici un aperçu des activités et programmes de choisi. De plus, le CRM et l’ISM ont débuté l’ISM : l’informatisation du processus de demande de bourse. Dès la prochaine année, les dossiers se- • Coordination et harmonisation des pro- ront acheminés électroniquement, facilitant ainsi e e grammes d’étude de 2 et 3 cycles la gestion de ces nombreuses candidatures et C’est la principale raison d’être de l’ISM, qui réduisant considérablement la quantité de res- vise à réunir les forces de ses départements sources utilisées dans le processus. membres pour en faire une grande école de mathématiques. Ainsi, l’Institut coordonne les Nous ne pouvons surestimer l’importance de ces programmes d’étude de 2e et 3e cycles des uni- stagiaires postdoctoraux dans nos universités : versités membres et favorise la mise en com- ils stimulent et collaborent avec les chercheurs mun des expertises des chercheurs ainsi que bien établis, ils sont une source d’idées nouvelles la circulation interuniversitaire des étudiants. provenant d’autres grands centres, et ils créent • Bourses d’excellence et soutien financier un lien essentiel entre les professeurs et les étu- L’ISM offre aux étudiants et jeunes chercheurs diants, organisant souvent de leur propre gré divers moyens matériels de poursuivre leurs des groupes de travail sur des sujets de pointe. recherches dans les meilleures conditions pos- 2004-2005 Postdoctoral Fellows : sibles. • Activités scientifiques Mostafa Gabbouhy (Ph.D. 2000, Université Ibn L’ISM a depuis sa création mis en place plu- Tofaïl, Maroc) travaille avec Daniel Leroux (GI- sieurs événements qui font désormais partie REF, Laval), et Jean-Loup Robert (GIREF, La- du paysage scientifique québécois. val) sur l’étude d’un modèle de Saint Venant 3- • Promotion des sciences mathématiques D avec couplage de la convection thermique et adaptation de maillage.

50 MATHEMATICAL EDUCATION

David Gay (Ph.D. 1999, UC Berkeley) a travaillé expérience en supervision de recherche. Les avec Vestislav Apostolov (UQÀM), Olivier Col- boursiers cette année étaient : lin (UQÀM) et François Lalonde (Montréal) sur Lory Ajamain (McGill) la topologie symplectique et de contact de basse Responsable de stage : Brian E. Moore dimension. David Gay a pris un poste de profes- seur à l’University of Cape Town en Afrique du Dominique Brunet (Laval) Responsable de stage : Sud, débutant en juillet 2005. Mario Roy Harald Helfgott (Ph.D. 2003, Princeton) a tra- François Charette (Montréal) Responsables de stage : vaillé avec Andrew Granville (Université de Alina Stancu et Octav Cor- Montréal) en théorie des nombres, courbes el- nea liptiques, formes automorphes et combinatoire. Maria Dorokhina (McGill) Harald Helfgott a accepté un poste de professeur Responsable de stage : Pete Clark à l’University of Bristol en Angleterre. Wai Chit Lam (McGill) Alexander Ivrii (Ph.D. 2003, Stanford) travaille Responsable de stage : Emily Dryden sur la topologie symplectique et les courbes Yuedan Liu (McGill) holomorphes-J avec Octav Cornea (Montréal), Responsable de stage : Pete Clark François Lalonde (Montréal) et Iosif Polterovich (Montréal). Clarence Simard (Montréal) Responsable de stage : Harald Helfgott Shannon Starr (Ph.D. 2001, UC Davis) a travaillé en physique mathématique et mécanique statis- tique avec Vojkan Jaksic (McGill) et John Toth “Sur la route” ISM Colloquium (McGill). Shannon Starr est maintenant profes- seur à l’University of California à Los Angeles. October 1–3, 2004, Université de Sherbrooke Organizing committee: Jennifer Bélanger, Syl- Ye Tian (Ph.D. 2003, Columbia) travaille avec vain Bérubé, Julie Dionne, Jean-Philippe Morin, Henri Darmon (McGill) sur la théorie des Charles Paquette, Jean-Simon Sénécal, David nombres. Smith, Anik Trahan. Stephan Tillmann (Ph.D. 2002, Melbourne) tra- Plenary speakers: Michael Barot (UNAM), Joël vaille sur la topologie de basse dimension et les Foisy (SUNY Potsdam), Jean Goulet (Sher- dégénérescences des structures hyperboliques brooke), Claude Le Bris (ENPC) avec Steven Boyer (UQÀM). Speakers: M. Valley (Laval), G. Chênevert (McGill), P. Poulin (McGill), A. Rémillard (Mont- Michèle Titcombe (Ph.D. 1999, UBC) travaille réal), J.-P. Morin (Sherbrooke), D. Smith (Sher- avec Jacques Bélair (Montréal) sur l’analyse ap- brooke), H. Bac (UQÀM), G. Paquin (UQÀM), X. pliquée (analyse asymptotique, méthodes de Provençal (UQÀM). perturbation), l’analyse numérique, la modélisa- Number of participants: 38 tion mathématique, la biologie mathématique, la dynamique des fluides et la dynamique non li- Inspiré par le colloque pan-québécois des étu- néaire. diants, un groupe d’étudiants de l’Université de Sherbrooke a décidé de lancer cette année le Undergraduate Summer Scholarships « Colloque ISM sur la route », un « mini » col- loque pan-québécois qui s’est déroulé du 1 au 3 En collaboration avec le CRM et les professeurs octobre 2004 à l’Université de Sherbrooke. Dans membres de l’ISM, la bourse d’été de premier la tradition des colloques ISM, cette rencontre cycle est offerte par l’ISM aux étudiants de pre- était organisée par des étudiants et était desti- mier cycle prometteurs qui désirent faire un née à l’ensemble de la communauté étudiante stage de recherche en mathématiques et éven- aux cycles supérieurs. En plus de pouvoir pré- tuellement poursuivre des études aux cycles su- senter leurs plus récents travaux, les participants périeurs. La supervision des boursiers d’été est ont eu le plaisir d’assister à quelques conférences assurée par des stagiaires postdoctoraux pour plénières. Le Colloque a attiré une quarantaine lesquels il s’agit généralement d’une première d’étudiants des universités de l’ISM.

51 CENTRE DE RECHERCHES MATHÉMATIQUES

Others Joint Initiatives ESSO/CMS Math Camps 2004 2004 AMQ Mathematics Camp May 23 – June 4, UQÀM The ESSO/CMS Math Camp Program started in 1999 with three camps, and the program has Organizer: Pierre Bouchard (UQÀM) now grown to include at least one camp in every For the fourth year in a row, the Camp was held province. The support received from the spon- at UQÀM. Participants are primarily prizewin- sors enables the Canadian Mathematic Society ners of the Quebec Mathematics Contest, on the to ensure these camps are accessible to students CEGEP level. For about twelve days, they had from across Canada who demonstrate en excel- the chance to meet with mathematicians and lence and interest in mathematics. people who use mathematics in their work. Ev- In 2004, there were thirteen regional math camps ery day, one or more lecturers presented a topic in ten provinces, as well as a national camp, in that would be of interest to the students. Partici- which 350 students participates pants shared in an unforgettable experience with Organized by Thomas Griffiths (Waterloo), the more than twenty other mathematics enthusi- national camp was held at University of West- asts. They also had access at all times to UQÀM’s ern Ontario from June 5 to 12, 2004. The Na- computers. tional Camp is designed primarily for younger Canadian students with at least two years re- 2004 IMO Training Seminar maining in high school and with the potential June 25 – July 4, UQÀM to compete at the mathematical Olympiad level. Organizer: Matthieu Dufour (UQÀM) Students are invited based upon their results in various mathematics competitions. Presenta- The International Mathematical Olympiad tions on particular topics and the various prob- (IMO) is the World Championship Mathemat- lem solving sessions are runs by local area teach- ics Competition for High School students and is ers and faculty member as well as former IMO held annually in a different country. The CMS team members. has been sending a team of Canadian students to the annual IMO since 1981. Canadian stu- The Regional Camps are intended to provide dents have always done extremely well, ob- some mathematics enrichment in a fun and re- taining a total of 93 medals (14 Gold, 27 Silver warding environment. Each camp invites be- and 52 Bronze). In 2004 the Olympiad was held tween 20 and 30 students (from grade 9 to 11) at Athens and the Canadian team obtained 4 on the basis of national or regional mathematics medals, 1 Gold and 3 Bronze. competition as well as recommendations from teachers. The 2004 regional camps took place at As with all competition, training is vital for suc- the University of Regina, Sir Wilfred Grenfell cess. The Canadian Team of six high school stu- College, the University of New Brunswick, the dents chosen from more than 200,000 students University of Prince Edward Island, Université who have participate in various local, provincial, du Québec à Rimouski, Simon Fraser University, national and international contests. Team mem- Dalhousie University, the University of Ottawa, bers and their coaches attended a training sem- the University of Western Ontario, Brock Uni- inar at UQÀMfor two weeks prior to their de- versity, the University of Alberta, and the Uni- parture to Athens. A few select students from versity of Manitoba. Québec, who have excelled in mathematics com- petitions, also attended the IMO training semi- The sponsors of the 2004 math camp program nar as observers for the first few days. were: Imperial Oil Foundation, Canadian Math- ematical Society, NSERC PromoScience, the The 2004 Canadian Olympiad “mathletes” were: Fields Institute, the Centre de recherches mathé- Oleg Ivrii (Toronto), János Kramár (Toronto), matiques, the Pacific Institute for the Mathemat- Dong Uk Rhee (Edmonton), Peng Shi (Toronto), ical Sciences, the Association Mathématique du Jacob Tsimerman (Toronto) et Yufei Zhao Québec, the host universities, the governments (Toronto). of New Brunswick, Alberta, Northwest Territo- ries, Newfoundland and Labrador, Nova Scotia, Québec, Ontario, and Saskatchewan.

52 MATHEMATICAL EDUCATION

Canadian Mathematics Education Forum Working groups May 6–8, 2005, University of Toronto • Mathematics education in the aboriginal com- munity, Co-chairs: Florence Glanfield (Saskatchewan), • Early numeracy: developing mathematical lit- Frédéric Gourdeau (Laval), Bradd Hart (McMas- eracy in the early years, ter) • Why is mathematics relevant in our society, The 2005 Canadian Mathematics Education Fo- • Supporting student success — Helping stu- rum (CMEF2005) was organized by the Cana- dents reach their potential, dian Mathematics Society (CMS). The Forum • Creating a curriculum that affords learners was held at the University of Toronto with some opportunity to develop powerful mathemat- activities at the nearby Fields Institute. This Fo- ics, rum follows the one held in 2003 in Montréal. • Learning in the presence of technology, The 2005 Forum is the third organized by the • Mathematics through the eyes of a child, CMS, the first national forum in mathematical • Classroom practice and mathematics educa- education being held in Québec in May 1995. tion research, The purpose of the 2005 invitational forum was • Developing a national mathematics teaching to develop a national on-going conversation, community, among educators at all levels of schooling, about • Supporting teacher success. important issues and concerns in the develop- ment and future of mathematics education in Partners Canada. The overall theme of the 2005 Forum • Canadian Mathematical Society was Why teach Mathematics? The Forum was • Alberta Education thought of as a working meeting and included • Fields Institute plenary panel sessions and talks as well eleven • Ministère de L’Éducation, du Loisir et du working groups. Sport du Québec The Forum brought together some 200 partici- • University of Saskatchewan pants coming from all sectors connected to edu- • Nova Scotia Department of Education cation in mathematics and from all the provinces • Pacific Institute for the Mathematical Sciences and territories of Canada: teachers and instruc- • Yukon Department of Education tors of mathematics at all the levels, researchers • McMaster University in mathematics and mathematics education, • Centre de recherches mathématiques consultants and education advisers, representa- • Institut des sciences mathématiques tives of associations of teaching and teachers • Toronto District School Board of mathematics, representatives of the provin- • Ontario Ministry of Education cial ministries for education, representatives of • Saskatchewan Learning other groups having a particular interest for the • Nunavut Department of Education teaching of mathematics: industry representa- • Canadian Applied and Industrial Mathemat- tives, parents, administrators, editors, textbook ics Society writers, etc. • Statistical Society of Canada It was the intent that groups working together in • Université Laval this forum will develop projects, initiatives, and • Nova Scotia Mathematics Teachers’ Associa- statements that will outline ways in which Cana- tion dians may address these issues and concerns. • Ontario Association for Mathematics Educa- The projects, initiatives, and statements devel- tion oped during this forum will be shared widely • BC Association of Mathematics Teachers with policy makers, school divisions, universi- • Saskatchewan Mathematics Teacher Society ties, colleges, parents, students, and the general • Association Mathématique du Québec public in a variety of ways. • Groupe des responsables en mathématiques au secondaire

53 Research Laboratories RESEARCH LABORATORIES

HE CRM now encompasses eight research laboratories at the heart of the Québec mathematical Tcommunity. 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 a doctoral fellows. One characteristic of this labo- very active area of research with a long tradition, ratory is the sustained collaboration of its mem- as well as many young faculty members in the bers with researchers in other fields: for in- greater Montreal area. With modern computing stance, André Bandrauk and Nilima Nigam are equipment, it has become possible to simulate members of RQMP (Regroupement québécois problems and compute solutions which one was des matériaux de pointe), Sebius Doedel and only able to dream of a few decades ago: this has Jacques Bélair are members of the Centre for been a tremendous driving force in recent devel- Nonlinear Dynamics in Physiology at McGill, opments in applied and computational mathe- Martin Gander and Michel Delfour are mem- matics. bers of GIREF, Anne Bourlioux collaborates with The objective of the laboratory is to further en- computer scientists and mechanical engineers courage scientific exchanges both amongst its in an industrial project sponsored by MITACS, members and outside the group. It is character- while Peter Bartello, André Bandrauk, and Se- ized by the intensity of its multidisciplinary col- bius Doedel hold positions completely or partly laborations, with all the members working on outside mathematics departments. the development of mathematical models and The laboratory organizes the annual Montreal numerical methods for applications to science Scientific Computing Days each February, as and engineering. The members of the labora- well as other workshops. It has two regular tory work in a wide range of applications (flu- seminars running during the academic year, a ids, solids, physics, biology, etc.) using a wide weekly applied mathematics seminar and a bi- variety of tools (optimization, numerical anal- weekly computational science and engineering ysis, dynamical systems, etc), and are very ac- seminar. It also supports postdoctoral fellows tive in both research and training, supervising and summer students as well as Canadian and a large number of graduate students and post- international visitors.

Activities of the laboratory in 2004–2005

Seminars

The regular core activity of the laboratory is with their students and postdoctoral fellows, but the weekly applied mathematics seminar which with significant participation of the Montréal- usually takes place on Mondays at McGill. This wide applied mathematics community. year it was organized by Paul Tupper, who Complementary to that core seminar, and in line lined up 32 speakers covering a very wide range with the strong multidisciplinary orientation of of interesting topics in applied mathematics. this group, the laboratory was also involved in Though most seminars were at McGill, there organizing and sponsoring the bi-weekly Com- were also seminars at Université de Montréal putational Science and Engineering (CSE) Sem- and one at Concordia. The series included joint inar at McGill, organized this year by Dennis seminars with the Analysis laboratory and with Giannacopoulos (Electrical and Computer Engi- the McGill departement of Atmospheric and neering, McGill), which included 13 speakers, in Oceanic Sciences and Computational Science addition to the three joint “Applied Mathemat- and Engineering. The seminar series was well ics/CSE” seminars. attended not just by laboratory members along 55 CENTRE DE RECHERCHES MATHÉMATIQUES

Workshops, special sessions and others

Besides its regular activities, the laboratory or- tions “General Program” and “Multidisciplinary ganized the second Montréal Scientific Com- Program.” puting Days in February. The objective of this In addition to these laboratory events, the labo- conference is to encourage scientific exchange ratory members were very active in the organi- within the scientific computing community in zation of activities related to the Theme Year. Québec and further afield. The two-day program included two short courses offered by interna- tional experts, at a level accessible to advanced • Anne Bourlioux was the principal organizer graduate students, as well as oral and poster for the CRM Thematic Year on “The Math- contributed sessions. Students and postdoctoral ematics of Stochastic and Multiscale Model- researchers were especially encouraged to par- ing,” and also organized the workshop “Front ticipate. The event was once again a great suc- Propagation and Nonlinear Stochastic PDEs cess, this year attracting over 100 participants, for Combustion and other Applications” and mostly from Québec and Ontario. the Summer School “Stochastic Calculus for Applications: Theory and Numerics.” Two one-day workshops were also organized by the laboratory on “Computational Aspects of • Paul Tupper organized another workshop, Dynamical Systems” and “Analysis and Com- “Extracting Macroscopic Information from putation of Lattice, Delay and Functional Differ- Molecular Dynamics.” ential Equations.” Michel Delfour was a mem- ber of the organizing committee for the Spring Details about all these activities can be found in School and Workshop “Mini-invasive proce- the chapter “Thematic program” of this report. dures in medicine and surgery: mathematical With over 30 seminar speakers from outside and numerical challenges.” Details on these Quebec, the laboratory members were also three workshops as well as on the Montreal Sci- hosts to a number of scientific visitors includ- entific Computing Days can be found in the sec- ing Dimitri Breda (Udine), Chris Elmer (NJIT), McKay Hyde (Rice), Olivier Lafitte (Paris 13), Peter Monk (Delaware) et David Nicholls (Notre Dame).

Members of the laboratory

Highlights of its members

During the year we welcomed three new mem- “Qualitative numerical analysis of high- bers; Jacques Bélair (Montréal), Robert Owens dimensional nonlinear systems,” at Univer- (Montréal) and Paul Tupper (McGill). sity of Bristol in March 2005. • The laboratory members were visible at the na- Martin Gander organized two minisymposia tional and international levels in applied and in- at 16th International Conference on “Domain dustrial mathematics. Decomposition Methods,” New York, January 2005 on “Optimized Schwarz Methods” and • Anne Bourlioux served on the board of di- “Space-Time Parallel Methods for PDE’s.” rectors of CAIMS, and several members of • Robert Owens organized a minisymposium the laboratory were involved in organizing on “High Order Methods for Complex Fluids” and participating in various symposia dur- at the International Conference on ““Spectral ing the Joint 2004 CAIMS/CMS meeting in- and High-Order Methods,” Brown, June 2004. cluding Peter Bartello, Jacques Bélair, Tony • Paul Tupper has been chosen as finalist for the Humphries, Sebius Doedel, Martin Gander 2005 Fox Prize in Numerical Analysis. and Sherwin Maslowe. • Eusebius Doedel organized workshops on During the year 2004–2005, 17 master’s students, “Analysis and Continuation of Bifurcations,” 20 Ph.D. students and 8 postdoctoral fellows at University of Seville in May 2004, and were supervised by laboratory members.

