A Word from the Director...... 2 CRM's 30th Anniversary ...... 4 Presenting the CRM...... 6 Personnel...... 7 Scientific Personnel...... 8 Members 8 Postdoctoral Fellows 9 Visitors 10 Management...... 12 Bureau 12 Advisory Committee 12 Computer Facilities 13 Scientific Activities...... 14 Theme Year 1999-2000: Mathematical Physics 14 Aisenstadt Chair 24 General Programme 27 CRM Prizes 34 Members’ Seminars & Special Events 37 CRM-ISM Colloquium 41 World Mathematical Year ...... 42 Coming Events ...... 44 Theme Year 2000-2001: Mathematical Methods in Biology and Medicine 44 General Programme 2000-2001 48 Theme Year 2001-2002: Groups and Geometry 51 General Programme 2001-2002 55 Theme Year 2002-2003: Mathematical Methods of Computer Science 57 Research Programmes...... 58 Collaborations ...... 74 Industrial Mathematics...... 76 Awards, Distinctions, and Landmarks...... 79 Publications...... 81 Recent Titles 81 Previous Titles 82 Research Reports 85 Financial Report ...... 88 Financial statements Erreur ! Signet non défini.

CRM Annual Report 1999-2000 1 A Word from the Director

The years follow each other all too rapidly, and be reported on next year was the three week it seems like only yesterday that I was writing a short programme on asymptotic series, similar page for last year’s report. differential algebra and finiteness problems in non-linear dynamical systems, run by Dana It has been a busy year at the CRM. The centre of Schlomiuk and Luc Bélair. The activity had some our scientific programme for the year was our courses for students, new interactions between thematic programme in Mathematical Physics. mathematicians from different areas, and most The year began with a remarkable Summer importantly, time for that interaction to happen. School, held at the Banff Centre for Conferences. A final thing to make a director happy is that a The theme was “Theoretical Physics at the end of book will be coming out of the workshop, and the Twentieth Century”, and it covered a will be published in a CRM series. remarkably wide variety of interesting areas of theoretical physics, with a range of topics going Speaking of which, our publication section saw a from quantum field theory to quantum major change this year with the departure of computing and protein folding. The very Martin Goldstein as deputy director in charge of breadth of the coverage brought an additional publications. Martin saw the programme bonus, in that the lecturers could not assume develop almost from scratch and his diligence that everybody had intimate knowledge of the and careful encouragement of authors material being presented, allowing relative contributed greatly to its development. amateurs like myself to take in the remarkable Fortunately, Jean Letourneux has agreed to take panorama being presented. The summer school his place, and the programme continues to do also saw what I believe to be a first for a CRM well, with 6 monographs and conference activity, in that two of the participants got proceedings appearing last year. One married during the event. The happy couple noteworthy feature was the purchase by Panjab shared a cake with the participants, and took the University of 200 copies of our edition of rest of the day off. While the more prosaically Sarvadaman Chowla’s collected works for minded might say that this is linked to the distribution throughout India. My thanks also go atmosphere of Banff, I prefer to think that the to the other three deputy directors who helped marriage is mostly due to the extraordinarily me do the work: Jacques Bélair, Yoshua Bengio, stimulating effect of a CRM summer school. and Steven Boyer.

With such a beginning, the rest of the year could On the industrial front, the Network for only go well, and indeed it did. My thanks are Computation and Mathematical Modelling due to the organisers of the year: Philippe Di (ncm2) to which the CRM belongs, launched a Francesco, Lisa Jeffrey, André LeClair, Yvan major call for proposals, to which the Saint-Aubin, and Luc Vinet. There were three membership has responded with enthusiasm. series of Aisenstadt lectures, by R. Jackiw, J. Twelve new projects are now being financed, Feldman, and D.H. Phong, as well as 14 and we are starting to see the true cross- workshops. The year closed with a remarkable disciplinary collaboration that is allowed by the two month concentration period on classical and network. One project that summarises much of quantum integrability, organised in a masterful the new interactions is one in “Nowcasting”, fashion by André Leclair. There were two talks which involves not only meteorologists but also per day, and a lot of work and discussion during experts in operations research and economists. the rest of the day, to a point where I have never The cross Canada MITACS network also seen such a “research buzz” at the CRM. finished its first year and a half of operation, and is progressing well, with the first annual general In our general programme, we hosted 4 meeting held in Toronto last May. The CRM is conferences, and contributed to 24 others, the host centre for this year's meeting in including 11 funded through the National Montréal. Programme which is run jointly through the three Canadian Mathematics Institutes. One One of the most striking features over the last particularly successful CRM activity which will year of all of these activities has been the arrival

2 Annual Report 1999-2000 CRM A w o r d f r o m t h e D i r e c t o r of new faces. Considerable changes are awaiting was hired after a postdoctoral fellowship during us over the next few years, as a significant a theme year at the CRM; not being one to do proportion of the Canadian mathematical things by halves, he will be publishing a book professorate retires and is replaced by new with the CRM next spring. I hope this will be faculty. In Montréal alone, the turnover will be repeated, and often. of the order of fifty percent. My own department has hired six new faculty members in the last two years. I am pleased to say that one of them Jacques Hurtubise

CRM Annual Report 1999-2000 3 CRM's 30th Anniversary

The beginnings coordinate graduate studies in mathematics and The first steps to establish a research centre in statistics and to facilitate student exchanges. mathematics at Université de Montréal were Since then, many research and training activities, undertaken in 1968. As was previously done in such as the funding of postdoctoral fellows, and many other countries, Canada was looking for a a weekly colloquium, are jointly organized by way to develop a research infrastructure that CRM and ISM. would allow researchers throughout Canada and the rest of the world to meet to create new New Initiatives mathematics. The visionary leadership of its Luc Vinet followed as director during a critical founders, a start-up grant from the National period when NSERC's programme funding Research Council (NRC), and the generosity of CRM and Fields Institute was to be cancelled. Université de Montréal led to the founding of Under his leadership, CRM not only survived, CRM, the first research centre in mathematics in but it grew considerably. Along with the other Canada. research centres in mathematical sciences of the CRM owes much of its success to the scientific Montréal area, CRM created the Network for and leadership qualities of its Directors. Maurice Computing and Mathematical Modelling (ncm2). L'Abbé was the first Director. The Salon where Also, CRM, Fields Institute, and PIms joined most of the CRM receptions take place is named forces to create the MITACS Network of Centres in his honour. Because of his numerous other of Excellence. All these initiatives offer responsibilities, he was soon followed by tremendous new possibilities for all researchers Jacques St-Pierre. Over the years, they were in the mathematical sciences. succeeded by Gert Sabidussi, Lucien Le Cam, Anatole Joffe, Carolyne van Vliet, David Sankoff, André Aisenstadt Francis Clarke, Luc Vinet, and Jacques As soon as he heard about a project to create a Hurtubise. research centre in mathematics, Mr. André Originally, the Centre had its own research Aisenstadt showed interest. Since then, he has personnel. It quickly became clear that it would shown his great devotion to the Centre by not be financially viable to keep a research team investing, among other things, in an endowment without responsibilities in an academic unit. In fund which finances a Chair and a Prize under 1982, the CRM researchers were integrated into his name. Moreover, since 1994, CRM and DMS the Department of Mathematics and Statistics are housed in the André-Aisenstadt Pavilion. We (DMS) at Université de Montréal. In return, DMS are all indebted to him for his great generosity. offers teaching release to some professors to do research and organize activities at CRM. CRM in 2000 CRM is proud of its heritage and continues its National Centre activities with renewed vigour. Now under the Under the leadership of Francis Clarke, CRM leadership of Jacques Hurtubise, CRM continues took on a national mandate in 1984 through a to stimulate research in the mathematical grant of NSERC's Programme of Special sciences by organizing numerous activities, by Collaborative Projects. Since then, CRM publishing and distributing books and systematically organizes numerous scientific monographs through collaborations with AMS activities benefiting the Canadian community. and Springer, by training young scientists, and Every year, concentrations of visitors, by producing many research results through its workshops, conferences, summer schools, etc., researchers. CRM fulfills its mandate thanks to are organized around themes and many the indefatigable financial support of Université researchers from everywhere gather to de Montréal, NSERC, FCAR, and various participate in these activities. donors. CRM is now part of an international network of mathematical research centres, and It is also during his mandate that the Institut de along with its partners in ncm , Fields Institute, sciences mathématiques (ISM) was created. Made 2 PIms, the MITACS network, ISM, and the other up of the mathematics and statistics departments universities of the area, CRM is more than ever of the Montréal area, its purpose is to better