56 RESEARCH LABORATORIES

Regular members

Tony Humphries (McGill) Director Martin Gander (Geneva and McGill) Numerical analysis, differential equations. Domain decomposition, preconditioning. Paul Arminjon (Montréal) Sherwin A. Maslowe (McGill) Numerical methods in fluid mechanics. Asymptotic methods, fluid mechanics. André Bandrauk (Sherbrooke) Nilima Nigam (McGill) Quantum chemistry. Applied analysis, numerical methods in electro- Peter Bartello (McGill) magnetism. Turbulence, CFD. Robert G. Owens (Université de Montréal) Jacques Bélair (Montréal) Mechanic and numerical simulation of complex Dynamical systems in physiology. fluids. Anne Bourlioux (Montréal) Georg Schmidt (McGill) Modeling, numerical simulation in turbulent Control of partial differential equations. combustion. Paul Tupper (McGill University) Michel Delfour (Montréal) Numerical analysis, stochastic processes, and Control, optimization, design, shells, calculus, statistical mechanics. biomechanics. Jian-Jun Xu (McGill) Eusebius J. Doedel (Concordia) Asymptotics and numerical analysis, non-linear Numerical analysis, dynamical systems, differ- PDEs material science. ential equations, bifurcation theory, scientific Jean-Paul Zolésio (INRIA) software. Control, optimization.

CICMA

Description

This centre comprises researchers working in Andrew Granville, one of the leaders in the field. number theory, group theory and algebraic ge- On the group theory side, Kharlampovich and ometry. Contemporary number theory follows Miasnikov are world-renowned specialists on two major courses. On the one hand, there is group varieties and McKay is one of the origi- the theory of special values of L-functions at- nators of the moonshine program. tached to arithmetic objects, originating in the Among the problems to be studied by the group work of Gauss and Dirichlet and leading to the in the coming years include the construction of modern conjectures of Deligne, Beilinson and rational points on elliptic curves both from al- Bloch–Kato. On the other hand, the Langlands gorithmic and theoretical viewpoints; Zeta func- program postulates a close link between arith- tions of varieties over finite fields on the al- metic L-functions and automorphic representa- gorithmic approach; canonical lifting of ellip- tions. An area where these two currents inter- tic curves and Abelian varieties; cryptography, sect is the study of elliptic curves. The center is Abelian varieties, and many aspects of analytic particularly well represented in this regard with number theory, as averages of special values of Darmon, Iovita, and Kisilevsky. CICMA also ac- L-functions, distribution of prime numbers and quired a new expertise in many aspects of an- prime divisors, and problems of additive num- alytic number theory with the recent arrival of ber theory.

57 CENTRE DE RECHERCHES MATHÉMATIQUES

Activities of the laboratory in 2004–2005

Seminars

The main scientific activity of the CICMA labo- mona (Nottingham), Gergely Harcos (Texas), ratory is the Québec–Vermont Number Theory Nyandwi Servat (University Tunis El Manar), Seminar, which is held every second Thursday R. Sujatha (Tata Institute), John Coates (Cam- for a full day, with about 30 regular participants bridge), Gregory Freiman (Tel Aviv) et Manfred from Montréal, Vermont, Québec and Ottawa. Einsiedler (Wien and Princeton). One can see from that list that the invited speak- A number of talks were also given by the local ers to the QVNTS are among the most prominent participants, and an important facet of QVNTS researchers in number theory, arithmetic geom- is to give to CICMA members an occasion to etry and related topics. In the academic year present to each other their latest research. The 2004–2005, the invited speakers to the QVNTS QVNTS are also important for the postdoctoral included: Haruzo Hida (UCLA) who gave a se- fellows, allowing them to present their research ries of lectures on his fundamental work on p- to the number theory community, and to share adic families of modular forms, which has pro- their expertise. One of the QVNTS day was en- foundly infuenced the development of the sub- tirely dedicated to the recent spectacular work ject and plays a key role in the work of Iovita of C. Khare proving Serre’s conjecture. The talks and Darmon (in collaboration with Bertolini); were given by David Savitt, a CICMA postdoc- and Akshay Venkatesh (Clay Fellow, NYU), one toral fellow whose work was important in the of the young leaders in number theory today, proof of Khare. who came to talk about his new and outstand- In addition to the main scientific event, the ing work on equidistribution, subconvexity and QVNTS, the members of CICMA are also in- spectral theory. volved in more informal and specialized sem- The complete list of invited speakers for inars, or working seminars, among smaller 2004–2005 is: Dino Lorenzini (Georgia), Kar- groups of postdoctoral fellows, graduate stu- tik Prasanna (UCLA), Haruzo Hida (UCLA), dents and faculty members. Those include: Jean-Louis Colliot-Thélène (Paris-Sud), Marvin Knopp (Temple), Akshay Venkatesh (Clay Fel- • The “Séminaire de Théorie analytique des low, NYU), Mark Kisin (Chicago), Jordan Ellen- nombres,” organized since 2003–2004 by a berg (Wisconsin), Gabor Kun (Eotvos Univer- group of postdocs and graduate students. The sity, Budapest), Romyar Shari (McMaster), Wen- topics covered in the seminars are influenced zhi Luo (Ohio State), David McKinnon (Wa- by the research interests of the participants. terloo), Denis Thérien (McGill), Farshid Hajir • A Working Seminar organized by Adrian (Amherst), Jason Lucier (Waterloo), Alexandru Iovita on the p-adic Banach spaces, and the L- Popa (Princeton), Jorge Devoto (Buenos Aires), invariants associated to modular forms. The Nora Ganter (Urbana-Champaign), Ali Ozluk participants included some faculty members, (Maine), Pierre Charollois (Bordeaux), John Cre- and several postdocs and graduate students.

Workshops, special sessions and others

Organized by CICMA members, the following tionales (division Amérique latine) and the cor- activities took place in the province: responding institution in Mexico. More details can be found in page 26. A conference on Analytic number theory, or- The annual “Québec–Maine Number Theory” ganized by Jean-Marie De Koninck at Université Conference which was held in Québec City Laval in October 2004, was organized by Claude May 19–21, 2005 Levesque. One of the goals of the conference was to encour- age scientific exchanges between researchers in In addition to (and including some of) the in- Québec and Mexico, following the collabora- vited speakers of the QVNTS mentioned above, tion of Florian Luca (UNAM, Mexico) and Jean- a number of long-term visitors, involved in Marie De Koninck. This conference was funded research projects with the CICMA members, in part by the Ministère des relations interna- were in Montreal during the year 2004–2005.

58 RESEARCH LABORATORIES

We mention a few here: Nora Ganter (Urbana- ton), Samit Dasgupta (Harvard), Pierre Charol- Champaign), Jorge de Voto (Buenos Aires), lois (Bordeaux) et Kristin Lauter (Microsoft). Haruzo Hida (UCLA), Alina Cojocaru (Prince-

Members of the laboratory

Highlights of its members

Other conferences and workshops organized by organized by Chantal David and Andrew CICMA members include: Granville. Both sessions were funded by the • A 5-day Workshop at BIRS entitled “Dio- CMS. phantine Approximation and Analytic Num- ber Theory” which was held on November 20– C. David, A. Iovita, H. Darmon (principal appli- 25, 2004, and whose organizers included An- cant), and E. Goren obtained a NSERC Leader- drew Granville. Several faculty member and ship Support Initiative Grant. postdoctoral fellows from Montréal partici- pated to the event. C. David, H. Kisilevsky, F. Thaine, H. Darmon • Two special sessions at the CMS Winter Meet- (director), and E. Goren obtained a FQRNT Team ing held at McGill University in Decem- Grant. ber 2004. A session on Arithmetic geometry During the year 2004–2005, 21 master’s students, was organized by Eyal Goren and Adrian 23 Ph.D. students and 12 postdoctoral fellows Iovita, and a session on Number theory was were supervised by laboratory members.

Regular members

Henri Darmon (McGill) Director Adrian Iovita (Concordia) Algebraic number theory, geometry, arithmetic, Number theory, p-adic cohomology. L-functions, Diophantine equations, elliptic Olga Kharlampovich (McGill) curves. Combinatorial theory of groups and Lie alge- Chris J. Cummins (Concordia) bras. Group theory, modular functions, Moonshine. Hershy Kisilevsky (Concordia) Chantal David (Concordia) L-functions, Iwasawa theory, elliptic curves, Analytical number theory, L-functions class field theory. Jean-Marie De Koninck (Laval) Claude Levesque (Laval) Analytic number theory: distribution of prime Algebraic number theory, units, class number, numbers, factorisation of numbers, asymptotic cyclotomic fields. behaviour of arithmetic functions, Riemann zeta Michael Makkai (McGill) function. Mathematical logic. Dave Dummit (Vermont) John McKay (Concordia) Algebraic number theory, arithmetic algebraic Computational group theory, sporadic groups, geometry, computational mathematics. computation of Galois groups. David Ford (Concordia) Alexei Miasnikov (McGill) Computational number theory, algorithmic Group theory. number theory. M. Ram Murty (Queen’s) Eyal Goren (McGill) Number Theory: Artin’s conjecture, elliptic Arithmetic geometry, algebraic number theory, curves, modular forms, automorphic forms, moduli spaces of abelian verieties, Hilbert mod- Langlands program, Selberg’s conjectures, Sieve ular forms, p-adic modular forms. methods, cryptography. Andrew Granville (Montréal) Jonathan Pila (McGill) Analytic number theory, arithmetic geometry, Number theory, especially algorithmic and Dio- combinatorics. phantine problems.

59 CENTRE DE RECHERCHES MATHÉMATIQUES

Damien Roy (Ottawa) Francisco Thaine (Concordia) Transcendental number theory. Cyclotomic fields, cyclotomy, rational points on Peter Russell (McGill) curves. Algebraic geometry.

CIRGET

Description

Geometry and topology are fundamental disci- and topology has been hired by Québec univer- plines of mathematics whose richness and vital- sities. The research centre, based at UQÀM, now ity have been evident throughout human history comprises seventeen professors-researchers to- and reflect their deep link to our experience of gether with a large number of postdoctoral fel- the universe. They are at a crucial crossing point lows and graduate students. of modern mathematics and in effect several do- The main themes to be pursued in the coming mains of mathematics have recently shown a years include Dehn surgery and Thurston ge- strong trend towards a geometrization of ideas ometrization; quantization of Hitchin systems and methods: two cases in point are mathemati- and geometric Langlands program; classifica- cal physics and number theory. tion of special Kähler metrics; the study of sym- During the last twenty-five years, a group of plectic invariants, especially in dimension 4; researchers of international calibre in geometry Hamiltonian dynamical systems.

Activities of the laboratory in 2004–2005

Workshops, special sessions and others

CIRGET members have organized various This began with the Séminaire de Mathéma- events in the Montreal area this year funded by tiques Supérieures (SMS), the annual NATO CIRGET, the CRM and other sources. A com- sponsored summer school held at the Univer- plete description of all these activities can be sité de Montréal. This year’s topic was “Morse found in the chapter “General Program .” theoretic methods in non-linear analysis and symplectic topology.” The School was held • Short Program on Riemannian Geometry from June 21 to July 2 with 91 students par- June 28 to July 16, CRM ticipating. In the framework of this informal Organizers: Vestislav Apostolov (UQÀM), An- semester, between October 14 and December drew Dancer (Oxford), Nigel Hitchin (Ox- 7, 17 invited lectures were given, with an in- ford), McKenzie Wang (McMaster) tensive two-week workshop held November 2 to November 12. The theme of this program was the study of special geometries (metrics whose curvature • Topics in Low-Dimensional Topology satisfies constraints), as well as the relation be- May 16–17, 2005, UQÀM tween curvature and topology. Organizers: Steven Boyer (UQÀM), Olivier Collin (UQÀM) • Special Semester on Symplectic Geometry and Topology The two main themes of the Workshop Fall 2004, CRM were applications of geometric methods in 3- Organizers: Octavian Cornea (Montréal), manifolds and the contact topology in dimen- François Lalonde (Montréal) sion 3.

60 RESEARCH LABORATORIES

Niky Kamran invited Stephan De Bièvre (Lille) to continue in graduate studies, began to bear to give a full-term course this winter on quan- fruit. Indeed, Apostolov’s two summer fellows tum field theory in curved space-time at McGill started a master’s in geometry in 2004. Further- to provide students and postdoctoral fellows more, each year, we receive many applications with the background for a workshop he is plan- from French students from the ENS, which is ning in 2005-2006. The course was a rigorous a good indication of the international spread of constructive quantum field theory course that the CIRGET. covered the classical theorems on CCR algebras One can see how well the CIRGET is known in- and concluded with a discussion of the Unruh ternationally by looking how many postdoctoral effect for accelerated observers near black holes. CRM-ISM applications it received: the third of This was the first time that a course on this im- all the applications were send to CIRGET mem- portant topic has been given in Montreal. The bers (110 to 330). Four of these candidate will lectures will be published as a book. joint the CIRGET next year. The presence of post- Added to the many seminar and conference doctoral fellows enhance CIRGET dynamism, visitors listed above, CIRGET also welcomed : they participate in organizing event, they invite Daryl Cooper (UCSB), Xingru Zhang (SUNY), many collaborators whom presence is benefic for Michel Boileau (Toulouse), Felix Finster (Re- all CIRGET members, they work with gradu- gensburg), Alexander Its (IUPUI), Gabriele Vez- ate students and collaborate with regular mem- zosi (Florence), Michael Batanin (Sidney), Marie- bers. Two publications resulted from these col- Françoise Ouedraougo (Ouagadougou), Viktor laborations: Hu and Lalonde published a paper Enolskii (Heriot-Watt) and Michael Gekhtman in symplectic geometry and Tillmann and Boyer (Notre-Dame). will publish soon a paper in low-dimensional The CIRGET Summer Scholarship program, that topology. encourages promising undergraduate students

Seminars

The three weekly CIRGET Seminars have been • The Geometric Group Theory Seminar, a more quite active. specialized seminar organized by Dani Wise, • The Geometry-Topology Seminar is the main met 17 times over this period with 11 talks regular activity of the laboratory, attended by given by speakers from outside Montreal. all CIRGET members. Organized by Olivier • Finally, the CIRGET Junior Seminar, orga- Collin, the seminar hosted 24 speakers of nized by Baptiste Chantraine for CIRGET stu- whom 17 were from outside Montreal. dent members, met 23 times.

Members of the laboratory

New members of the laboratory

CIRGET welcomed two new members this year. tive role in CIRGET. Their presence will rein- Steven Lu (Ph.D. Harvard 1990) accepted a posi- force the geometrical analysis domain, in which tion at UQÀM after spending four years in Ger- Apostolov and Kamran already work. With now many at the Max Plank Institute and two years four researchers working in the area, geometri- at the University of Essen. Pengfei Guan (Ph.D. cal analysis will become an important CIRGET Princeton 1989) came to McGill as a senior CRC research nucleus. after spending many years at McMaster Univer- During the year 2004–2005, 22 master’s students, sity. 15 Ph.D. students and 10 postdoctoral fellows Both have integrated smoothly into the Mon- were supervised by laboratory members. treal mathematical scene and have played an ac-

Regular Members

Steven Boyer (UQÀM) Director Syed Twareque Ali (Concordia) Topology of manifolds, low-dimensional geom- Coherent states, wavelets, quantization tech- etry and topology. niques, harmonic analysis, Wigner functions. 61 CENTRE DE RECHERCHES MATHÉMATIQUES

Vestislav Apostolov (UQÀM) André Joyal (UQÀM) Complex geometry, Kähler geometry. Algebraic topology, category theory. Abraham Broer (Montréal) Niky Kamran (McGill) Algebraic transformation groups, invariant the- Geometric approach to partial differential equa- ory. tions. Olivier Collin (UQÀM) François Lalonde (Montréal) Invariants of knots and 3-manifolds arising from Symplectic topology and geometry, global anal- global analysis. ysis on manifolds, infinite dimensional transfor- mation groups. Octavian Cornea (Montréal) Algebraic topology, dynamical systems. Steven Lu (UQÀM) Pengfei Guan (McGill) Chern number inequalities, semi-stability of ten- Partial differential equations, geometric analy- sorial sheaves, log jets, log and hyperbolic geom- sis, several complex variables. etry, algebraic degeneracy. John Harnad (Concordia) Iosif Polterovich (Montréal) Mathematical physics, classical and quantum Geometric applications of spectral geometry. physics, geometrical methods, integrable sys- Peter Russell (McGill) tems, group theoretical methods, random ma- Algebraic geometry. trices, isomonodromic deformations, isospectral John A. Toth (McGill) flows. Microlocal analysis, partial differential equa- Jacques Hurtubise (McGill) tions. Algebraic geometry, integrable systems, gauge Daniel T. Wise (McGill) theory, moduli spaces. Geometric group theory, low-dimensional topol- ogy.

LaCIM

Description

LaCIM is a research lab- revival of the concrete computational aspect in oratory of the Université mathematics after decades of abstract structural- du Québec à Montréal, ism. Algebra is enriched in a fundamental man- which was officially es- ner by combinatorics, as the commutative alge- tablished in 1989. Its re- bra book by Eisenbud demonstrates, highlight- search activities concen- ing constructive geometric methods. Moreover, trate on enumerative al- combinatorics applies to computer science (the- gebra, algebraic combi- ory of automata, analysis of algorithms), to sta- natorics, computer sci- tistical physics (computation of configuration ence and their applications to other scientific do- spaces and of critical exponents, discrete mod- mains, such as the analysis of algorithms, sta- els), bio-informatics (combinatorics of words ap- tistical mechanics and computational biology. plied to genomic sequences). The youth, dy- Since 2002, LaCIM is one of the eight research namism, utility and applicability of this research laboratories of the CRM. domain are highlighted in the modern world, where discrete structures (trees, graphs, permu- Research areas tations) are more and more present in communi- cations, networks and research engines, of which Discrete mathematics has lately become an im- the use is growing exponentially in this 21st cen- portant field of practical research, witness the tury. new heading in Mathematical Reviews 05E of al- gebraic combinatorics with subheadings indicat- The researchers ing interactions with the newest areas of math- ematics, such as group representations, quan- The laboratory is comprised of thirteen principal tum groups, discrete algebraic geometry, spe- researchers, ten of them professors at UQÀM, cial functions. Combinatorics benefits from the one at McGill, one at Université de Montréal

62 RESEARCH LABORATORIES and one at École Polytechnique de Montréal; of the emergence of the UQÀM combinatorics twelve collaborator and five associated mem- group about twenty years ago. From that time bers in North America, one in Chile and two research has diversified greatly at LaCIM: in Europe. Notably, Christophe Reutenauer (reg- ular member) and Nantel Bergeron (associate • classical enumerative combinatorics and its member) hold Canadian research chairs. A team applications (counting of discrete configura- of four LaCIM members is supported by a tions and planar maps); grant from FQRNT. André Joyal, past member • algebraic combinatorics; of LaCIM and current member of CIRGET, is • theoretical computer science; involved in several activities at LaCIM, both • bio-informatics. formal and informal. LaCIM is the largest re- search group in combinatorics in Canada and is Seminars and others known worldwide in its field. The UQÀM team has contributed to the emergence and establish- The LaCIM Combinatorics and Theoretical In- ment of combinatorics as a mathematical dis- formatics Seminar is an important and suc- cipline. For example, several LaCIM members cessful integrating element. Cédric Chauve and have played and continue to play an important Christophe Reutenauer are the organizers. These role in the organization of the international col- seminars were held on Fridays 25 times during loquium “Formal Power Series and Algebraic the year and about 25 people attended the talks. Combinatorics,” which is bilingual and is held yearly, alternately in Europe and North Amer- During 2004 – 2005, the LaCIM hosted sev- ica. Its success is without question. eral visitors: David Barrington (Amherst), Jean- Pierre Borel (Limoges), Ricard Gavalda (UPC Research activities at LaCIM Barcelona), Mark Haiman (Berkeley), Cristoffer Hansen (Århus), Christian Kassel (Strasbourg), André Joyal enriched the counting theory of Michal Koucky (Prague), Clemens Lautemann Polya by including the theories of group repre- (Mainz), Francois Lemieux (UQÀC), Julia Mi- sentations and symmetric functions. Under the tacki (Bielefeld), Mathieu Raffinot (Paris), Klaus name of theory of species, this theory marked Reinhardt (Tübingen)and Jens Stoye (Bielefeld).