4 Annual Report 1999-2000 CRM C R M ' s 3 0 t h A n n i v e r s a r y before able to meet the challenges of research in Geometry of Groups and Analysis in C* Algebras. mathematical sciences. Dusa McDuff of SUNY-Stony Brook presented her latest results on Symplectic Topology Today. In 30th Anniversary Conference the afternoon, Bong Lian of Brandeis University To celebrate its heritage on this 30th anniversary, talked about The Potential Function of a Calabi-Yau CRM organized a one-day conference on Threefold. Currently a hot topic, Probabilistic December 10, 1999. It was held just before the Aspects of Finance, was presented by Ioannis Winter Meeting of the Canadian Mathematical Karatzas of Columbia University. Finally, Bill Society which was also in Montréal. Miller of IMA gave us his perspective in a talk The first conference was presented by Peter entitled Mathematics in Industry : The IMA Sarnak of Princeton University and it was on Experience. This nice celebration concluded with Equidistribution on Arithmetic Surfaces. He was a reception in the Main Pavilion of Université de followed by Nigel Higson of Pennsylvania State Montréal. University. The title of his talk was Asymptotic

From left to right: Jacques Hurtubise, CRM Director, Robert Lacroix, Rector of Université de Montréal, Danielle Ménard, NSERC Director of Research Grants in the Physical and Mathematical Sciences, Luc Vinet, Past- Director of CRM and Richard Kane, President of the Canadian Mathematical Society, during CRM’S 30th anniversary. Many participants at the Canadian Mathematical Society’s Winter Meeting also celebrated CRM’s 30th anniversary.

CRM Annual Report 1999-2000 5 Presenting the CRM

The Centre de recherches mathématiques (CRM) and Complex Systems) proposal. Another was created in 1969 by the Université de example is found in the National Montréal through a special grant from the NRC. Programme Committee which provides It became an NSERC national research centre in funding for offsite research activities. 1984. It is currently funded by NSERC (Natural This national mandate is complemented by, and Sciences and Engineering Research Council), by indeed supported by, a long-standing vocation the Government of Québec through the FCAR of promoting research in the Montréal area. (Fonds pour la formation et l'aide à la Indeed the CRM recherche), the Université de Montréal, and by • supports, through partnership agreements, a private donations. The mission of the CRM is to local group of researchers chosen mainly do research in mathematics and closely related from departments of mathematics and disciplines and to provide leadership in the statistics, but also from departments of development of the mathematical sciences in computer science, physics, economics, Canada. engineering, etc.; The CRM accomplishes its mission in several • organizes many series of regular seminars ways. As part of its national mandate, on different areas of mathematical sciences; • it organizes a series of scientific events each • sponsors joint activities with the ISM year, around a given theme (distinguished (Institut des sciences mathématiques) lecture series, workshops, conferences, including the weekly CRM/ISM colloquium, summer schools, visitor programmes, etc.); graduate courses offered by distinguished • it has a general programme which helps to visitors and a programme of postdoctoral fund conferences and special events at CRM fellowships. and across the country; • works actively at developing contacts with • each year it invites, through the Chair industry. Its joint activities with liaison and Aisenstadt, one or two prestigious research centres (CERCA, CIRANO and mathematicians, to give advanced courses as CRIM) and research centres doing applied part of its thematic programme; research (CRT, GERAD and INRS Télécom) • it awards four prizes yearly: the CRM-Fields led to the creation of the Network for Prize recognizing major contributions to Computing and Mathematical Modelling

mathematics, the Aisenstadt Prize given for (ncm2). This network is funded by NSERC outstanding work done by a young and about 20 partners such as financial Canadian mathematician, the CAP-CRM institutions, hightech companies and Prize for exceptional achievement in ministries. theoretical and mathematical physics, and The CRM fulfils its national mission by the CRM-SSC Prize for exceptional involving the largest possible number of contributions to statistics in early career; Canadian mathematicians in its scientific • it publishes some 150 technical reports and programmes, both as participants and as about half a dozen books per year. Some of organizers. It also supports many events taking its collections are published jointly with the place outside Montréal and the Province of AMS and with Springer Verlag; Québec. It is recognized worldwide as one of the • it has an extensive postdoctoral fellowship major institutes in the mathematical sciences. programme, with 39 postdoctoral fellows in place last year, funded either solely by the The director of the CRM is supported by two CRM or in partnership with other managerial structures: the Bureau and the organisations; Advisory Committee. The Advisory Committee • it informs the community of its activities is a prestigious group of internationally through its web site at renowned mathematicians from Canada and the rest of the world, who approve scientific www.CRM.UMontreal.CA programmes and thematic years, choose • it participates, with the other two Canadian recipients of the CRM-Fields and Aisenstadt centres, in groundbreaking national prizes, and suggest new scientific ventures to initiatives such as the MITACS explore. The president of the Canadian (Mathematics of Information Technology Mathematical Society is a member ex officio.

6 Annual Report 1999-2000 CRM Personnel

The Director’s Office

Jacques Hurtubise Director Martin Goldstein Deputy Director for Publications Jacques Bélair Deputy Director for Scientific Affairs Yoshua Bengio Deputy Director for MITACS Steven Boyer Deputy Director for Scientific Affairs Diane Poulin Secretary

Administration

Béatrice Kowaliczko Head of Administration Vincent Masciotra Financial and Administrative Officer Michèle Gilbert Administrative Assistant Muriel Pasqualetti Administrative Assistant Josée Simard Secretary

Scientific Activities

Louis Pelletier Coordinator Josée Laferrière Assistant Coordinator Diane Brulé-De-Filippis Secretary

Publications

André Montpetit TeX Expert Louise Letendre Technician

Computer Services

Daniel Ouimet UNIX Systems Manager Simon Mailhot Web expert

MITACS/MaTISC

Marie Pineau Business Development Officer

CRM Annual Report 1999-2000 7 Scientific Personnel Since its foundation in 1969, the CRM has supported a wide variety of research in mathematics by having various members attached to it, either as research staff, or through exchange agreements with neighbouring universities and industries, or as long-term visitors. These people perform their research at the CRM, and their presence has brought many benefits. In particular, the CRM’s national programme is greatly facilitated by having on hand a large reserve of willing organisers, who have even contributed financially to the organisation of activities. The largest partnership is with the Université de Montréal, which gives annually the equivalent of 5 full-time teaching positions in release time to the CRM. The CRM has release agreements with the other Montréal area universities, providing for the equivalent of two more full time positions. Facilities are also provided to researchers attached to junior colleges. In addition, each year, a certain number of visiting researchers spend the year at the CRM and are given visiting member status. There are also members whose presence is due to industrial agreements with Atlantic Nuclear Services and Lockheed Martin.