Members of the laboratory

Highlights of its members

Denis Thérien is a James McGill Professor at • François Bergeron, in collaboration with Sara McGill University (2002–2009) and Christophe Faridi (former LaCIM postdoctoral fellow), Ric- Reutenauer has a Canada Research Chair cardo Biagioli (LaCIM postdoctoral fellow) and in “Combinatorial Algebra and Mathematical Tony Geramita, organized, in January 2005, the Computing ” (2001–2008). Second Invariants and Combinatoric Workshop, held Two former members of the LaCIM, Marni in Ottawa (the first took place in Kingston in Jan- Mishna (Ph.D.) and Sara Faridi (postdoctoral fel- uary 2004). low) received this year a NSERC Faculty Sup- The main achievement of this event has been the port Programs (Each year, only 25 candidate are establishment of an on-going dialogue between chosen). Also, Marni Mishna received in 2004 two separate research communities that had the Governor General’s Academic Medal for her been using similar techniques to study different Ph.D. Thesis. mathematical problems. The two groups are al- LaCIM integrated a new regular member: John gebraic combinatorialists working on the repre- Mullins, Professor at the Computer Engineer- sentation theory of symmetric groups, and com- mutative algebraists studying resolutions and ing Department of the École Polytechnique de inverse systems. The connections between these Montréal; he is director of CRAC (Conception topics were highlighted in a successful meeting et réalisation des applications complexes). He al- that took place in January 2004 at Queen’s Uni- ready collaborates with Srecko Brlek. versity in Kingston. In this meeting, through a During the year 2004–2005, LaCIM members series of expository lectures by Tony Geramita were active in the organization of many large- and François Bergeron, among others, it was scale events:

63 CENTRE DE RECHERCHES MATHÉMATIQUES made evident that interesting special cases of the mittee Anne Bergeron, Sylvie Hamel, Cédric notion of Macaulay’s inverse systems of commu- Chauve and Vladimir Makarenkov. tative algebra are essentially the same objects as JOBIM is a multidisciplinary event that brings coinvariants spaces studied in algebraic combi- together experts in biology, computer science, natorics and representation theory. This year’s mathematics and physics. In 2004, the pro- meeting will continue in the same tradition. gram was divided in six sessions on: repetitions, • Vladimir Makarenkov was president of the patterns, gene expression and regulation net- Scientific Committee (which also include Anne works; comparative genomic, predictions, mod- Bergeron and Cédric Chauve) of the Société fran- els; data bases, exploration, classification and cophone de Classification Colloquium, which took visualization; phylogeny, evolution and popu- place at UQÀM in May 2005. lation; structure and families of ARN or pro- teins; and metabolism classification, biological Beside the usual classification thematic, the fol- systems. lowing themes were privileged in Montréal: Bioinformatics, evolution and phylogenic anal- The program included 20 long presentations, ysis, consensus methods, data search and sym- 33 “flash" presentations and 6 invited talks. bolic data analysis. This year the invited speakers were Tom Hud- son (McGill), Bernard Dujon (Institut Pasteur), Invited speakers: Francisco De Carvalho (Univer- Hervé Philippe (Montréal), Mathieu Blanchette sidade Federal de Pernambucol), Pierre Hansen (McGill), David Sankoff (Ottawa) and Shoshana (HÉC), Melvin F. Janowitz (DIMACS Center, Wodak (Hospital for Sick Children, Toronto). JO- Rutgers University), Sabine Krolak-Schwerdt BIM also held a poster session: around 40 posters (Universität des Saarlandes), Bruno Leclerc were presented. (École des Hautes Études en Sciences Sociales), Maurizio Vichi (Universitá “La Sapienza” di • An Invited Minisymposia on “Genome Rear- Roma). rangements” was organized by Anne Bergeron in June 2004 during the SIAM conference Dis- • A special session on “Algebraic Combina- crete Mathematics held at Nashville, Tennessee. torics” of the CMS Meeting, held at McGill in De- cember 2005, was organized by François Berg- The recent spectacular growth of genome se- eron and Christophe Reutenauer, together with quencing projects provides a fertile ground for the two postdoctoral fellows Peter MacNamara new problems that are both relevant to biolo- and Riccardo Biagioli. Topics included all as- gists, and challenging to mathematicians and pects of algebraic combinatorics and their rela- computer scientists. In an unexpected way, chro- tions with other parts of mathematics. One par- mosomes happen to be ordering devices for the ticular focus was on recent work concerning re- various genes that encode information about lations among symmetric functions. species. The content and order of these genes varies from species to species, and different Invited speakers: Nantel Bergeron (York), genomes are modeled as permutations and Francesco Brenti (Tor Vergata), Sergey Fomin words. This symposium will focus on the issues (Michigan), Adriano Garsia (UC San Diego), Ian raised by whole genome comparisons: These Goulden (Waterloo), David Jackson (Waterloo), range from central applied problems such as Mercedes Rosas (York), Mark Skandera (Dart- gene function prediction or phylogeny recon- mouth), Richard Stanley (MIT), John Stembridge struction, to hard combinatorial problems whose (Michigan), Stephanie van Willigenburg (UBC) solution requires the development of new theo- et Mike Zabrocki (York). retical tools. • The 2004 International JOBIM Conference (Journées Ouvertes en Biologie, Informatique et During the year 2004–2005, 34 master’s students, Mathématiques) included in its program com- 22 Ph.D. students and 7 postdoctoral fellows were supervised by laboratory members.

Regular members

Christophe Reutenauer (UQÀM) Director Robert Bédard (UQÀM) Algebraic combinatorics, non-commutative al- Representations of finite groups, Lie theory. gebra, automata, codes, free algebras. Anne Bergeron (UQÀM) Bio-informatics.

64 RESEARCH LABORATORIES

François Bergeron (UQÀM) Vladimir Makarenkov (UQÀM) Combinatorics, algebras, representations of fi- Computational biology, mathematical classifica- nite groups. tion. Srecko Brlek (UQÀM) John Mullins (École Polytechnique de Mont- Combinatorics of words, algorithmics. réal) Logic and Algebra applications to mod- elization, concurrent systems analysis, in partic- Cedric Chauve (UQÀM) ular, safety systems analysis. Enumerative combinatorics, trees, bio- informatics. Denis Thérien (McGill) Theory of complexity of computation, logic, Sylvie Hamel (Montréal) combinatorics, probability. Bio-informatics and algorithms, language and automaton theory, algebraic combinatorics. Timothy Walsh (UQÀM) Algorithmics, enumerative combinatorics, Gilbert Labelle (UQÀM) graphs. Enumerative combinatorics, analysis Pierre Leroux (UQÀM) Enumerative and algebraic combinatorics.

Associate members

Michel Bousquet (Cegep du Vieux-Montréal) alternating matrices, involution enumeration re- lated to divers parameters, use of pfaffiens and Alain Goupil (Cegep du Vieux-Montréal) determinants in enumeration. Combinatorics, algebra, finite group representa- Cédric Lamathe (UQÀM) tions, symmetrical groups and extensions. Luc Lapointe (University of Talca, Chili) Pierre Lalonde (Cegep Maisonneuve) Algebraic Combinatorics, symmetrical func- Enumerative and bijective combinatorics, sign tions, integrable systems, supersymmetries.

Collaborating members

Marcello Aguiar (Texas A&M University) Algebraic combinatorics, symmetrical func- Algebraic Combinatorics, non-commutative al- tions, Harmonic and co-invariant spaces, quasi- gebra, Hopf algebras and quantum groups, cat- harmonic and quasi-invariant functions. egory theory. André Joyal (UQÀM) Luc Bélair (UQÀM) Algebraic topology, Category theory. Mathematical logic, model theory. Jacques Labelle (UQÀM) Nantel Bergeron (York Univ.) Combinatorics, topology. Applied algebra. Louise Laforest (UQÀM) Pierre Bouchard (UQÀM) Data structures, combinatorics, asymptotical Commutative algebra, algebraic geometry and analysis, quaternary trees. combinatorics. Simon Plouffe Yves Chiricota (UQÀC) Xavier G. Viennot (Université Bordeaux I) Sylvie Corteel (CNRS) Enumerative, algebraic and bijective combina- Enumerative and bijective combinatorics, inte- torics, interaction between combinatorics, theo- gers partitions and q-series. retical informatics and theoretical physics. Adriano Garcia (University of California at San Diego)

65 CENTRE DE RECHERCHES MATHÉMATIQUES

Mathematical Analysis

Description

At the same time classical and central to modern ables, potential theory, functional analysis, Ba- mathematics, analysis involves studying contin- nach algebras, microlocal analysis, analysis on uous systems from dynamical systems to solu- manifolds, nonsmooth analysis, spectral theory, tions of partial differential equations and spec- partial differential equations, geometric analy- tra of operators. The analysis laboratory was sis, ergodic theory and dynamical systems, con- formed three years ago. Currently the laboratory trol theory, mathematical physics, applied math- has 36 (regular and associate) members work- ematics, probability, nonlinear analysis, nonlin- ing at eight different universities in Quebec, ear differential equations, topological methods the USA and France. The research areas of the in differential equations, fluid dynamics and tur- members of the laboratory are harmonic analy- bulence. sis, complex analysis and several complex vari-

Activities of the laboratory in 2004–2005

Workshops, special sessions and others

Workshop on Spectral Theory of Schrödinger This workshop, also organized in the framework Operators of the 2003 – 2004 CRM theme year, was devoted July 26-30, 2004, CRM to the study of dynamical properties of (classi- Organizers: Vojkan Jaksic (McGill), Yoram Last cal and quantum) open systems. In particular, (Hebrew) through the study of noisy or forced dissipative This workshop, organized in the framework of systems, or Hamiltonian systems with a large the 2003 – 2004 CRM theme year, focused on number of degrees of freedom, our understand- the spectral theory of random and quasiperiodic ing of the mathematical structure of nonequilib- Schrödinger operators. In solid state physics rium statistical mechanics has greatly improved. random and almost periodic Schrödinger opera- The aim of this meeting was to present the latest tors serve as models of disordered systems, such results and discuss the possible future directions as alloys, glasses and amorphous materials. The of research in this area. The program included disorder of the system is reflected by the depen- short courses to be given by H. Araki (Kyoto), B. dence of the potential on some random parame- Derrida (École Normale), J. Froehlich (ETH), J.- ters. P. Eckmann (Geneva). The workshop was held This workshop brought together the world lead- in conjunction with the preceding one. ers in spectral theory of random and quasiperi- Conference on Fixed Point Theory and its Ap- odic Schrödinger operators. Its goal was to re- plications in Honour of Andrzej Granas view the state of the art of the field and to August 16-20, 2004, CRM map new directions of the research. The pro- Organizer: Marlène Frigon (Montréal) gramme included short courses given by M. The Centre de Recherches Mathematiques Aizenman (Princeton), B. Simon (Caltech), and (CRM), in collaboration with the Department S. Jitomirskaya (Irvine). The workshop was held of Mathematics and Statistic of the Université de in conjunction with the following one. Montréal, organized this conference in honour Workshop on Dynamics in Statistical Mechan- of Andrzej Granas on the occasion of his 75th ics birthday. The main themes of the conference August 2-6, 2004, CRM were fixed point theory and its applications to Organizers: Vojkan Jaksic (McGill), Claude-Alain problems arising in non-linear analysis, differ- Pillet (Toulon) ential equations and dynamical systems. Details

66 RESEARCH LABORATORIES about this activity can be found in page of this is no need to invite many speakers from abroad, report. but to let the members give the talks, so they will Analysis Day know each other’s research areas. 29 April 2005, CRM During 2004–2005, the Mathematical Analysis Organizers: Thomas Ransford (Laval), Chris- Laboratory hosted several visitors: H. Araki (Ky- tiane Rousseau (Montréal), Alina Stancu (Mont- oto), J. Artes (Barcelona), L. Bruneau (Warsaw), réal), Galia Dafni (Concordia), Dmitry Jakobson M. Cojocaru (Queen’s), S. De Bievre (Lille), J. (McGill). Derezinski (Warsaw), F. Dumortier (Limburgs This laboratory is one of the most numerous and Universitair Centrum), A. Fedotov (Physics In- is present in all the universities of the province. stitute, St-Petersbourg), B. Helffer (Paris Sud), V. This forces sub-groups of the laboratory to work Ivrii (Toronto), F. Klopp (Paris Nord), Y. Last, in parallel. To remedy the problem, and since (Hebrew), J. Llibre (Barcelona) M. Mrozek (Jag- a lot of the members do not know each other, ellon), N. Nadirashvili (CNRS, Marseille), C.-A. we started in 2004–2005 a tradition of organiz- Pillet (Toulon), L. Rey-Bellet (UMass Amherst), ing each year an Analysis Day, to which all the N. Vulpe, (Moldavian Academy), A. Sobolev members will be invited. For the moment, there (Sussex), S. Zelditch (Johns Hopkins) et E.S. Ze- ron (Cinvestav-IPN).

Seminars

Several Analysis Seminars take place in Québec Seminar in Nonlinear Analysis and Dynamical universities. The following were organized by Systems (Montréal) the members of the laboratory in 2004–2005. Organizers: Christiane Rousseau, Alina Stancu, 25 talks. Analysis (Laval): 20 talks in the regular seminar Analysis and Related Topics (Sherbrooke/Bishop’s) and 18 in the working group. Organizers: Madjid Allili, Tilak Bhattacharya, Analysis (McGill/Concordia) François Dubeau, Tomasz Kaczynski, 15 con- Organizers: Galia Dafni, Dmitry Jakobson, 22 férences. talks. Student Analysis Seminar (McGill) Analysis (Montréal) Organizer: Eugene Kritchevski Organizers: Paul Gauthier, Richard Fournier. This weekly seminar focused on complex analy- sis, organized mainly for students, 20 talks.

Members of the laboratory

Highlight of the members

• P. Guan (McGill), A. Kokotov (Concordia) ing Organization Committee, together with have recently become associate members of the presidents of the Canadian and French the laboratory and A. Shnirelman (Concordia) mathematical societies. has become regular member. • Paul Gauthier (Montréal) and Richard • P. Guan (McGill) and A. Shnirelman (Con- Fournier (Dawson) organized a sessions in cordia) have recently been awarded Senior Approximation theory and Galia Dafni (Con- Canada Research Chair Positions. cordia) organized a session in Harmonic anal- • Christiane Rousseau (Montréal) organized, in ysis at the 2004 CMS Winter Meeting in Mon- collaboration with Pavao Mardesic, a Confer- treal. ence for the 60th anniversary of Robert Rous- • Pengfei Guan (McGill) organized a Geometric sarie in June 2004 at Luminy. analysis session at AMS Meeting in Newark, • Christiane Rousseau (Montréal) organized, in Delaware, April 2005. collaboration with Robert Roussarie, the ses- sion “Dynamical systems ” during the first During the year 2004–2005, 30 master’s students, France-Canada Colloquium in July 2004 at 26 Ph.D. students and 6 postdoctoral fellows Toulouse. She was also member of the Meet- were supervised by laboratory members.

67 CENTRE DE RECHERCHES MATHÉMATIQUES

Regular members

Dmitry Jakobson (McGill) Director Niky Kamran (McGill) Pure mathematics, global analysis, spectral ge- Geometric approach to partial differential equa- ometry, quantum chaos, harmonic analysis, tions. eigenvalues and eigenfunctions Ivo Klemes (McGill) Line Baribeau (Laval) Harmonic analysis, trigonometric series. Complex and functional analysis, Banach alge- Paul Koosis (McGill) bras, holomorphic iterations, discrete groups. Analyse harmonique.Harmonic analysis. Abraham Boyarsky (Concordia) Dmitry Korotkin (Concordia) Dynamical systems Integrable systems, isomonodromic deforma- Francis Clarke (Lyon I) tions, classical and quantum gravity, Frobenius Nonlinear and dynamic analysis, control theory, varieties. calculus of variations. Javad Mashreghi (Laval) Galia Dafni (Concordia) Complex analysis, harmonic analysis, Hardy Harmonic analysis, partial derivative equations, spaces. complex variables. Iosif Polterovich (Montréal) Donald Dawson (Carleton) Geometric applications of spectral geometry. Probability, stochastic process. Thomas Ransford (Laval) Stephen Drury (McGill) Complex and harmonic analysis, functional Harmonic analysis, matrix theory. analysis and theory of operators, spectral anal- Richard Fournier (Collège Dawson) ysis, potential theory. Probability, stochastic processes. Dominic Rochon (UQTR) Marlène Frigon (Montréal) Numbers, analysis, dynamic complexes. Nonlinear analysis, differential equations, fixed Jérémie Rostand (Laval) point theory, critical point theory, multivalent Complex analysis, experimental mathematics. analysis. Christiane Rousseau (Montréal) Paul Gauthier (Montréal) Dynamical systems, bifurcations, qualitative Complex analysis, holomorphy, harmonicity, an- theory, polynomial systems, analytic invariants, alytic approximation. integrable systems. Pawel Góra (Concordia) Dana Schlomiuk (Montréal) Ergodic theory, dynamic systems, fractal geom- Global analysis, dynamical systems, singulari- etry. ties, bifurcations, algebraic curves, primary inte- Frédéric Gourdeau (Laval) gral. Banach algebras, cohomology, amenability, func- Alexander Shnirelman (Concordia) tional analysis. Applications of geometrical analysis to fluids John Harnad (Concordia) and “weak” solutions of the Euler and Navier– Mathematical physics, classical and quantum Stokes equations. physics, geometrical methods, integrable sys- Ron Stern (Concordia) tems, group theoretical methods, random ma- AFunctional analysis and theory of operators, trices, isomonodromic deformations, isospectral linear and non-linear systems, non-smooth anal- flows. ysis, stability, optimal order. Vojkan Jaksic (McGill) John Toth (McGill) Quantum mechanics, statistics, random Spectral theory, semi-classical analysis, micro- Schrödinger operators. local analysis, Hamiltonian mechanics. Tomasz Kaczynski (Sherbrooke) Topological methods, Conley index, applica- tions to dynamical systems.