Members

Ali, Syed Twareque Durand, Stéphane Joffe, Anatole Rosenberg, Ivo Math. & Stat., U. Concordia Collège Édouard-Montpetit Math. & Stat., UdeM Math. & Stat., UdeM Angers, Jean-François El-Mabrouk, Nadia Joyal, André Rousseau, Christiane Math. & Stat., UdeM DIRO, UdeM Math., UQAM Math. & Stat., UdeM Arminjon, Paul Fournier, Richard Kamran, Niky Roy, Roch Math. & Stat., UdeM Collège Dawson Math. & Stat., U. McGill. Math. & Stat., UdeM Beaulieu, Liliane Fleischer, Isidore Koosis, Paul Saint-Aubin, Yvan Collège Rosemont U. Windsor Math. & Stat., U. McGill Math. & Stat., UdeM Bélair, Jacques Gagnon, Langis Korotkin, Dmitri Sankoff, David Math. & Stat., UdeM Lockheed Martin Canada Math. & Stat., U. Concordia Math. & Stat., UdeM Benali, Habib Gander, Martin Lalonde, François Schlomiuk, Dana INSERM, France Math. & Stat., U. McGill Math., UQAM Math. & Stat., UdeM Bengio, Yoshua Gauthier, Paul Langlands, Robert Shahbazian, Elisa DIRO, UdeM Math. & Stat., UdeM Institute for Advanced Lockheed Martin Canada Study, Princeton Bergeron, François Goldstein, Martin Sharp, Robert Math., UQAM Math. & Stat., UdeM Léger, Christian Physique, U. McGill Math. & Stat., UdeM Bergeron, Nantel Goulard, Bernard Stern, Ron Math. & Stat., U. York Physique, UdeM Lessard, Sabin Math. & Stat., U. Concordia Math. & Stat., UdeM Bourlioux, Anne Goren, Eyal Toth, John Math. & Stat., UdeM Math. & Stat., U. McGill LeTourneux, Jean Math. & Stat., U. McGill Physique, UdeM Boyer, Steven Granas, Andrzej Valin, Pierre Math., UQAM Math. & Stat., UdeM Lina, Jean-Marc Lockheed Martin Canada CRM, UdeM Broer, Abraham Grundland, Michel Van Vliet, Carolyne Math. & Stat., UdeM Math., UQTR McKay, John U. Florida Math. & Stat., U. Concordia Clarke, Francis Hall, Richard L. Vinet, Luc Univ. de Lyon Math. & Stat., U. Concordia Nekka, Fahima Math./Phys., U. McGill Faculté de Pharmacie, Darmon, Henri Harnad, John UdeM Winternitz, Pavel Math. & Stat., U. McGill Math. & Stat., U. Concordia Math. & Stat., UdeM Patera, Jiri Delfour, Michel Hurtubise, Jacques Math. & Stat., UdeM Worsley, Keith Math. & Stat., UdeM Math. & Stat., U. McGill Math. & Stat., U. McGill Perron, François Dssouli, Rachida Hussin, Véronique Math. & Stat., UdeM Zolésio, Jean-Paul DIRO, UdeM Math. & Stat., UdeM CNRS, France Rogers, Colins U. New South Wales, Australia

8 Annual Report 1999-2000 CRM S c i e n t i f i c P e r s o n n e l

Postdoctoral Fellows

Each year the CRM receives several postdoctoral fellows. The source of their funding can be a national programme like the NSERC postdoctoral programme, the NATO international programme administered by NSERC, the CRM (alone or with the ISM or the Fields Institute), or personal grants from the members. Since 1993-1994 we have added to this list the CRM industrial programme which, in association with its ncm2 partners, now offers postdoctoral fellowships. In the following list, the university refers to the one where the Ph. D. was obtained.

Aassila, Mohamed Brightwell, Mark Fowler, Thomas Loutsenko, Igor Univ. de Strasbourg Univ. of Glasgow The Georgia Inst. of Tech. Univ. de Montréal Aguiar, Marcello Bryant, David Guimond, Louis-Sébastien Rajaei, Ali Cornell Univ. Univ. of Canterbury Univ. de Montréal Princeton Univ. Amblard, Cécile Caprioglio, Myriam Hagedorn, Thomas Spiteri, Raymond Inst. Nat. Polytechnique Univ. de la Méditerranée Harvard Univ. Univ. of British Bertola, Marco Aix-Marseille II Klucznik, Michael Columbia S.I.S.S.A. De Guise, Hubert Brandeis Univ. Zaugg, Philippe Univ. of Toronto Univ. de Genève Bracken, Paul Lapointe, Luc Univ. of Waterloo Deteix, Jean Univ. de Montréal Zabrocki, Michael Univ. de Montréal Univ. of California

Following is a list of postdoctoral fellows working on projects attatched to CRM’s MITACS network. The affiliation listed indicates where the research is being done.

Chavez, Francisco Kagabo, Issa Schaefer, Carsten Villeneuve, Daniel Univ. of Toronto Polytechnique Univ. McGill Polytechnique Deerakhchan, Katayoun Langdell, Stephen Shinagawa, Kaori Weisheng, Bao Institut de cardiologie Univ. de Montréal Institut de cardiologie Institut de cardiologie de Montréal de Montréal de Montréal Mladenovic, Nenad Farhat, Abdeljelil Stojkovic, Goran Ziarati, Koorush Nagai, Yoshihilo CIRANO Polytechnique Iran Univ. McGill Gu, Hong Sun, Hui Nagih, Anass Univ. of Waterloo Institut de cardiologie HEC de Montréal Hadjar, Ahmed Rousseau, Guillaume Polytechnique Tateno, Katsumi Univ. of Toronto Univ. McGill

CRM Annual Report 1999-2000 9 S c i e n t i f i c P e r s o n n e l

Visitors Each year the CRM receives a large number of visitors. Most of these are here to participate in scientific activities: in the year 1999-2000, 804 participants registered for workshops run solely by the CRM. In addition, the CRM helped fund about 15 other scientific events. The following list does not include any of these, but only those who visited for longer periods, ranging from over a week to several months.

Abbondandolo, Alberto Eynard, Bertrand Lesage, Frédéric Patera, Jan Scuola Normale di Pisa CEA Saclay Lockheed Martin Canada Czech Technical Univ. Aizenberg, Lev Fedorov, Yuri N. Levi, Decio Phong, Duong H. Abromovich Bar-Ilan Univ. Lomoosov Moscow Univ. di Roma Columbia Univ. State Univ. Arnéodo, Alain Lohmus, Jaak Pleasants, Peter C.N.R.S. Fehér, Laszlo Univ. of Tartu Univ. of South Pacific Jozsef Attila Univ. Bahri, Chairul Long, Ling Pogosyan, Georges Univ. of Toronto Feldman, Joel S. Queen's Univ. Joint Institute for Nuclear Univ. of British Columbia Research (Dubna) Bégin, Luc Loutsenko, Igor Univ. Laval Frenkel, Edward Lockheed Martin Canada Posta, Severin C Univ. of California Technical Univ. Czech Berest, Yuri Lupercio, Ernesto Republic Cornell Univ. Gazeau, Jean-Pierre Univ. of Michigan Univ. de Paris VII Ragnisco, Orlando Bogoyavlenskij, Oleg I. Maréchal, Pierre Univ. Roma 3 Queen's Univ. Ghoussoub, Nassif Univ. de Montpellier Univ. of British Columbia Rowe, David Boivin, André Masakova, Zuzana Univ. of Toronto Univ. of Western Ontario Grammaticos, Basile Faculty of Nuclear Sc. and Univ. de Paris VII Physics Eng. Runkel, Ingo Buono, Pietro-Luciano (Czech Republic) King's College London Univ. of Warwick Güngör, Faruk Istanbul Technical Univ. Mathieu, Pierre Schmidt, Georg Butler, Leo Univ. Laval McGill Univ. Queen's Univ. Hansen, Wolfhard Univ. Bielefeld McLeod, Ian A. Sheftel, Misha B. Chavent, Guy Univ. of Western Ontario North-Western INRIA (France) Jackiw, Roman W. Correspondence MIT Michel, Louis Polytechnical Inst. (Russia) Cummins, Chris IHES, France Concordia Univ. Jacob, Patrick Sklyanin, Evgueni Univ. Laval Monastyrsky, Michael ENS-Lyon Daboul, Jamil ITEP Ben Gurion Univ. Jaksic, Vojkan Stoll, Manfred Univ. of Ottawa Moody, Robert V. Univ. of South Carolina Daoud, Mohamed Univ. of Alberta Univ. Mohammed V Jeffrey, Lisa Sweldens, Wim Univ. of Toronto Nishino, Akinori Bell Lab., Lucent Techn. de Montigny, Marc Gunmaa College of Univ. of Alberta Karrakchou, Jamila Technology Thiriet, Marc Univ. Mohammed V INRIA Derezinski, Jan Ohyama, Yousuke Univ. of Warsaw Kjiri, Mounia Osaka Univ. Thomova, Zora Univ. de Montréal SUNY-Institute of Techn. Desrosiers, Patrick Orlov, Aleksander Univ. Laval Komori, Yasushi Landau, Moscow Turbiner, Alexander Gunmaa College of UNAM Dorodnitsyn, Vlad, D. Technology Ouansafi, Abdellatif Russian Academy of Univ. Mohammed V Ujino, Hideaki Sciences Lemire, Frank Gunmaa College of Univ. of Windsor Paramonov, Petr Technology Duval, Christian Steklov Institute, Moscow Univ. d'Aix-Marseille II Leng, Xiaodan Vartanian, Arthur H. Pasadena City College Univ. of Alberta