68 RESEARCH LABORATORIES

Associate members

Richard Duncan (Montréal) Nilima Nigam (McGill) Ergodic theory, probability. Applied analysis, numerical methods in electro- Kohur GowriSankaran (McGill) magnetism. Potential theory. Yiannis Petridis (CUNY, Lehman College) Pengfei Guan (McGill) Automorphic forms and spectral theory. L- Geometric analysis. Functions, quantum chaos. Alexei Kokotov (Concordia) Samuel Zaidman (Montréal)

Mathematical Physics

Description

The mathematical physics group is one of the cal physics: Coherent nonlinear systems in flu- oldest and most active at the CRM. It consists ids, optics and plasmas; classical and quantum of nineteen regular members, all full-time fac- integrable systems; the spectral theory of ran- ulty at five Quebec Universities, and four asso- dom matrices; percolation phenomena; confor- ciate members. A new associate member was mal field theory; quantum statistical mechan- added this year: Alexander Shnirelman, who ics; spectral and scattering theory of random was named to a Canada Research Chair in Schrödinger operators; quasi-crystals; relativ- Applied Mathematics at Concordia University. ity; spectral transform methods; asymptotics of The Laboratory also includes two attachés de eigenstates; foundational questions in quanti- recherches, fourteen postdoctoral fellows (some, zation; coherent states; wavelets; supersymme- jointly with the Analysis and CIRGET Labo- try; the symmetry analysis of PDE’s and dif- ratories), and lab members supervise, or co- ference equations; representation theory of Lie supervise the thesis work of about forty masters groups and quantum groups; and the mathemat- and doctoral students. ical structure of classical and quantum field the- The group carries out research in many of ories. the currently most active areas in mathemati-

Activities of the laboratory in 2004–2005

Workshops, special sessions and others

Much of the year was spent in preparation for Arefijamaal (Meshhed), H. Braden (Edinburgh), the CRM “Short Program on Random Matrices, L. Chekhov (Moscow), S. De Bièvre (Lille), R. Random Processes and Integrable systems,” or- Conte (Paris), C. Eilbeck (Edinburgh), A. El ganized by two Lab members: John Harnad and Gradechi (Artois), V. Enolskii (Heriot-Watt), B. Jacques Hurtubise, which took place as part of Eynard (Saclay), M. Fels (Utah State), F. Fin- the CRM General Program on June 20 – July 8, ster (Regensburg), R. Floreanini (IFIN Trieste), 2005. Details about this activity will be found in M. Gekhtman (Notre Dame), A. Its (IUPUI), C. the 2005 – 2006 CRM annual report. Klein (Bonn), M. Knopp (Temple), A. Kokotov The members of the laboratory maintain active (St. Petersburg), D. Levi (Rome), D. Majard (Aix- ties and ongoing collaborations with other re- Marseille), N. Nadirashvili (Chicago), S. Norton searchers from centers in mathematical physics (Cambridge), E. Previato (Boston), I. Rivin (Tem- around the world. The list of scientific visitors to ple), Nasser Saad (UPEI), A. Safapour (Mesh- the laboratory this academic year included: A. hed), A. Sergyeyev (Silésie), M.K. Tavassoly (Is- pahan), P. Tempesta (SISSA Trieste), Z. Thomova

69 CENTRE DE RECHERCHES MATHÉMATIQUES

(SUNY Syracuse), S. Venakides (Duke), N. Witte The titles of these courses were: (Melbourne) and Ismet Yurdusen (Middle East Technical). Integrable systems, exactly solvable lattices and Lie groups In addition, within the framework of ISM spon- Concordia, Michael Gekhtman. sored doctoral level courses, two special series September to December 2004. of lectures were given by visiting researchers who were at the CRM for the Fall and Winter Topics in Analysis V : An Introduction to free semesters, while on sabbatical leave from their Bose fields home institutions: Professors Michael Gekht- McGill, Stephan De Bièvre. man (Notre Dame) and Stefan De Bièvre (Lille). January to April 2005.

Seminars

• The regular CRM Mathematical Physics semi- graduate students near to completion of their nar series was continued throughout the aca- doctorates. demic year, with weekly talks given both by invited visitors and local members of the • From January until April, 2005, a second Lab, including postdoctoral fellows and some “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 the “Wavelets 2005,” VIIth International Work- Royal Society of Canada. shop on Wavelets, Differential Equations, and • Alexander Shnirelman, our new Associate Quantization Member, was named a Tier I Canada Research February 21–25, 2005, University of Havana Chair at Concordia University. Organizer: Syed Twareque Ali (Concordia).

In addition the following conferences/workshops Research in teams program “Random Matrices, were organized by members of the laboratory: Multi-orthogonal Polynomials and Riemann– Special Session “In the Wake of Hamilton and Hilbert Problems” Jacobi 200 Years Later” April 30–May 14, 2005, BIRS AMS Joint Mathematics Meeting Organizer: John Harnad (Concordia). January 5–8, 2005, Atlanta, Georgia Organizers: Maria Clara Nucci (Perugia), Pavel Winternitz (Montréal).

Regular members

John Harnad (Concordia) Director Chris Cummins (Concordia) Mathematical physics, classical and quantum Group theory, modular functions, Moonshine. physics, geometrical methods, integrable sys- Alfred Michel Grundland (UQTR) tems, group theoretical methods, random ma- Symmetry of differential equations in physics. trices, isomonodromic deformations, isospectral flows. Richard L. Hall (Concordia) Spectra of Schrödinger, Klein-Gordon, Dirac, Syed Twareque Ali (Concordia) and Salpeter operators; many-body problems, Coherent states, wavelets, quantization tech- relativistic scattering theory, iterative solution to niques, harmonic analysis, Wigner functions. ode’s and boundary-value problems. Marco Bertola (Concordia) Jacques Hurtubise (McGill) Axiomatic quantum field theory, invariant Algebraic geometry, integrable systems, gauge theory of discrete groups, random matrices, theory, moduli spaces. isomonodromic deformations.

70 RESEARCH LABORATORIES

Véronique Hussin (Montréal) Pierre Mathieu (Laval) Group theory, Lie algebra and application in Conformal field theory, classical and quantum physics, supersymmetries in classic and quan- integrable systems, affine Lie algebras. tum mechanics. JiˇríPatera (Montréal) Dmitry Jakobson (McGill) Applications of group theory, quasi-crystals, Lie Pure mathematics, global analysis, spectral ge- algebras. ometry, quantum chaos, harmonic analysis. Yvan Saint-Aubin (Montréal) eigenvalues and eigenfuntions. Conformal field theory, statistical mechanics, 2- Vojkan Jaksic (McGill) dimensionalphase transition model. Mathematical physics, quantum statistical me- John Toth (McGill) chanics, random Schrödinger operators. Microlocal analysis, partial differential equa- Niky Kamran (McGill) tions. Geometric approach to partial differential equa- Luc Vinet (McGill) tions. Symmetric properties of systems, special func- Dmitry Korotkin (Concordia) tions. Integrable systems, isomonodromic deforma- Pavel Winternitz (Montréal) tions, classical and quantum gravity, Frobenius Methods of group theory in physics, nonlinear varieties. phenomena, symmetries of difference equations, Jean LeTourneux (Montréal) superintegrability. Symmetry properties of systems, special func- tions.

Associate members

Stéphane Durand (Collège Edouard-Montpetit) Carolyne Van Vliet (Miami) Classical and quantum physics, mathemati- Non-equilibrium statistical mechanics, fluctua- cal physics, symmetries, parasupersymmetries, tions and stochastic processes, quantum trans- fractional supersymmetries, KdV, quantum me- port in condensed matter, electronic behavior in chanics, relativity. submicron quantum devices. François Lalonde (Montréal) Alexander Shnirelman (Concordia) Symplectic topology and geometry, global anal- Applications of geometrical analysis to fluids ysis on manifolds, infinite dimensional transfor- and “weak” solutions of the Euler and Navier– mation groups. Stokes equations.

PhysNum

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’Unité 494 de l’INSERM (Paris), (dirigé par Habib Be- nali). La plupart des ressources financières sont Description du laboratoire consacrées à des étudiants qui poursuivent leur recherche au CRM. Notre recherche avec ces En tant que laboratoire propre au CRM, Phys- groupes porte sur l’imagerie mathématique, es- Num est un laboratoire dont une grande part sentiellement dans le domaine médical, avec les des activités de recherche est hébergée par le thèmes suivants : CRM. Cette particularité, qui contribue à la vi- sibilité du Centre dans le champ des mathéma- tiques appliquées, explique sa taille relativement • l’analyse et la modélisation en ondelettes réduite par rapport à l’étendue de ses collabo- (formalisme thermodynamique, modèles gra- rations dans les milieux de la neuro-imagerie à phiques),

71 CENTRE DE RECHERCHES MATHÉMATIQUES

• l’analyse fractale et multifractale (analyse des Ces outils sont utilisés dans plusieurs domaines matériaux, angiogénèse, signaux turbulents), cliniques et cognitifs. Les différentes équipes, • l’approche probabiliste pour la résolution de mentionnées plus haut, centrées sur la neurolo- problèmes inverses (inférence par Maximum gie, sont intéressées à voir se développer de la d’Entropie, graphes d’indépendance). “méthodologie fine” dans leur problématique et donc, une interaction à long terme avec notre équipe est envisagée.

Principaux th`emes de recherche du laboratoire pour l’ann´ee2004–2005

Maximum d’entropie et inf´erence en Magn´eto- démontrent que celle-ci permet de mieux inter- Enc´ephaloGraphie (MEG) préter les expériences, avec beaucoup moins de signaux collectés. Le travail a porté sur la version “bayésien em- pirique” du MEM qui permet de mieux contrô- Localisation de sources en MEG/EEG ler la loi de référence présente dans le for- malisme du MEM. Des algorithmes itératifs, La détection des activités cérébrales en IRMf proches d’algorithmes d’apprentissage de type et EEG/MEG reste un problème ouvert. En ef- EM (Expectation-Maximisation), ont été évalués fet, en IRMf, les modèles linéaires multidimen- sur des simulations en MEG à temps fixe et sur sionnels, actuellement utilisés, ne prennent pas des données EEG en épilepsie. Le formalisme du en compte les corrélations spatio-temporelles du maximum d’entropie continue de démontrer sa bruit présent dans les données. Souvent, ces stabilité et sa robustesse dans l’estimation des corrélations ne peuvent être négligées car elles sources dipolaires distribuées (10 000 sources) risquent d’engendrer une mauvaise estimation sur le cortex (Erwig Lapalme, Jean-Marc Lina, Jé- de la carte d’activité fonctionnelle. Pour en te- rémie Mattout, 2005). Dernière étape dans ce vo- nir compte, nous avons récemment proposé des let de recherche, l’estimation des séries tempo- modèles non séparables de covariance spatio- relles en MEG et l’évaluation des performances temporelle du bruit et calculé des cartes statis- du MEM sur des données réelles sont actuelle- tiques d’activation plus robustes. En MEG, pour ment en cours et font l’objet de la rédaction d’un extraire les distributions spatio-temporelles des article (Erwig Lapalme, Jean-Marc Lina, Bernard activités neurales, nous avons montré, au tra- Goulard, 2005). Les travaux ont fait l’objet de la vers de la thèse de Jérémie Mattout (directeurs : thèse de doctorat d’Erwig Laplame (directeurs : Habib Benali, Line Garnero), l’intérêt de combi- Jean-Marc Lina, Bernard Goulard). ner les informations spatiales issues de l’IRMf et les informations temporelles issues du signal Estimateur du signal EEG en pr´esence d’arte- MEG. Ce travail se poursuit actuellement à par- facts oculaires tir d’acquisitions simultanées IRMf/EEG et fait l’objet de la thèse de doctorat de Jean Dauni- Ce volet de recherche est une collaboration entre zeau (Thèse en cotutelle avec l’Université de PhysNum (Lina, Goulard, Basile-Bellavance) et Montréal ; directeurs : Habib Benali, Jean-Mark le département de Pédo-psychiatrie de l’Hôpital Lina et Bernard Goulard). L’intégration des in- Sainte-Justine (Robey, Liang, Basile-Bellavance). formations IRMf (imagerie de Résonance Ma- Le problème consiste à réduire le nombre de ré- gnétique Nucléaire fonctionnelle) dans la détec- pétitions de stimuli dans les expériences EEG en tion de sources en MEG/EEG (Magnéto-Electro- neuropsychiatrie chez les enfants, en proposant Encéphalographie) est l’objectif de ce volet de une méthode robuste de détection et d’élimina- recherche. L’étude d’une méthodologie d’infé- tion des artefacts oculaires dans les signaux. Ces rence sur le décours temporel des sources d’un artefacts sont la principale source de difficulté modèle dipolaire distribué, capable de prendre d’interprétation des signaux, voire du rejet des en compte des connaissances a priori multi- mesures. Le contrôle oculaire chez les jeunes en- modales, est actuellement dans sa phase d’éva- fants demeurant difficile a obtenir, la solution luation de performance. Le modèle retenu par proposée par la collaboration consiste a détec- Jean Daunizeau (doctorant en cotutelle entre ter les mouvements oculaires dans les signaux Montréal et Paris 11, codirection Benali, Gou- bruts projetés dans le plan temps-échelle par lard, Lina) s’apparente à celui développé dans une analyse en ondelettes continues. Les évalua- le cadre du Maximum d’entropie en exprimant tions de la méthode sur des signaux cliniques la dépendance temporelle à l’échelle de « par-

72 RESEARCH LABORATORIES celles » (construites à partir des données) qui gions, nous avons introduit une nouvelle défini- contiennent des sources élémentaires qui sont tion de la connectivité qui donne un rôle central contrastées localement par la méthode d’infé- à la notion de corrélation partielle. Nous avons rence (Daunizeau, Mattout, Goulard, Lina, Be- proposé un modèle théorique original, auto- nali, 2004). Soulignons que ces méthodes ont fait adaptatif aux données et guidé par des connais- l’objet d’une évaluation de performance dans un sances a priori sur le réseau fonctionnel étudié. cas clinique bien défini (Grova, Daunizeau, Lina, Ce modèle repose sur les modèles graphiques Benali, Gotman, 2004, 2005). d’association et le principe de l’échantillonnage Activité 2005 liée à ce thème : bayésien. Il permet une évaluation statistique ra- pide et robuste des différents graphes de connec- Atelier (deux journées) Inférence bayésienne et tivité possibles. Cette méthode a été validée sur Imagerie cérébrale (en collaboration avec Jean- des données de simulation et des données réelles François Angers) issues de protocoles cognitifs. Nous la validons Conférenciers : Ali Mohammad-Djafari (SupE- actuellement sur des données cliniques (chirur- lec, France), Charles A. Bouman (Purdue, USA), gie de tumeurs cérébrale). Ce travail a fait l’ob- Christophe Phillips (Liège, Belgique), Keith jet de la thèse de G. Marrelec (directeur : H. Worsley (McGill), Christophe Grova (McGill), Benali). Le modèle de connectivité développé Jean Daunizeau (Montréal). nécessite l’identification préalable du réseau de Atelier qui mit l’accent sur la modélisation de régions fonctionnellement connectées. Pour ce l’activité cérébrale et les aspects liés à la connec- faire, nous avons développé une méthode de dé- tivité. Aspects méthodologiques et implémenta- tection du réseau spatial basée sur le calcul des tion numérique. Les détails de l’activité peuvent corrélations entre les fluctuations lentes du si- être trouvés au chapitre « Programme général ». gnal IRMf (< 0.1 Hz) et le signal d’une région « cible » préalablement identifiée. Ainsi, nous Etudes´ de la connectivit´efonctionnelle en IRMf avons pu construire un réseau de régions plus étendu que celui de la carte d’activation, et indé- Les modèles pour l’étude des connectivités entre pendant de la tâche sensori-motrice considérée. populations de neurones à partir du signal IRMf Seul, le niveau de corrélation entre les noeuds et MEG/EEG sont en plein essor. La connec- du réseau identifié semble varier d’une tâche à tivité fonctionnelle est définie comme étant la l’autre. Ce travail fait l’objet de la thèse de Pierre corrélation entre deux régions du cerveau. Afin Bellec (directeur : Habib Benali). de mesurer les connectivités directes entre ré-

Membres du laboratoire

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

Membres r´eguliers

Jean-Marc Lina (ETS) responsable Line Garnero (CHU Pitié-Salpêtrière) Ondelettes, modélisation statistique et imagerie Magnéto-Encéphalo-Graphie (MEG) cérébrale, algorithmes d’apprentisage. Bernard Goulard (Montréal) Alain Arnéodo (CNRS) Imagerie cérébrale Fractales et ondelettes. Fahima Nekka (Montréal) Habib Benali (CHU Pitié-Salpêtrière) Analyse fractale, systèmes poreux, ondelettes Analyse quantitative en imagerie cérébrale, ima- Frédéric Lesage (Montréal) gerie médicale et systèmes multi-modaux Théorie conforme, systèmes intégrables, pro- blèmes inverses imagerie optique.