10 Annual Report 1999-2000 CRM S c i e n t i f i c P e r s o n n e l

Viallet, Claude Vulpe, Nicolae Yamilov, Ravil Zakrzewski, Wojciech Univ. Pierre et Marie Curie Academy of Sciences of Russian Academy of Univ. of Durham Moldova Sciences Vrana, Leopold Zhedanov, Alexei Faculty of Nuclear Sc. and Walton, Mark Yau, Shing-Tung Donetsk Univ. Physics Eng. (Czech Univ. of Lethbridge Harvard Univ. Republic) Xudous, Yorgo Yui, Noriko Univ. Laval Queen's Univ.

CRM Annual Report 1999-2000 11 Management Bureau Advisory Committee

The Bureau consists of members from the The Advisory Committee is constituted of Université de Montréal (8 to 11 members) and distinguished researchers from Canada and from the outside (2 to 5 members). The rector of abroad. Its members are either mathematicians the Université and the dean of the Faculté des or scientists with close ties to the mathematical arts et des sciences are represented on the sciences. The rector of the Université de Bureau. Its role is to adopt the policies of the Montréal or his representative and the director Centre, to recommend the nomination and the of the CRM also take part in the meetings. The promotion of researchers and the appointment Advisory Committee is informed periodically of regular members, to advise the director on of the activities of the Centre, through the the preparation of the budget and the director, and transmits any advice that it deems Université on the choice of the director. relevant to the Bureau.