Membre associ´e

Keith J. Worsley (McGill) Géométrie et analyse d’images aléatoires en médecine et en astrophysique

73 CENTRE DE RECHERCHES MATHÉMATIQUES

Statistics

Description

Statistics is central to many endeavours in soci- Data-mining is one of the tools used. The labora- ety. Whether it be through surveys from sam- tory aims at structuring the Québec community pling, clinical trials to study various biomedi- to engage with this revolution at a time of an cal treatments or experimental designs in agri- important renewal of academic personnel. This culture or industry, statistical methodology can structure allows the Québec community to ben- be found everywhere in science. Recently, statis- efit from a new pan-Canadian program in analy- tics has been undergoing a revolution in its tech- sis of complex data organized by the three Cana- niques and its approaches. This revolution has dian mathematics institutes. The laboratory is been driven by the need to analyze very large composed of the leaders of the Québec school data sets, data with more complex structure, and of statistics who work on subjects such as sta- by the advent of powerful computers. For ex- tistical learning and neuronal networks, survey ample, statistical methodology is now address- sampling, analysis of functional data, statisti- ing problems whose structure is more complex, cal analysis of images, dependence structures, such as brain images or genome data and new Bayesian analysis, analysis of time series and fi- methodology is developed for large data sets. 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- on “Latent Variable Models and Survey Data for ratory were held in Montréal and in Québec in Social and Health Sciences Research” organized 2004–2005. A detailed description of these activ- by the NPCDS, in collaboration with SAMSI, ities can be found in the “General Program” and took place at the CRM in May 2005. With more the “Joint Initiatives” sections of this report. than 80 participants coming from the Nether- The annual meeting of the Statistical Society of lands, the United Kingdom, the United States Canada took place at the CRM in June 2004. and the Canada, the workshop was a success, The Program Committee was chaired by Chris- notably considering the diversity of the partic- tian Genest; Local Arrangements were coordi- ipants. Beside the experienced researchers par- nated by Christian Léger. Many commented on ticipation, the workshop was also attended by the highquality of several aspects of the meet- scientists working in statistical agencies, for in- ing organized by “the two Christian” Meeting. stance: Statistique Canada, US Census Bureau, Notably, with more than 550 participants, it was Bureau of Labor Statistics, together with re- financially the most profitable. search groups such as the Research Unit on Chil- dren’s Psychosocial Maladjustment (GRIP) and The Laboratory is proud of its association with la Direction de santé publique (Québec). the PhysNum Laboratory in the organization of the joint Workshop “Bayesian Inference and The major scientific activity of the laboratory this Functional Brain mapping.” Organized by Jean- year was the Quatrième Colloque francophone François Angers and Jean-Marc Lina, this two- sur les sondages held in Québec City in May. day workshop attended by 30 participants, With more than 225 participants, this interna- aimed to promote interaction between the spe- tional Congress welcomed world-renowed spe- cialists and researchers in functional brain im- cialists in survey methods. The Scientific Com- agery. mittee was chaired by Louis-Paul Rivest; Thierry Duchesne and Christian Léger were members of The Laboratory organizes NPCDS workshops in the Organizing Committee. Proceedings will be collaboration with the Fields and PIMS and is published. involved in its research projects. The Workshop

74 RESEARCH LABORATORIES

Seminars

The scientific life of the laboratory is fed, on support and the organization of the Statistics a weekly basis, with the CRM–ISM–GERAD Colloquium. This collaboration between CRM Statistics Colloquium in Montréal and the Statis- and GERAD is mutually beneficial for the two tics Seminar at Université Laval. As one can see, centres and their members. The complete list of GERAD joined CRM and ISM in the financial the 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- and work in Statistics. He gave a lecture at the tory: Belkacem Abdous (Laval), Masoud As- SSC meeting. gharian (McGill), Pierre Duchesne (Montréal), • In December, Russ Steele, Alain Vandal and Thierry Duchesne (Laval), Charles Dugas David Wolfson organized a session on “Math- (UdeM), Debbie Dupuis (HEC), Sorana Froda ematical Methods in Statistics” during the (UQÀM), Arush Sen (Concordia), Russ Steele Winter 2004 Meeting of the Canadian Mathe- (McGill) and Alain Vandal (McGill). matic Society. There was a strong participation • During its annual meeting in June, the Sta- from the members of the laboratory. tistical Society of Canada (SSC) granted a Gold Medal to Keith Worsley. This Medal During the year 2004–2005, 63 master’s students, is awarded to a Canadian mathematician in 44 Ph.D. students and 4 postdoctoral fellows recognition of his exceptional achievement were supervised by laboratory members.

Regular Members

Christian Léger (Montréal) Director Pierre Duchesne (Montréal) Resampling methods, adaptive estimation, Time series, sampling, multivariate analysis. model selection, robustness, applications in data Thierry Duchesne (Laval) mining. Survival analysis, longitudinal data analysis, Belkacem Abdous (Laval) missing data, modeling of losses, insurance of Biostatistics, health research methodology, con- catastrophic incidents, nonparametric inference, struction and validation of measuring tools in model selection, warranty. the health sector. Charles Dugas (Montréal) Jean-François Angers (Montréal) Actuarial science, finance, learning algorithms, Decision theory, Bayesian statistics, robustness neural networks, universal approximation, sur- with respect to prior information, function esti- vival analysis. mation. Debbie Dupuis (HEC) Masoud Asgharian (McGill) Extreme values, robustness. Survival analysis, change-point Problems, simu- René Ferland (UQÀM) lated annealing and its variants, optimization. Probability, statistic processes, applications to Yoshua Bengio (Montréal) mathematical finance. Statistical learning algorithms, neural networks, Sorana Froda (UQÀM) nucleus models, probabilistic models, data min- Nonparametric methods in function estimation, ing, applications in finance and statistical lan- applications of stochastic modeling in biology guage modeling. and medicine. Martin Bilodeau (Montréal) Christian Genest (Laval) Multivariate analysis, decision theory, asymp- Multidimensional data analysis, dependence totic methods. measures, nonparametric statistics, decision the- Yogendra Chaubey (Concordia) ory, applications in actuarial science, finance and Sampling, linear models, resampling, survival psychology. analysis.

75 CENTRE DE RECHERCHES MATHÉMATIQUES

Nadia Ghazzali (Laval) Roch Roy (Montréal) Multidimensional data analysis, neural net- Time series analysis, predictive methods, appli- works and genetic algorithms, applications in cations in econometrics and epidemiology. astrophysics and biostatistics. Arush Sen (Concordia) Brenda MacGibbon (UQÀM) Statistical inference of truncated data, nonpara- Mathematical statistics, decision theory, bio- metric function estimation. statistics. Russ Steele (McGill) François Perron (Montréal) Bayesian approaches to mixing modeling, mul- Decision theory, multidimensional data analysis, tiple imputation. Bayesian statistics. Alain Vandal (McGill) James Ramsay (McGill) Biostatistics, nonparametric survival estimation Functional data analysis, smoothing and non- and graph theory, imaging, capture-recapture. parametric regression, curve registration. David B. Wolfson (McGill) Bruno Rémillard (HEC Montréal) Changepoint problems, survival analysis, Probability, empirical processes, time series, Bayesian statistics, optimal design, applications nonlinear filtering, applications in finance. in medicine. Louis-Paul Rivest (Laval) Keith J. Worsley (McGill) Linear models, robustness, directional data, Statistics of brain mapping, geometry of random sampling, applications in finance. images in medicine and astrophysics.

76 Publications CENTRE DE RECHERCHES MATHÉMATIQUES

HE CRM publishes monographs, lecture notes, proceedings, software, videos and research re- T 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 Mathematical Society (AMS) and Springer. Since 1992, two collections, edited by CRM, have been published and distributed by the AMS. They are the CRM Monograph Series and the CRM Proceedings and Lecture Notes. Springer publishes the CRM Series in Mathematical Physics and the Subseries of the Springer Lecture Notes in Statistics. An asterisk preceding an author indicates that this is a monograph from an Aisenstadt Chair holder.

Recent Titles

The following list of Recent Titles contains books AMS that appeared in 2004 – 2005 or that will be pub- CRM Proceedings & Lecture Notes lished soon. Vestislav Apostolov, Andrew Dancer, Nigel AMS Hitchin & McKenzie Wang (eds.), Perspectives in CRM Monograph Series Comparison, Generalized and Special Geometry (to appear). Olga Kharlampovich & Alexei Myasnikov, Alge- Pavel Winternitz, David Gomez-Ullate, Arieh braic Geometry for a Free Group (to appear). Iserles, Decio Levi, Peter J. Olver, Reinout Quis- Victor Guillemin & Reyer Sjamaar Convexity pel, & Piergiulio Tempesta, Group Theory and Nu- Properties of Hamiltonian Group Actions, vol. 26, merical Analysis, vol. 39, 2005. 2005. Jacques Hurtubise & Eyal Markman, Algebraic *Andrew J. Majda, Rafail V. Abramov & Mar- Structures and Moduli Spaces, vol. 38, 2004. cus J. Grote, Information Theory and Stochastics for Piergiulio Tempesta, Pavel Winternitz, John Har- Multiscale Nonlinear Systems, vol. 25, 2005. nad, Willard Miller Jr., Georgo Pogosyan & Dana Schlomiuk, Andrei A. Bolibrukh, Sergei Miguel A. Rodriguez, Superintegrability in Clas- Yakovenko, Vadim Kaloshin & Alexandru sical and Quantum Systems, vol. 37, 2004. Buium, On Finiteness in Differential Equations and Hershy Kisilevsky & Eyal Z. Goren, Number The- Diophantine Geometry, vol. 24, 2005. ory, vol. 36, 2004. Prakash Panangaden & Franck van Breugel H. E. A. Eddy Campbell & David L. Wehlau, In- (eds.), Mathematical Techniques for Analyzing Con- variant Theory in All Characteristics, vol. 35, 2004. current and Probabilistic Systems, vol. 23, 2004. Pavel Winternitz, John Harnad, C.S. Lam & Jirí Montserrat Alsina & Pilar Bayer, Quaternion Or- Patera, Symmetry in Physics, vol. 34, 2004. ders, Quadratic Forms, and Shimura Curves, vol. 22, 2004.

Previous Titles

AMS Michael Barr, Acyclic Models, vol. 17, 2002. CRM Monograph Series *Joel Feldman, Horst Knörrer & Eugene Trubowitz, Fermionic Functional Integrals and the Andrei Tyurin, Quantization, Classical and Quan- Renormalization Group, vol. 16, 2002. tum Field Theory and Theta Functions, vol. 21, 2003. Jose I. Burgos, The Regulators of Beilinson and Borel, vol. 15, 2002. Joel Feldman, Horst Knörrer & Eugene Trubowitz, Riemann Surfaces of Infinite Genus, Eyal Z. Goren, Lectures on Hilbert Modular Vari- vol. 20, 2003. eties and Modular Forms, vol. 14, 2002. *Laurent Lafforgue, Chirurgie des grassmanni- Michael Baake & Robert V. Moody (eds.), Direc- ennes, vol. 19, 2003. tions in Mathematical Quasicrystals, vol. 13, 2000. *George Lusztig, Hecke Algebras with Unequal Pa- Masayoshi Miyanishi, Open Algebraic Surfaces, rameters, vol. 18, 2003. vol. 12, 2001.

78 PUBLICATIONS

Spencer J. Bloch, Higher Regulators, Algebraic John Harnad, Gert Sabidussi & Pavel Winternitz K-Theory, and Zeta Functions of Elliptic Curves, (eds.), Integrable Systems: From Classical to Quan- vol. 11, 2000. tum, vol. 26, 2000. James D. Lewis, A Survey of the Hodge Conjecture, Decio Levi & Orlando Ragnisco (eds.), SIDE 2e édition, vol. 10, 1999 (with an appendix by III — Symmetry and Integrability of Difference B. Brent Gordon). Equations, vol. 25, 2000. *Yves Meyer, Wavelets, Vibrations and Scaling, B. Brent Gordon, James D. Lewis, Stefan Müller- vol. 9, 1997. Stach, Shuji Saito & Noriko Yui (eds.), The Arith- *Ioannis Karatzas, Lectures on Mathematics of Fi- metic and Geometry of Algebraic Cycles, vol. 24, nance, vol. 8, 1996. 2000. John Milton, Dynamics of Small Neural Popula- Pierre Hansen & Odile Marcotte (eds.), Graph tions, vol. 7, 1996. Colouring and Applications, vol. 23, 1999. *Eugene B. Dynkin, An Introduction to Branching Jan Felipe van Diejen & Luc Vinet (eds.), Al- Measure-Valued Processes, vol. 6, 1994. gebraic Methods and q-Special Functions, vol. 22, 1999. Andrew M. Bruckner, Differentiation of Real Func- tions, vol. 5, 1994. Michel Fortin (ed.), Plates and Shells, vol. 21, 1999. *David Ruelle, Dynamical Zeta Functions for Piece- Katie Coughlin (ed.), Semi-Analytic Methods for wise Monotone Maps of the Interval, vol. 4, 1994. the Navier – Stokes Equations, vol. 20, 1999. V. Kumar Murty, Introduction to Abelian Varieties, Rajiv Gupta & Kenneth S. Williams (eds.), Num- vol. 3, 1993. ber Theory, vol. 19, 1999. Maximilian Ya. Antimirov, Andrei A. Kolyshkin Serge Dubuc & Gilles Deslauriers (eds.), Spline & Rémi Vaillancourt, Applied Integral Transforms, Functions and the Theory of Wavelets, vol. 18, 1999 vol. 2, 1993. Olga Karlampovich (ed.), Summer School in *Dan V. Voiculescu, Kenneth J. Dykema & Group Theory in Banff, 1996, vol. 17, 1998. Alexandru Nica, Free Random Variables, vol. 1, Alain Vincent (ed.), Numerical Methods in Fluid 1992. Mechanics, vol.16, 1998. François Lalonde (ed.), Geometry, Topology and AMS Dynamics, vol. 15, 1998. CRM Proceedings & Lecture Notes John Harnad & Alex Kasman (eds.), The Bispec- André D. Bandrauk, Michel C. Delfour & Claude tral Problem, vol. 14, 1998. Le Bris (eds.), Quantum Control: Mathematical and Michel Delfour (ed.), Boundaries, Interfaces and Numerical Challenges, vol. 33, 2003. Transitions, vol. 13, 1998. Vadim B. Kuznetsov (ed.), The Kowalevski Prop- Peter G. Greiner, Victor Ivrii, Luis A. Seco & erty, vol. 32, 2002. Catherine Sulem (eds.), Partial Differential Equa- John Harnad & Alexander R. Its (eds.), Isomon- tions and their Applications, vol. 12, 1997. odromic Deformations and Applications in Physics, Luc Vinet (ed.), Advances in Mathematical Sci- vol. 31, 2002 ences: CRM’s 25 Years, vol. 11, 1997. John McKay & Abdellah Sebbar (eds.), Proceed- Donald E. Knuth, Stable Marriage and Its Relation ings on Moonshine and Related Topics, vol. 30, 2001. to Other Combinatorial Problems, vol. 10, 1996. Alan Coley, Decio Levi, Robert Milson, Colin Decio Levi, Luc Vinet, & Pavel Winternitz (eds.), Rogers & Pavel Winternitz (eds.), Bäcklund and Symmetries and Integrability of Difference Equa- Darboux Transformations, vol. 29, 2001. tions, vol. 9, 1995. John C. Taylor (ed.), Topics in Probability and Lie Joel S. Feldman, Richard Froese & Lon M. Groups: Boundary Theory, vol. 28, 2001. Rosen (eds.), Mathematical Quantum Theory II: Israel M. Sigal & Catherine Sulem (eds.), Nonlin- Schrödinger Operator, vol. 8, 1995. ear Dynamics and Renormalization Group, vol. 27, Joel S. Feldman, Richard Froese, & Lon M. Rosen 2001. (eds.), Mathematical Quantum Theory I: Field The- ory and Many-Body Theory, vol. 7, 1994.

79 CENTRE DE RECHERCHES MATHÉMATIQUES

Guido Mislin (ed.), The Hilton Symposium 1993, Nadia El-Mabrouk, Thomas Lengauer & David vol. 6, 1994. Sankoff (eds.), Currents in Computational Molecu- Donald A. Dawson (ed.), Measure-Valued Pro- lar Biology, 2001. cesses, Stochastic Partial Differential Equations and James G. Huard & Kenneth S. Williams (eds.), Interacting Systems, vol. 5, 1994. The Collected Papers of Sarvadaman Chowla Vol- Hershy Kisilevsky & M. Ram Murty (eds.), Ellip- ume I 1925-1935; Volume II 1936-1961; Vol- tic Curves and Related Topics, vol. 4, 1994. ume III 1962-1986, 2000. Andrei L. Smirnov & Rémi Vaillancourt (eds.), Michael Barr & Charles Wells, Category Theory for Asymptotic Methods in Mechanics, vol. 3, 1993. Computing Science, 1999. Philip D. Loewen, Optimal Control via Nonsmooth Maximilian Ya. Antimirov, Andrei A. Kolyshkin Analysis, vol. 2, 1993. & Rémi Vaillancourt, Mathematical Models for Eddy Current Testing, 1998. M. Ram Murty (ed.), Theta Functions, vol. 1, 1993. Xavier Fernique, Fonctions aléatoires gaussiennes, Springer vecteurs aléatoires gaussiens, Montréal, 1997. CRM Series in Mathematical Physics Faqir Khanna & Luc Vinet (eds.), Field Theory, In- tegrable Systems and Symmetries, Montréal, 1997. David Sénéchal, André-Marie Tremblay & Paul Koosis, Leçons sur le théorème de Beurling at Claude Bourbonnais, Theoretical Methods for Malliavin, 1996. Strongly Correlated Electrons, 2003. David W. Rand, Concorder Version Three, 1996 *Roman Jackiw, Lectures on Fluid Dynamics, 2002. (software and user guide). Yvan Saint-Aubin & Luc Vinet (eds.), Theoretical Jacques Gauvin, Theory of Nonconvex Program- Physics at the End of the Twentieth Century, 2001. ming, 1994. Yvan Saint-Aubin & Luc Vinet (eds.), Algebraic Decio Levi, Curtis R. Menyuk & Pavel Win- Methods in Physics, 2000. ternitz (eds.), Self-Similarity in Stimulated Raman Jan Felipe van Diejen & Luc Vinet (eds.), Scattering, 1994. Calogero – Moser – Sutherland Models, 1999. Rémi Vaillancourt, Compléments de mathématiques Robert Conte (ed.), The Painlevé Property, 1999. pour ingénieurs Montréal, 1993. Richard MacKenzie, Manu B. Paranjape & Woj- Robert P. Langlands & Dinakar Ramakrishnan ciech J. M. Zakrzewski (eds.), Solitons, 1999. (eds.), The Zeta Functions of Picard Modular Sur- Luc Vinet & Gordon Semenoff (eds.), Particles faces, 1992. and Fields (Banff, 1994), 1998. Florin N. Diacu, Singularities of the N-Body Prob- lem, 1992. Springer Jacques Gauvin, Théorie de la programmation CRM Subseries of the Lecture Notes in mathématique non convexe, 1992. Statistics Pierre Ferland, Claude Tricot, & Axel van de Marc Moore (ed.), Spatial Statistics: Methodologi- Walle, Analyse fractale, 1992 (software and user cal Aspects and Applications, 2001. guide). S. Ejaz Ahmed & Nancy Reid (eds.), Empirical Stéphane Baldo, Introduction à la topologie des en- Bayes and Likelihood Inference, 2001. sembles fractals, 1991. Robert Bédard, Groupes linéaires algébriques, 1991. CRM Publications Rudolf Beran & Gilles R. Ducharme, Asymptotic Luc Lapointe, Ge Mo-Lin, Yvan Saint-Aubin & Theory for Bootstrap Methods in Statistics, 1991. Luc Vinet, Proceedings of the Canada-China Meet- James D. Lewis, A Survey of the Hodge Conjecture, ing on Theoretical Physics, 2003. 1991. Armel Mercier, Fonctions de plusieurs variables : David W. Rand & Tatiana Patera, Concorder, 1991 Différentiation, 2002. (software and user guide). David W. Rand & Tatiana Patera, Le Concordeur, 1991 (software and user guide).

80 PUBLICATIONS

Véronique Hussin (ed.), Lie Theory, Differential *Robert Hermann, Physical Aspects of Lie Group Equations and Representation Theory, 1990. Theory, 1974. John Harnad & Jerrold E. Marsden (eds.), Hamil- *Mark Kac, Quelques problèmes mathématiques en tonian Systems, Transformation Groups and Spectral physique statistique, 1974. Transform Methods, 1990. *Sybreen de Groot, La transformation de Weyl et la M. Ram Murty (ed.), Automorphic Forms and An- fonction de Wigner: une forme alternative de la mé- alytic Number Theory, 1990. canique quantique, 1974. Wendy G. McKay, JiˇríPatera & David W. Rand, Tables of Representations of Simple Lie Algebras. Other Collaborations with Publishers Volume I. Exceptional Simple Lie Algebras, 1990. Anthony W. Knapp, Representations of Real Re- Marc Moore, Sorana Froda & Christian Léger ductive Groups, 1990. (eds.), Mathematical Statistics and Applications: Festschrift for Constance van Eeden, Lecture Wendy G. McKay, JiˇríPatera & David W. Rand, Notes – Monograph Series, vol. 42, 2003 (a col- SimpLie, 1990 (software and user guide). laboration with the Institute of Mathematical Francis H. Clarke, Optimization and Nonsmooth Statistics). Analysis, Montréal, 1989. Duong H. Phong, Luc Vinet & Shing-Tung Yau Samuel Zaidman. Une introduction à la théorie des (eds.), Mirror Manifolds and Geometry, AMS/IP équations aux dérivées partielles, 1989. Studies in Advanced Mathematics, vol. 10, 1998 *Yuri I. Manin, Quantum Groups and Noncommu- (a collaboration with the AMS and the Interna- tative Geometry, Les Publications CRM, 1988. tional Press). Lucien Le Cam, Notes on Asymptotic Methods in Pierre Ferland, Claude Tricot & Axel van de Statistical Decision Theory, 1974. Walle, Fractal Analysis User’s Guide, 1994 (a col- laboration with the AMS). Les Presses de l’Universit´ede Montr´eal Hedy Attouch, Jean-Pierre Aubin, Francis Aisenstadt Chair Collection Clarke & Ivar Ekeland (eds.), Analyse non linéaire, 1989 (a collaboration with Gauthiers-Villars). Laurent Schwartz, Semimartingales and Their Stochastic Calculus on Manifolds, 1984. Videos *Yuval Ne0eman, Symétries, jauges et variétés de groupe, 1979. Efim Zelmanov, Abstract Algebra in the 20th Cen- *R. Tyrrell Rockafellar, La théorie des sous- tury, 1997. gradients et ses applications à l’optimisation, fonc- Serge Lang, Les grands courants, 1991 tions convexes et non convexes, 1979. Robert Bédard, Brouiller les cartes, 1991. *Jacques-Louis Lions, Sur quelques questions d’analyse, de mécanique et de contrôle optimal, 1976. Serge Lang, Les équations diophantiennes, 1991. *Donald E. Knuth, Mariage stables et leurs relations Laurent Schwartz, Le mouvement brownien,1990. avec d’autres problèmes combinatoires, 1976. Laurent Schwartz, Une vie de mathématicien, 1989.

CRM Preprints

Bertola, M., Eynard, B., Harnad, J., Semiclas- Cornea, O., Lalonde, F., A universal Floer theory, sical orthogonal polynomials, matrix models and localization and applications, Centre de recherches isomonodromic tau functions, Centre de recher- mathématiques, CRM-3172, 2004. ches mathématiques, CRM-3169, October 2004; Dryanov, D., Fournier, R., On a discrete vari- arXiv:nlin.SI/0410043. ant of Bernstein’s polynomial inequality, Centre de Bertola, M., Gekhtman, M., Biorthogonal Laurent recherches mathématiques, CRM-3178, January polynomials, Töplitz determinants, minimal Toda or- 2005. bits and isomonodromic tau functions, Centre de El Boukili, A., Madrane, A., Vaillancourt, R., recherches mathématiques, CRM-3182, March Multifrontal solution of sparse unsymmetric matri- 2005. ces arising from semiconductor equations, Centre

81 CENTRE DE RECHERCHES MATHÉMATIQUES de recherches mathématiques, CRM-3125, June Rousseau, C., Christopher, C., Modulus of analytic 2004. classification for the generic unfolding of a codimen- Ghidaoui, M. S., Kolyshkin, A. A., Vaillancourt, sion one resonant diffeomorphism or resonant sad- R., Transient turbulent flow in a pipe, Centre de dle, Centre de recherches mathématiques, CRM- recherches mathématiques, CRM-3176, January 3167, September 2004. 2005. Saidi, A., Consistent testing for independence of Grundland, A. M., Strasburger, A., Zakrzewski, two partially nonstationary vector ARMA time se- W. J. M., Surfaces immersed in su(N + 1) Lie alge- ries, Centre de recherches mathématiques, CRM- bras obtained from the CPN sigma models, Centre de 3173, November 2004. recherches mathématiques, CRM-3180, February Schlomiuk, D., Vulpe, N., Integrals and phase por- 2005. traits of planar quadratic differential systems of in- Mélard, G., Roy, R., Saidi, A., Exact maximum variant lines of at least five total multiplicity, Cen- likelihood estimation of structured or unit root mul- tre de recherches mathématiques, CRM-3181, tivariate time series models, Centre de recherches March 2005. mathématiques, CRM-3129, June 2004. Schlomiuk, D., Vulpe, N., The full study of pla- Nguyen-Ba, T., Kolyshkin, A. A., Vaillancourt, nar quadratic differential systems possessing exactly R., Hermite – Birkhoff differential equation solvers, one line of singularities, finite or infinite, Centre Centre de recherches mathématiques, CRM- de recherches mathématiques, CRM-3183, April 3175, December 2004. 2005. Ratnarajah, T., Vaillancourt, R., Quadratic forms Yoshikawa, M., Gong, Y., Ashino, R., Vaillan- on complex random matrices and channel capac- court, R., Case study on SVD multiresolution analy- ity, Centre de recherches mathématiques, CRM- sis, Centre de recherches mathématiques, CRM- 3126, June 2004. 3179, January 2005. Ratnarajah, T., Vaillancourt, R., Alvo, M., Com- Zhao, M., Ghidaoui, M. S., Kolyshkin, A. A., plex random matrices and Rician channel capac- Vaillancourt, R., On the stability of oscillatory ity, Centre de recherches mathématiques, CRM- pipe flows, Centre de recherches mathématiques, 3174, October 2004. CRM-3168, October 2004.

For other preprints by CRM members see page 90.

82 Scientific Personnel CENTRE DE RECHERCHES MATHÉMATIQUES

CRM Members in 2004-2005

N contrast with most other mathematics institutes around the world, the CRM can count on the Isolid 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 researchers attached to the CRM in 2004–2005 as part of exchange agreements with neighbouring universities and industry or are long-term visitors from Canadian and foreign institutions. The presence at the CRM of such an active group of researchers has brought many benefits to the Centre. In particular, the CRM’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 partnership is with the Université de Montréal, which gives the equivalent of five fulltime teaching positions in release time to the CRM. Release agreements with the other Montréal area universities provide for the equivalent of two more full-time positions. Facilities are also provided to researchers attached to junior colleges. Several members are attached to the CRM through industrial agreements.

Regular Members

Syed Twareque Ali, Concordia Chantal David, Concordia Vestislav Apostolov, UQÀM Michel C. Delfour, Montréal Paul Arminjon, Montréal Eusebius J. Doedel, Concordia André D. Bandrauk, Sherbrooke Rachida Dssouli, Concordia Nadia El-Mabrouk, Montréal Line Baribeau, Laval Marlène Frigon, Montréal Peter Bartello, McGill Martin J. Gander, Gèneve and McGill Robert Bédard, UQÀM Paul M. Gauthier, Montréal Jacques Bélair, Montréal Eyal Z. Goren, McGill Habib Benali, INSERM Bernard Goulard, Montréal Yoshua Bengio, Montréal Andrew Granville, Montréal Anne Bergeron, UQÀM Alfred Michel Grundland, UQTR François Bergeron, UQÀM Gena Hahn, Montréal Marco Bertola, Concordia Richard L. Hall, Concordia Yves Bourgault, Ottawa Michael Hallett, McGill Anne Bourlioux, Montréal John Harnad, Montréal Steven Boyer, UQÀM Antony R. Humphries, McGill Gilles Brassard, Montréal Jacques Hurtubise, McGill Véronique Hussin, Montréal Abraham Broer, Montréal Adrian Iovita, Concordia Robert C. Brunet, Montréal Dmitry Jakobson, McGill David Bryant, McGill Vojkan Jaksic, McGill Vašek Chvátal, Concordia Niky Kamran, McGill Francis H. Clarke, Lyon I Olga Kharlampovich, McGill Olivier Collin, UQÀM Hershy Kisilevsky, Concordia Claude Crépeau, McGill Paul Koosis, McGill Miklós Cs˝urös,Montréal Dmitry Korotkin, Concordia Chris Cummins, Concordia Gilbert Labelle, UQÀM Galia Dafni, Concordia Jacques Labelle, UQÀM Henri Darmon, McGill François Lalonde, Montréal

84 SCIENTIFIC PERSONNEL

Robert P. Langlands, Institute for Advanced JiˇríPatera, Montréal Study Iosif Polterovich, Montréal Christian Léger, Montréal Thomas J. Ransford, Laval Pierre Leroux, UQÀM Christophe Reutenauer, UQÀM Frédéric Lesage, Polytechnique Montréal Ivo G. Rosenberg, Montréal Sabin Lessard, Montréal Christiane Rousseau, Montréal Jean LeTourneux, Montréal Roch Roy, Montréal Claude Levesque, Laval Peter Russell, McGill Jean-Marc Lina, ETS Gert Sabidussi, Montréal Brenda MacGibbon, UQÀM Yvan Saint-Aubin, Montréal François Major, Montréal David Sankoff, Ottawa Vladimir Makarenkov, UQÀM Dana Schlomiuk, Montréal Michael Makkai, McGill E.J.P. Georg Schmidt, McGill Patrice Marcotte, Montréal Alexander Shnirelman, Concordia Javad Mashreghi, Laval Ron J. Stern, Concordia Sherwin A. Maslowe, McGill John A. Toth, McGill Pierre Mathieu, Laval Luc Vinet, McGill John McKay, Concordia Pavel Winternitz, Montréal Alexei G. Miasnikov, McGill Daniel T. Wise, McGill Nilima Nigam, McGill Keith J. Worsley, McGill

Associate Members

Liliane Beaulieu, Vieux-Montréal Yannis N. Petridis, CUNY-Lehman College Nantel Bergeron, York Elisa Shahbazian, Lockheed Martin Robert Conte, CEA Saclay Francisco Thaine, Concordia Stéphane Durand, Édouard-Montpetit Pierre Valin, Défense Canada-Valcartier Richard Fournier, Dawson and Montréal Carolyne M. Van Vliet, Miami Decio Levi, Roma Tre Jean-Paul Zolésio, INRIA Sophia-Antipolis Fahima Nekka, Montréal

Invited Members

Jean-François Angers, Montréal Jun Li, Montréal Octav Cornea, Montréal François Perron, Montréal Louis G. Doray, Montréal Damien Roy, Ottawa Pierre Duchesne, Montréal Abdellah Sebbar, Ottawa Charles Dugas, Montréal

Postdoctoral Fellows

Each year the CRM plays host to a great number of postdoctoral fellows. The sources for their funding include 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 individual research grants from CRM members. The list below includes postdoctoral fellows in residence at the

85 CENTRE DE RECHERCHES MATHÉMATIQUES

CRM and those co-funded by the CRM. Some of the fellows were in residence at the CRM for only part of the year. The affiliation is that where their doctoral degree was obtained.

Alain Bourget, McMaster University Ramin Mohammadalikhani, University of Abdellatif Bourhim, Université Mohammed V Toronto Chadi Nour, Université de Lyon I Guillaume Bourque, University of Southern California Ambrus Pal, Columbia University Peter S. Campbell, University of Alberta Yan Pautrat, Université de Grenoble I Raquel Casesnoves, Université de Montréal Bélà Gabor Pusztai, University of Szeged Stéphane Dellacherie, Université de Paris VII Mario Roy, Universität Göttingen Mostafa Gabbouhy, Université Ibn Tofaïl Anupam Saikia, University of Cambridge David T. Gay, University of California at Mohamed Noureddine Senhadji, Université Berkeley d’Oran Libor Snobl, Czech Technical Institute Yoshitaka Hachimori, University of Tokyo Shannon Lee Starr, University of California at Harald Andres Helfgott, Princeton University Davis Alexander Ivrii, Stanford University Phi Long Thanh (Nguyen), Columbia Sergei Krutelevich, Yale University University Marcelo Lanzilotta Mernies, Stanford Ye Tian, Columbia University University Stephan Tillmann, University of Melbourne Tony Lelièvre, École nationale des ponts et Michèle Suzanne Titcombe, University of chaussées British Columbia Jun Li, Université de Montréal José Manuel Urquiza, Université de Paris VI Peter McNamara, Massachusetts Institute of Dimiter Vassilev, Purdue University Technology Ismet Yurdusen, Middle East Technical Marco Merkli, University of Toronto University Man Yue Mo, Oxford University 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 participate in 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 and 324 in those of the industrial and multidisciplinary program. The following list includes only visitors who were in residence for at least four weeks:

Huzihiro Araki, Kyoto Ibrahim Fatkullin, Caltech Harry W. Braden, Edinburgh Alexander Fedotov, ITEP Moscou Laurent Bruneau, Warsaw Mark Fels, Utah State Pierre Charollois, Bordeaux I André Garon, Polytechnique Montréal Monica-Gabriela Cojocaru, Queen’s Michael Gekhtman, Notre Dame Robert Conte, CEA Saclay Rajendra Gurjar, Tata Institute Stephan De Bièvre, Lille I Bernard Helffer, Paris Sud Jan Derezinski, Warsaw Thomas Yizhao Hou, Caltech Alain Desgagné, Drake Alexander Its, IUPU Indianapolis Amine El Gradechi, Artois Yael Karshon, Toronto

86 SCIENTIFIC PERSONNEL

Ely Kerman, Illinois at Urbana-Champaign Mohamad Reza Pouryayevali, Isfahan Boualem Khouider, Victoria Igor Rivin, Temple Frédéric Klopp, Paris XIII Stephan Ruscheweyh, Würzburg Alexey Kokotov, Concordia (LTA) Pavle Saksida, Ljubljana Pierre Lafaye de Micheaux, Grenoble II Gerald Schmieder, Oldenburg Yoram Last, Hebrew Artur Sergyeyev, Silesia Claude Le Bris, ENPC Jean-Claude Sikorav, ENS Lyon Claude LeBrun, SUNY Stony Brook Panagiotis Souganidis, Texas A&M Decio Levi, Roma Tre Piergiulio Tempesta, SISSA Trieste Michael Levitin, Heriot-Watt Loïc Teyssier, Strasbourg Andrew J. Majda, Courant Inst. Marc Thiriet, INRIA Rocquencourt Kayo Masuda, Himeji Institute of Technology Masayoshi Miyanishi, Kwansei Gakuin Zora Thomova, SUNY Syracuse Nikolai Nadirashvili, Chicago Jiri Tolar, Czech Technical Institute Soghra Nobakhtian, Isfahan Eric Vanden-Eijnden, Courant Inst. Renata Otahalova, Silesia Nicolae Vulpe, Academy of Sciences, Moldova Lubomir Pekar, Faculty Hospital Motol Eduardo Santillan Zeron, Cinvestav-IPN Claude-Alain Pillet, Toulon Jean-Paul Zolésio, INRIA Sophia-Antipolis

Short-term Visitors

Visitors who were in residence for less than four weeks:

Casim Abbas, Michigan State Eric Friedlander, Northwerstern Michael T. Anderson, SUNY Stony Brook Line Garnero, Hôpital de la Salpêtrière Silvia Anjos, Instituto Superior Technico Paul Gauduchon, École Polytechnique Meenaxi Bhattacharjee, Würzburg Palaiseau Jean-Pierre Gazeau, Paris VII Michel Bernadou, Pôle universitaire Léonard de Vinci Peter Gibson, Toronto Anne-Laure Biolley, Toronto Victor Ginzburg, UC Santa Cruz Olivier Biquard, Strasbourg Peter Glynn, Stanford Daniel R. Grayson, Illinois at Frédéric Bourgeois, UL Bruxelles Urbana-Champaign Charles P. Boyer, New Mexico Karsten Grove, Maryland Robert Bryant, Duke Alexander Gutfraind, Waterloo Leonid Chekhov, Steklov Mathematical Institute Gergely Harcos, UT Austin Andrew Dancer, Oxford Kevin Hare, Waterloo Hassan Doosti, Mashhad Samvel Haroutiunian, Yerevan State University C. Eilbeck, Celera Genomics Richard Hind, Notre Dame Yakov Eliashberg, Stanford Nigel J. Hitchin, Oxford Misha Entov, Institut Weizmann Rick Jardine, Western Ontario Alexandre Ern, ENPC George Kesidis, Penn State Catalin Fetita, Institut National des Manfred Kolster, McMaster Télécommunications Vladimir E. Korepin, SUNY Stony Brook Felix Finster, Regensburg Olivier Lafitte, Paris XIII

87 CENTRE DE RECHERCHES MATHÉMATIQUES

Michael Lamoureux, Calgary Yongbin Ruan, UW Madison Jibin Li, Kunning University of Science and Simon Salamon, Imperial College London Technology Paul Seidel, Chicago Chiu-Chu Liu, Harvard Anders Skrondal, London School of Economics Joachim Lohkamp, Augsburg Raj Srinivasan, Saskatchewan Grégoire Malandain, INRIA Andrei Teleman, Aix-Marseille I Gary Margrave, Calgary Mary E. Thompson, Waterloo Dusa McDuff, SUNY Stony Brook Alexander Turbiner, UNAM Arian Novruzi, Ottawa Tom Osborn, Manitoba Ravi Vakil, Stanford Charles Peskin, Courant Inst. Stephanos Venakides, Duke Martin Pinsonnault, Fields Inst. McKenzie Y. Wang, McMaster Alexandru-Anton Popa, Princeton Katrin Wehrheim, ETH Zürich Emma Previato, Boston Jean-Yves Welschinger, ENS Lyon Sophia Rabe-Hesketh, UC Berkeley Hongmei Zhu, York

88 Preprints and Research Reports CENTRE DE RECHERCHES MATHÉMATIQUES

HE quality of the CRM members’ research can be measured by the abundance of their scientific Tpublications. Here follows a list of research reports, preprints and articles submitted during 2004– 2005.

Aberkane, A., Brlek, S., Sequences with com- International Journal of Quantum Chem- plexity given by that of Thue-Morse, Discrete istry, submitted. Mathematics, submitted. Bandrauk, A., Nguyen, H. S., Attosecond Ali, S. T., Bagarello, F., Some physical appear- molecular spectroscopy, Canadian Journal of ances of vector coherent states and CS related Chemistry, submitted. to degenerate Hamiltonians, Journal of Math- Baron, M., Bell, M. G., Bookman, A., Jerome, ematical Physics, 46 (May 2005), 053518. D., Kamiska, E., Lupton, T., Pope, J., Steele, Anjos, S., Lalonde, F., The homotopy type of the R., Reliability and validity of ophthalmoscopic space of symplectic balls in S2XS2 above the capillaroscopy in systemic sclerosis, Journal of critical value, arXiv:math.SG/0406129, July Experimental Rheumatology (2005), sub- 2004. mitted. Apostolov, V., Calderbank, M. J., Gauduchon, Bengio, Y., Delalleau, O., Le Roux, N., P.,Tonnesen-Friedman, C. W., Hamiltonian The curse of dimensionality for local kernel 2-forms in Kaehler geometry III: Compact ex- machines, Département d’informatique et amples, math.DG/0501516, January 2005. recherche opérationnelle, Technical Report no. 1258, March 2005. Apostolov, V., Tonnesen-Friedman, C. W., A remark on Kähler metrics of constant scalar Bengio, Y., Larochelle, H., Implantation et curvature on ruled complex surfaces, The Bul- analyse d’un modèle graphique à entraîne- letin of the London Mathematical Society, ment supervisé, semi-supervisé et non su- to appear. pervisé pour la désambiguïsation sémantique, Département d’informatique et recherche Arminjon, P., Touma, R., Central finite volume opérationnelle, Technical Report no. 1252, methods with constrained transport divergence 2004. for ideal MHD, Journal of Computational Physics, 204:2 (May 2005), 737–759. Bengio, Y., Monperrus, M., Discovering shared structure in manifold learning, Départe- Arminjon, P., Touma, R., Central schemes with ment d’informatique et recherche opéra- constrained transport divergence treatment for tionnelle, Technical Report no. 1250, July two-dimensional ideal MHD, SIAM Journal 2004. on Scientific Computing, submitted. Bergeron, A., Stoye, J., On the similarity of sets Asgharian, M., Wolfson, D. B., Zhang, X., of permutations and its applications to genome Checking stationarity of incidence rate using comparison, Journal of Computational Biol- prevalent cohort survival data, Statistics in ogy, submitted. Medicine, submitted. Bergeron, F., Biagioli, R., Tensorial square of the Asgharian, M., Wolfson, D. B., Zhang, X., hyperoctahedral group coinvariant space, sub- A simple criterion for the stationarity of the mitted. incidence rate from prevalent cohort studies, Statistics in Medicine, submitted. Bergeron, F., McNamara, P., Some positive differences of products of Schur functions, Aval, J., Bergeron, F., Bergeron, N., Diago- arXiv:math.CO/0412289, December 2004. nal Temperley-Lieb invariants and harmonics, arXiv:math.CO/0411568, November 2004. Bergeron, M., Mullins, J., SOCLE project : UML and OCL Semantics in ASM, National De- Azambre, D., Bergeron, M., Mullins, J., SOCLE fense of Canada, 2004. project : UML to UCFG compilation : Compos- ability and source code generation, National Bergeron, N., Gao, Y., Hu, N., Drinfel’d doubles Defense of Canada, 2004. and Lusztig’s symmetries of two-parameter quantum groups, arXiv:math.RT/0505614, Bandrauk, A., Chelkowski, S., Nguyen, H. S., May 2005. Attosecond control of electrons in molecules,

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Bergeron, N., Hohlweg, C., Coloured for pseudo-telepathy, Quantum Information peak algebras and Hopf algebras, and Computation, to appear. arXiv:math.AC/0505612, May 2005. Brlek, S., Melançon, G., Paquin, G., Properties Bergeron, N., Reutenauer, C., Rosas, M. H., of the extremal intinite smooth words, Jour- Zabrocki, M., Invariants and coinvariants nal of Automata, Languages and Combi- of the symmetric group in noncommuting natorics, submitted. variables, arXiv:math.CO/0502082, Febru- Brlek, S., Pergola, E., Roques, O., Non Uniform ary 2005. Random Generation of Generalized Motzkin Bergeron-Brlek,√ A., Brlek, S., Labelle, J., Irra- Paths, Acta Informatica, submitted. tionality of 3 — A geometric proof, Mathe- Bumagin, I., Kharlampovich, O., Mias- matics Magazine, submitted. nikov, A. G., Isomorphism problem for Bertola, M., Eynard, B., Harnad, J., Semi- finitely generated fully residually free groups, classical orthogonal polynomials, matrix mod- arXiv:math.GR/0502496, February 2005. els and isomonodromic tau functions, Centre Caffarelli, L. A., Guan, P., Ma, X.-N., A general de recherches mathématiques, CRM-3169, convexity principle for fully nonlinear elliptic October 2004,; arXiv:nlin.SI/0410043. equations . Bertola, M., Gekhtman, M., Biorthogonal Lau- Chelkowski, S., Bandrauk, A., Apolonski, A., rent polynomials, Töplitz determinants, mini- Phase-dependent asymmetries in strong-field mal Toda orbits and isomonodromic tau func- ionization, Physical Reviews A, submitted. tions, Centre de recherches mathémati- ques, CRM-3182, March 2005. Chelkowski, S., Bandrauk, A., Corkum, P., Control of nuclear processes with super intense Bertolini, M., Darmon, H., The rationality of laser fields, Physics Reviews Letters, sub- Stark-Heegner points over genus fields of real mitted. quadratic fields, submitted. Chen, Y., Dinwoodie, I. H., MacGibbon, Beuter, A., Lambert, B., MacGibbon, B., Quan- B., Sampling for conditional inference on tifying postural tremor changes in workers ex- case/control data, Journal of the Royal Sta- posed to low levels of manganese, Journal of tistical Society B, submitted. Neuroscience Methods, submitted. Clarke, F. H., Continuity of solutions to a basic Blomer, V., Granville, A., Estimates for the rep- problem in the calculus of variations, Annali resentation numbers of binary quadratic forms, della Scuola Normale Superiore de Pisa, Duke Mathematical Journal, submitted. submitted. Bouchard, M., Carrier, G., Brunet, R. C., Coleman, R., Iovita, A., Hidden structures on Noisel, N., Labarre, G., Dumas, P., We- curves, submitted. ber, J. P., Biological monitoring of exposure to organophosphorus insecticides in horticultural Colin, F., Frigon, M., Systems of singular Pois- greenhouse workers, Science of Total Envi- son equations in unbounded domains, Ad- ronment, submitted. vances in Differential Equations, 2005:9 (September 2005), 1035–1052. Bourlioux, A., Khouider, B., A rigorous asymp- totic perspective on the large scale simulations Cornea, O., Lalonde, F., A universal Floer of turbulent premixed flame fronts, Multiscale theory, localization and applications, Centre Modelling and Simulations, submitted. de recherches mathématiques, CRM-3172, 2004. Brassard, G., Broadbent, A., Tapp, A., Quan- tum pseudo-telepathy, Foundations of David, C., Fearnley, J., Kisilevsky, H., Vanish- Physics, to appear. ing of L-functions of elliptic curves over num- ber fields, arXiv:math.NT/0406012, June Brassard, G., Broadbent, A., Tapp, A., Re- 2004. casting Mermin’s multi-player game into the framework of pseudo-telepathy, Quantum In- De Koninck, J.-M., Doyon, N., Esthetic numbers formation and Computation, to appear. and game theory, submitted. Brassard, G., Méthot, A. A., Tapp, A., Min- imum entangled state dimension required

91 CENTRE DE RECHERCHES MATHÉMATIQUES

De Koninck, J.-M., Doyon, N., Kátai, I., Count- Goulard, B., Lina, J.-M., St-Jean, P., Stationary ing the number of twin Niven numbers, sub- multiscale graphical models, Applied Proba- mitted. bility, to appear. De Koninck, J.-M., Kátai, I., Subbarao, M. V., Goupil, A., Chauve, C., Combinatorial operators A consequence of a theorem of Filaseta, sub- for Kronecker powers of representations of Sn, mitted. arXiv:math.RT/0503307, March 2005. Desrosiers, P., Lapointe, L., Mathieu, P., Sym- Gouyou-Beauchamp, D., Leroux, P., Enumera- metric functions in superspace, Advances in tion of symmetry classes of convex polyominoes Mathematics, to appear. on the honeycomb lattice, Theoretical Com- puter Science, to appear. Doray, L. G., Luong, A., Najem, E. H., Ef- ficiency of some estimators for a generalized Granville, A., Cycle lengths in a permutation are Poisson autoregressive process of order 1, Jour- typically Poisson distributed, submitted. nal of Statistical Computation and Simula- Granville, A., Prime divisors are Poisson dis- tion, submitted. tributed, submitted. Dryanov, D., Fournier, R., On a discrete variant Granville, A., Kurlberg, P., Poisson statistics via of Bernstein’s polynomial inequality, Centre the Chinese remainder theorem, Journal für de recherches mathématiques, CRM-3178, die Reine und Angewandte Mathematik, January 2005. submitted. Duchesne, P., Testing for serial correlation for un- Granville, A., Martin, G., Prime number known form in cointegrated time series models, races, American Mathematical Monthly, ac- GERAD, G-2004-76, October 2004. cepted. El Boukili, A., Madrane, A., Vaillancourt, Granville, A., Soundararajan, K., Large char- R., Multifrontal solution of sparse unsym- acter sums: Pretentious characters and the metric matrices arising from semiconductor Polya–Vinogradov theorem, Journal of the equations, Centre de recherches mathéma- American Mathematical Society, submit- tiques, CRM-3125, June 2004. ted. Fortin, J.-F., Jacob, P., Mathieu, P., SM(2,4κ;) Granville, A., Soundararajan, K., Extreme val- fermionic characters and restricted jagged par- ues of |ζ(1 + it)|, Journal of the Ramanujan titions, Journal of Physics A, 38 (February Mathematical Society, submitted. 2005), 1699–1709. Granville, A., Soundararajan, K., An uncer- Fortin, M., Reutenauer, C., A note on compres- tainty principle for arithmetic sequences, An- sion spaces, submitted. nals of Mathematics, submitted. Frenette-Charron, J.-B., Pelletier, M., Danyluk, Grundland, A. M., Snobl, L., Description of J., Chauve, C., Sarhan, F., The plant Lipocalin surfaces associated with Grassmannian sigma gene family, submitted. models on Minkowski space, Journal of Math- Frigon, M., Montoki, E., Multiplicity results for ematical Physics, 46:8 (2005), 3508–3520. systems of second order differential equations, Grundland, A. M., Snobl, L., Description of sur- Nonlinear Studies, submitted. faces associated with CPN−1 sigma models on Gagarin, A., Labelle, G., Leroux, P., Minkowski space, arXiv:math.DG/0405513. Charactererization and enumeration of Grundland, A. M., Snobl, L., Description of toroidal K -subdivision-free graphs, 3,3 surfaces associated with Grassmannian sigma arXiv:math.CO/0411356, November 2004. models on Minkowski space, Journal of Math- Gauthier, G., Rémillard, B., Turcotte, D., Pric- ematical Physics, 46:8 (2005), 3508–3520. ing variance options in a GARCH setting, Grundland, A. M., Strasburger, A., Za- GERAD, G-2004-57, July 2004. krzewski, W. J. M., Surfaces immersed in Ghidaoui, M. S., Kolyshkin, A. A., Vail- su(N+1) Lie algebras obtained from the CPN lancourt, R., Transient turbulent flow in a sigma models, Centre de recherches mathé- pipe, Centre de recherches mathématiques, matiques, CRM-3180, February 2005. CRM-3176, January 2005.

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Guan, P., Lin, C.-S., Ma, X.-N., The Christoffel– rics of finite volume, Journal of Differential Minkowski problem. II. Weingarten curvature Geometry, submitted. equations, submitted. Kokotov, A., Korotkin, D., Isomonodromic tau- Guan, P., Lin, C.-S., Ma, X.-N., The existence function of Hurwitz Frobenius manifolds and problem for curvature measures . its applications, International Mathematics Research Notices, submitted. Guan, P., Lin, C.-S., Wang, G., On quotient equations in conformal geometry, submitted. Korotkin, D., On some integrable system arising in differential geometry and general relativity, Guan, P., Ma, X.-N., Zhou, F., The Christoffel– Annales des sciences mathématiques du Minkowski problem. III. Existence and convex- Québec, submitted. ity of admissible solutions, submitted. Labelle, G., Leroux, P., Gagarin, A., Struc- Guan, P., Wang, G., Conformal deformations of ture and labelled enumeration of K - the smallest eigenvalue of the Ricci tensor, 3,3 subdivision-free projective-planar graphs, Max Planck Institute for Mathematics in arXiv:math.CO/0406140, June 2004. the Sciences, 43/2005, May 2005. Labute, J., Lemire, N., Minac, J., Swallow, J., Guignon, V., Chauve, C., Hamel, S., Distance Cohomological Dimension and Schreier’s for- d’édition entre “tige-boucles”, submitted. mula in Galois cohomology, Bulletin of the Gurjar, R., Masuda, K., Miyanishi, M., Rus- London Mathematical Society, submitted. sell, P., Affine lines on affine surfaces and the Labute, J., Lemire, N., Minac, J., Swallow, J., Makar–Limanov Invariant, submitted. Demuskin groups, Galois Modules, and the el- Hahn, G., Composing directed hypergraphs, Jour- ementary type conjecture, to appear. nal of Combinatorial Theory. Series B, sub- Lapalme, E., Lina, J.-M., Mattout, J., Sources mitted. clustering and entropic inference in MEG, Hanley, J. A., MacGibbon, B., Creating non- IEEE Transactions on Biomedical Engi- parametric bootstrap samples using Poisson neering, submitted. frequencies, Computer Methods and Pro- Léger, C., MacGibbon, B., On the bootstrap in grams in Biomedicine, submitted. cube root asymptotics, Canadian Journal of Iovita, A., Pollack, R., On Iwasawa theory of Statistics, accepted. elliptic curves over at primes of supersin- Q Lepage, T., Lawi, S., Tupper, P., Bryant, D., gular reduction over -extensions of num- Zp Continuous and tractable models for the varia- ber fields, Journal für die Reine und Ange- tion of evolutionary rates, Mathematical Bio- wandte Mathematik accepted. sciences, 199:2 (February 2006), 216–233. Iovita, A., Stevens, G., On p-adic families of Lu, S., Dethloff, G., Logarithmic surfaces an hy- modular forms, submitted. perbolicity, arXiv:math.AG/0406287, June Jakobson, D., Levitin, M., Nadirashvili, N., 2004. Polterovich, I., Spectral problems with mixed Mélard, G., Roy, R., Saidi, A., Exact maxi- Dirichlet–Neumann boundary conditions: mum likelihood estimation of structured or Isospectrality and beyond, Journal of Com- unit root multivariate time series models, Cen- putational and Applied Mathematics, to tre de recherches mathématiques, CRM- appear. 3129, June 2004. Jakobson, D., Polterovich, I., Estimates from be- M’Lan, C.-E., Joseph, L., Wolfson, D. B., low for the spectral function and for the re- Bayesian sample size determination for case mainder in local Weyl’s law, submitted. control studies, Journal of American Statis- Jaksic, V., Last, Y., Simplicity of singular spec- tical Association, submitted. trum in Anderson type Hamiltonians, submit- Ngan, K., Straub, D. N., Bartello, P., Aspect ra- ted. tio effects in quasi-2D turbulence, Physics of Kokotov, A., Korotkin, D., Tau-functions on Fluids, submitted. spaces of Abelian and quadratic differentials Nguyen-Ba, T., Kolyshkin, A. A., Vaillan- and determinants of Laplacians in Strebel met- court, R., Hermite-Birkhoff differential equa-

93 CENTRE DE RECHERCHES MATHÉMATIQUES

tion solvers, Centre de recherches mathé- Schlomiuk, D., Vulpe, N., Integrals and phase matiques, CRM-3175, Décember 2004. portraits of planar quadratic differential sys- tems of invariant lines of at least five total mul- Ollivier, Y., Wise, D. T., Kazhdan groups tiplicity, Centre de recherches mathémati- with infinite outer automorphism group, ques, CRM-3181, March 2005. arXiv:math.GR/0409203, September 2004. Schlomiuk, D., Vulpe, N., The full study of pla- Ratnarajah, T., Vaillancourt, R., Quadratic nar quadratic differential systems possessing forms on complex random matrices and chan- exactly one line of singularities, finite or infi- nel capacity, Centre de recherches mathé- nite, Centre de recherches mathématiques, matiques, CRM-3126, June 2004. CRM-3183, April 2005. Ratnarajah, T., Vaillancourt, R., Alvo, M., Com- Waite, M. L., Bartello, P., Stratified turbulence plex random matrices and Rician channel ca- generated by internal gravity waves, Journal pacity, Centre de recherches mathémati- of Fluid Mechanics, submitted. ques, CRM-3174, October 2004. Waite, M. L., Bartello, P., The transition from Rochon, D., A bicomplex Riemann zeta function, geostrophic to stratified turbulence, Journal of Tokyo Jounal of Mathematics, submitted. Fluid Mechanics, submitted. Rousseau, C., Divergent series: past, present, fu- Walsh, T. R. S., Enumeration of unrooted maps in ture. . . , American Mathematical Monthly, the plane, Technical report submitted. , UQÀM, Technical Report no. 2005-01, February 2005. Rousseau, C., Christopher, C., Modulus of an- alytic classification for the generic unfold- Winternitz, P., Levi, D., Continuous ing of a codimension one resonant diffeomor- symmetries of difference equations, phism or resonant saddle, Centre de recher- arXiv:nlinSI/0502004, to appear. ches mathématiques, CRM-3167, Septem- Yoshikawa, M., Gong, Y., Ashino, R., Vaillan- ber 2004. court, R., Case study on SVD multiresolution analysis Russell, P., Koras, M., Contractible surfaces with , Centre de recherches mathémati- a quotient singularity, submitted. ques, CRM-3179, January 2005. Saidi, A., Consistent testing for independence Zhao, M., Ghidaoui, M. S., Kolyshkin, A. A., of two partially nonstationary vector ARMA Vaillancourt, R., On the stability of oscillatory pipe flows time series, Centre de recherches mathéma- , Centre de recherches mathéma- tiques, CRM-3173, November 2004. tiques, CRM-3168, October 2004. Sauer, N. W., Rosenberg, I. G., Interval cardi- Zlobec, I., Steele, R., Nigam, N., Compton, C., A predictive model of rectal tumor response to nality in the lattice of clones, submitted. pre-operative radiotherapy using classification Schlomiuk, D., Vulpe, N., Planar quadratic vec- and regression tree (CART) methods, Clinical tor fields with invariant lines of total multiplic- Cancer Research (2005), submitted. ity at least five, submitted.

94 Committees Heading the CRM CENTRE DE RECHERCHES MATHÉMATIQUES

Bureau de direction

HE Bureau consists of members from the Université de Montréal (eight to eleven members) and T from 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 the Centre, 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 Université de Montréal on the choice of the Director.

Yoshua Bengio François Lalonde Université de Montréal Université de Montréal François Bergeron Christian Léger Université du Québec à Montréal Université de Montréal Alain Caillé, Vice-Rector, Research Christiane Rousseau Université de Montréal Université de Montréal Joseph Hubert, Dean Peter Russell Arts and Sciences Faculty McGill University Université de Montréal Yvan Saint-Aubin Hershy Kisilevsky Université de Montréal Concordia University

Chantal David (Concordia University) and Jean LeTourneux (Université de Montréal), both Deputy Directors of the CRM, were invited members.

Scientific Advisory Committee

HE Scientific Advisory Committee is constituted of distinguished researchers from Canada and T abroad. 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 the Director. The Committee transmits recommendations about the general scientific orientation of the CRM and gives advice about proposeded scientific activities.

Jerry Bona is a Pro- of twenty-five scientific journals and of several fessor at the Depart- academic committees and panels. Jerry Bona is a ment of Mathemat- co-organizer of the Mathematicians and Educa- ics, Statistics and tional Reform Network. Computer Science Jean-Pierre Bour- at The University of guignon received Illinois at Chicago. an engineering de- He received a B.Sc. gree from École degree from Wash- Polytechnique and a ington University in Ph.D. in mathemat- Saint Louis (1966) ics. A differential and a Ph.D. from geometer by train- Harvard University ing, he has been (1971). His research experience is vast. His re- interested by the search interests include fluid mechanics, par- mathematical as- tial differential equations, computational math- pects of physical theories: Dirac operators and ematics and the associated numerical analysis, spins, and general relativity. His areas of spe- oceanography, coastal engineering and mathe- cialty are the geometrical estimation of eigen- matical economics. He is an Elected Fellow of values of Laplace-Beltrami operators, Kählerian the American Association for the Advancement geometry and, more recently, Finslerian geom- of Science and a member of the editorial board etry. Jean-Pierre Bourguignon directs advanced

96 SCIENTIFIC PERSONNEL research classes at CNRS. He is the Director of Fields Institute and a Council member of the Institut des hautes études scientifiques (IHES) at American Mathematical Society. Bures-sur-Yvette and Professor of Mathematics Peter Glynn is Thomas at École Polytechnique. From 1990 to 1992, he W. Ford Professor in the served as President of the Société mathématique School of Engineering at de France and from 1995 to 1998 of the European Stanford University. He Mathematical Society. He is a member of several received his Ph.D in Op- scientific advisory committees in Europe. Since erations Research from 1996, he is a member of Academia Europaea Stanford University in and since 2002 a foreign associate of the Spanish 1982. He is a Fellow of Royal Academy. the Institute of Mathe- Jean-Louis Colliot- matical Statistics and his Thélène is directeur research interests focus de recherche at the on computational proba- Centre national de bility, queueing theory, statistical inference for la recherche scien- stochastic processes, and stochastic modeling. tifique (CNRS) at Mark Haiman is a UMR 8628 (Univer- Professor at the De- sité de Paris-Sud, partment of Math- Orsay). He special- ematics of the Uni- izes in algebraic ge- versity of Califor- ometry and its links nia, Berkeley. He to arithmetic. He obtained a Doctorat d’État received his de- (1978) from Paris-Orsay. He is a member of the grees from the Mas- editorial boards of Annales scientifiques de l’École sachusetts Institute Normale Supérieure (of which he was editor-in- of Technology in chief until recently), the Journal of Number Theory Computer Science and the Journal of K-Theory. Jean-Louis Colliot- and Electrical Engi- Thélène is one of the main organizers of the neering (B.Sc., 1979) and in Mathematics (Ph.D., 2005-2006 Thematic Program at MSRI (Berke- 1984). His research interests are in algebraic ley). combinatorics, algebraic geometry, representa- Walter Craig is tion theory, and lattice theory. He is a member of Canada Research the editorial board of Algebra universalis. Chair of Mathemat- Nigel Hitchin is ical Analysis and Savilian Professor of its Applications at Geometry at New the Department of College, Oxford Mathematics and University. He holds Statistics of McMas- a Ph.D. degree in ter University. He Mathematics (1972) received degrees from Wolfson Col- from the University lege of Oxford Uni- of California, Berke- versity. He is prin- ley (B.A., 1977) and cipally interested in from the Courant Institute of Mathematical Sci- differential and algebraic geometry and its re- ences, New York University (M.Sc., 1979, and lationship with the equations of mathematical Ph.D., 1981) and has held positions at Brown physics. Current projects include the areas of hy- University and Stanford University before join- perkähler geometry, special Lagrangian geome- ing McMaster. He is principally interested in lin- try and mirror symmetry, geometric solutions of ear and nonlinear partial differential equations, Painlevé equations, magnetic monopoles, vector Hamiltonian dynamical systems, fluid dynam- bundles on algebraic curves, and the theory of ics, quantum mechanics, and nonlinear func- gerbes. tional analysis. He is a member of the editorial boards of SIAM: Mathematical Analysis and the

97 CENTRE DE RECHERCHES MATHÉMATIQUES

Richard Lockhart is a Pro- M. Ram Murty is a fessor at the Department of Professor of Mathe- Statistics and Actuarial Sci- matics and Queen’s ence Simon Fraser Univer- Research Chair at sity. He received a B.Sc. in Queen’s University. Mathematics from the Univer- He holds a Ph.D. de- sity of British Columbia (1975) gree in Mathemat- and degrees in Statistics from ics (1980) from MIT. the University of California, A specialist in alge- Berkeley (M.A., 1976, Ph.D., braic and analytic 1979). A former Editor of the number theory, his Canadian Journal of Statistics , he has also served researches focus on on the Advisory Committee on Statistical Meth- Artin’s conjecture, ods of Statistics Canada. He was President of the elliptic curves, modular forms, automorphic Statistical Society of Canada in 1996-1997. Much forms, Langland’s program, Selberg’s conjec- of his work is in the area of model assessment, tures, and cryptography. generally in the form of goodness-of-fit. Carl Pomerance Mitchell Luskin is a Professor at is a Professor of the Department Mathematics at the of Mathematics of University of Min- Dartmouth College. nesota, a Fellow of From 1999 to 2003, the Minnesota Su- he was a member percomputing Insti- of the technical staff tute and a member of Bell Labs-Lucent of the graduate fac- Technologies. He ulty of the Depart- holds degrees from ment of Aerospace Engineering and Mechanics Brown University of the University of Minnesota. He holds degrees (B.A., 1966) and in Mathematics from Yale University (B.Sc., from Harvard University (M.A., 1970, Ph.D., 1973) and the University of Chicago (M.Sc., 1976, 1972). A number theory specialist, he has re- Ph.D., 1977). His research interests include nu- ceived numerous prizes and awards including merical analysis, scientific computing, applied the Levi L. Conant Prize of the American Math- mathematics, partial differential equations, com- ematical Society. He is one of the editors-in-chief putational materials science, and computational of Integers : The Electronic Journal of Combinato- physics. He delivered an invited lecture at the rial Number Theory and a member of the editorial International Congress of Mathematicians held board of the Journal of Supercomputing and the in Beijing in 2002. He is a member of the editorial AMS Undergraduate Book Series. boards of Dynamics and Differential Equations, the International Journal of Computational and Numer- ical Analysis and Applications, Communications in Applied Analysis, the International Journal of Dif- ferential Equations and Applications, and the Inter- national Journal of Pure and Applied Mathematics.

98 SCIENTIFIC PERSONNEL

Peter Shalen is a Steven Zelditch is a Professor at the De- Professor of Math- partment Mathe- ematics at Johns matics, Statistics Hopkins Univer- and Computer Sci- sity. He received his ence at The Uni- Ph.D. from the Uni- versity of Illinois versity of California, at Chicago. He re- Berkeley, in 1981. A ceived his B.A. from past member of the Harvard College editorial board of (1966) and his Ph.D. Annales Scientifiques from Harvard Uni- de l’École Normale versity (1972). He also spent a year as an under- Supérieure, he is presently on the editorial board graduate at École Normale Supérieure in Paris. of the American Journal of Mathematics. His re- His main research interests are 3-dimensional search centers around applications of microlo- topology, hyperbolic geometry, and geometric cal analysis to problems concerning: asymp- and combinatorial group theory. He is associate totics of eigenfunctions/eigenvalues on Rieman- editor of the Journal of Knot Theory and its Rami- nian manifolds, statistical algebraic geometry, fications and was the geometric topology editor problems of mathematical physics ranging from of the Transactions of the American Mathematical quantum chaos to 2D Yang – Mills to string/M Society from 1992 to 2000. theory.

Alain Caillé, Vice-Principal (Research), Université de Montréal, François Lalonde, CRM Director and Eddy 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 (Concordia University) and Jean LeTourneux (Université de Montréal), all Deputy Directors of the CRM, were invited members of the Committee.

99 CRM Administrative and Support Staff CRMADMINISTRATIVE AND SUPPORT STAFF

The Director’s Office

François Lalonde Chantal David Director Deputy Director, Theme Years François Bergeron Jean LeTourneux Acting Director (Summer 2004), Deputy Deputy Director, Publications Director

Administration

Vincent Masciotra Guillermo Martinez-Zalce Head of Administration Research Laboratories Administrative Michèle Gilbert Coordinator Administrative Assistant Diane Brulé-De-Filippis Muriel Pasqualetti Secretary Administrative Assistant Josée Simard Secretary

Scientific Activities

Louis Pelletier Sakina Benhima Coordinator Project Manager Josée Laferrière Assistant

Computer Services

Daniel Ouimet François Cassistat Systems Administrator Technical Assistant André Montpetit Frédéric Loisier Office Systems Manager (half time) Technical Assistant

Publications

André Montpetit Louise Letendre TeX Expert (half time) Technician

Communications

Suzette Paradis Communications Officer and Webmaster

101 Statement of Revenue and Expenditures for the Fiscal Year Ending on May 31, 2005 STATEMENT OF REVENUEAND EXPENDITURES 42,695 50,000 29,865 30,000 38,355 16,557 36,514 34,278 37,967 64,777 28,117 14,971 15,142 82,485 15,931 73,193 17,553 510,000 356,000 120,000 100,000 210,447 150,345 278,874 244,465 TOTAL 1,478,100 3,183,671 527 — — — — — — — — — — — — 4,683 8,418 4,175 38,355 16,557 36,514 34,278 64,777 28,117 18,506 32,134 81,718 28,800 Other 218,597 sources 6,000 9,251 — — — — — — — — — — — — — — — — — — — — 35,485 50,736 23,210 210,447 210,447 funds Matching 4,000 4,000 37,967 37,967 25,455 — — — — — — — — — — — — — — — — — — — — — — Endowments 50,000 29,865 30,000 — — — — — — — — — — — — — — — — — — — — — 120,000 100,000 329,865 Other universities 252 200 252 — — — — — — — — — — — — — — — — — — — — — 510,000 356,000 866,000 UdeM CÉDAR 1,330 7,030 5,878 4,548 — — — — — — — — — — — — — — — — — — — — 42,695 455,000 497,695 Centre FQRNT- — — — — — — — — — — — — — — — — — — — — — — — — 57,100 57,100 13,378 NPCDS NSERC- 7,285 7,513 1,740 — — — — — — — — — — — — — — — — 47,000 44,393 966,000 966,000 122,336 106,852 185,874 Centre NSERC- Aisenstadt Chairs Visitors Postdoctoral fellows (PDF) Summer school 2004 Workshops Total— Thematic program REVENUE Operating grants Equipment grant Univ. de Montréal grant (Professors) Univ. de Montréal,grant (Operations) UQÀM grant McGill U. grant Concordia U. grant U. Laval grant U. of Ottawa,grant Contributions from researchers (PDFs, workshops) Contributions from MITACS & SAMSI Contributions from ISM & GERAD,forOther Colloquium contributions for activities Publications (royalties, sales, etc.) Endowments (Aisenstadt & Bissonnette) Registration fees Service contracts and other revenue TOTAL REVENUE EXPENDITURES SCIENTIFIC PROGRAMS — CENTRE Thematic program General program Industrial and multidisciplinary program National Program on Complex Data Structures (NPCDS) (continued on the next page)

103 CENTRE DE RECHERCHES MATHÉMATIQUES 2,800 40,000 75,200 84,585 78,075 21,846 62,962 19,524 22,500 12,560 26,730 67,538 203,211 243,211 216,764 542,231 508,237 589,552 735,044 168,635 223,374 TOTAL 2,960,297 490 (200) (200) (184) (386) (570) — — — — — — — — — — 1,798 2,288 31,955 12,212 26,085 Other 192,512 sources 97 (97) — — — — — — — — — — — — — — — — — 136,500 136,500 210,544 funds Matching 22,500 22,500 51,955 (13,988) — — — — — — — — — — — — — — — — — — Endowments 2,800 30,000 30,000 52,700 61,085 76,667 33,865 17,342 29,846 25,561 — — — — — — — — — — 274,304 304,304 Other universities 7,500 1,089 3,774 3,393 — — — — — — — — 24,000 22,185 54,774 13,518 52,538 38,415 508,237 525,530 190,898 862,607 UdeM CÉDAR 4,688 5,786 — — — — — — — — — 15,000 23,500 30,018 73,206 19,524 25,311 15,000 96,685 62,432 212,153 435,263 Centre FQRNT- — — — — — — — — — — — — — — — — — — — — 13,378 43,722 NPCDS NSERC- 2,395 1,202 — — — — — — — — 66,911 10,000 76,911 22,025 12,722 13,924 21,323 76,266 116,097 140,517 299,941 889,734 Centre NSERC- CRM-ISM fellows University of Ottawa Total— Other PDF Course releases Admin. and research support Postdoctoral fellows Students Visitors Workshops and seminars Other Total— Research Laboratories College researchers’ projects UdeM professors Course releases Scientific advisory committee and representationPublicity, exp. Bulletin, Annual Report Total— Other scientific expenditures EXPENDITURES (continued) Other Postdoctoral fellows SCIENTIFIC PROGRAM — RESEARCH LABORATORIES Other scientific expenditures Personnel Executive Operating and computing expenditures TOTAL EXPENDITURES YEAR-END BALANCE

104 Mission of the CRM CENTRE DE RECHERCHES MATHÉMATIQUES

HE Centre de recherches mathématiques provinces through AARMS, and other ac- T(CRM) was created in 1969 by the Univer- tivities organized outside the three institute. sité de Montréal through a special grant from the They also participate in the National Program National Research Council of Canada. It became on Complex Data Structures jointly with the an NSERC national research centre in 1984. It is Canadian statistical community. currently funded by NSERC (Natural Sciences and Engineering Research Council), by the Gov- This national mandate is complemented by, and ernment of Québec through the FQRNT (Fonds indeed supported by, a long-standing vocation québécois de la recherche sur la nature et les of promoting research in the mathematical sci- technologies), by the Université de Montréal, as ences in Québec. For instance: well as McGill University, Université du Québec à Montréal, Concordia University, University of • the CRM supports research through its eight Ottawa, Université Laval and by private dona- research laboratories spanning most of the im- tions. The mission of the CRM is to do research portant areas of the mathematical sciences, in mathematics and closely related disciplines • it supports, through partnership agreements, and to provide leadership in the development of a group of local researchers chosen mainly the mathematical sciences in Canada. from departments of mathematics and statis- tics, but also computer science, physics, eco- The CRM carries on its mission and national nomics, engineering, etc., mandate in several ways: • it organizes series of regular seminars and lec- • its general program and its multidisciplinary ture courses on different areas of the mathe- and industrial program provide funding for matical sciences, conferences and special events at the CRM • it sponsors joint activities with the ISM (In- and across the country, stitut des sciences mathématiques) including • each year it invites, through the Aisenstadt the weekly CRM/ISM colloquium, graduate Chair, one or more distinguished mathemati- courses offered by distinguished visitors and cians, to give advanced courses as part of its a program of postdoctoral fellowships, thematic program, • it works actively at developing contacts with • it awards four prizes yearly: the CRM- industry. Its joint activities with liaison and re- Fields Prize recognizing major contributions search centres (CIRANO, CRIM and MITACS) to mathematics, the Aisenstadt Prize given and research centres doing applied research for outstanding work done by a young Cana- (CRT, GERAD, INRS-EMT, and INSERM) led dian mathematician, the CAP-CRM Prize to the creation of industrial networks. The for exceptional achievement in theoretical previous involved, in 2004-2005, Bombardier and mathematical physics, and the CRM-SSC Aerospace and the Brain Imaging Unit CRM- Prize for exceptional contributions to statistics IUGM-INSERM in early career, • it publishes technical reports and about ten books per year. Some of its collections are pub- The CRM fulfils its national mission by involv- lished jointly with the AMS and with Springer, ing the largest possible number of Canadian • it has an extensive postdoctoral fellowship mathematicians in its scientific programs, both program, with more than thirty postdoctoral as participants and as organizers. It also sup- fellows in place last year, funded in partner- ports many events taking place outside Mont- ship with other organizations and researchers, réal and the Province of Québec. It is recognized • it informs the community of its activities worldwide as one of the major institutes in the through its newsletter, Bulletin du CRM, and mathematical sciences. its web site at www.CRM.UMontreal.CA, The director of the CRM is assisted by two man- • it participates, with the other two Canadian agerial structures: the Bureau de direction and institutes, in groundbreaking national initia- the Scientific Advisory Committee. The Advi- tives. One example is the MITACS project sory Committee is a group of internationally (Mathematics of Information Technology and renowned mathematicians from Canada and Complex Systems). They sponsor the Annual abroad, who approve scientific programs and Meetings of the Mathematical Sciences Soci- thematic years, choose recipients of the Aisen- eties (SMC, SSC, SCMAI), the development stadt Prize and suggest new scientific ventures of the mathematical sciences in the Atlantic to explore.

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