Bélair, Jacques Hubert, Joseph Bélair, Jacques Lawless, Jerry Dep. Dir. CRM, Assoc. Dean, Dep. Dir. CRM, Univ. of Waterloo Univ. de Montréal Research, FAS Univ. de Montréal Univ. de Montréal Melrose, Richard Bengio, Yoshua Bengio, Yoshua MIT Dep. Dir. CRM, Hurtubise, Jacques Dep. Dir. CRM, Univ. de Montréal Director CRM, Univ. de Montréal Miller, Willard Univ. McGill IMA Bergeron, François Boyer, Steven UQAM Hussin, Véronique Dep. Dir. CRM, Murty, Ram Univ. de Montréal UQAM Queen’s Univ. Boyer, Steven Dep. Dir. CRM, Jeffrey, Lisa Goldstein, Martin Odlyzko, Andrew UQAM Univ. of Toronto Dep. Dir. CRM, AT&T Labs Univ. de Montréal Brassard, Gilles Lessard, Sabin Pianzola, Arturo Univ. de Montréal Univ. de Montréal Hambleton, Ian Univ. of Alberta McMaster Univ. Caillé, Alain Ransford, Thomas J. Putnam, Ian Vice-rector, Research Univ. Laval Hurtubise, Jacques Univ. of Victoria Univ. de Montréal Director CRM, Treves, Francois Rousseau, Christiane Univ. McGill Cléroux, Robert Univ. de Montréal Rutgers Univ. Univ. de Montréal Kane, Richard Vaillancourt, Jean Univ. of Western Ward, Michael Goldstein, Martin Univ. de Sherbrooke Ontario Univ. of British Dep. Dir. CRM, Columbia Kowaliczko, Béatrice Univ. de Montréal Lalonde, François Kowaliczko, Secretary UQAM Béatrice Secretary

12 Annual Report 1999-2000 CRM M a n a g e m e n t

Computer Facilities

The CRM offers its members and visitors a Unix Since 1999, the CRM operates its own private environment based on a Sun Enterprise-450 local area network (LAN) : four BayNetworks equipped with four 400-MHz Ultra-Sparc Baystack-450 switches, providing 96 ports on processors and 2 Gb of memory as a main twisted-pair at 10/100 Mb/s and 4 optic fiber server, and a secondary server Sun Sparc-1000 links supporting Gigabit Ethernet. This private with eight 40-MHz processors and 384 Mb of local network is linked to the network of memory for lightweight CPU tasks. In 2000, the Université de Montréal which maintains the file server has grown by 18 Gigabytes (for the connections with RISQ (Réseau interordinateurs research group Physnum). This computing scientifique québécois) and CA*net (the power is distributed through the offices and Canadian internet transit service). Members and common rooms via 35 Sun workstations (from guests can now connect their personal laptops Sparc-4 to Ultra-10) and several X-terminals. (or computers) directly to the CRM private Note that the main server (Enterprise-450), 22 network, or if they are outside CRM offices, they Sun Ultra-5 and Ultra-10 workstations and the can connect through phone links to our PPP Local Area Network installed in 1999 were server and its 4 modems. obtained through a grant from the Canadian The support staff works on Sun stations, X- Foundation for Innovation with contributions terminals or on Macintoshes linked to the Sun from the Government of the Province of Québec, server for all services, such as mail and backups. Sun Microsystems and Anixter. A 3-year plan for replacement of all support staff The software libraries include compilers computers has started in 1999. (SparcWorks environment for C, C++ and For printing, the CRM has acquired a new HP- Fortran, GNU compilers, Java, etc.), symbolic 8000DN workgroup printer (1200-dpi double- manipulation programs (Mathematica, Maple, sided) and a jet-ink network printer Epson-900N Macaulay), several text editors, web browsers, a for colour-printing. web server, mail tools, and most utilities The CRM has its servers installed in a room common to the mathematical world (SPLUS, designed for this purpose, with an etc.). Upgrades to TeX and its dialects are independently controlled environment and UPS uploaded whenever they are released. Unix (Uninterruptible Power Supply). software to exchange with the PC and Mac platforms, such as SAMBA (PC file and printer server), StarOffice (Office suite), and AUFS (file server for Macintosh), are also installed. In 1999, security awareness has increased and new measures, such as the installation of surveillance software, were put in place with more to come in the future.

CRM Annual Report 1999-2000 13 Scientific Activities

The core of each year’s scientific programme at the CRM is its thematic programme. The topic is chosen by the Advisory Committee for its scientific importance, its timeliness, and its impact on the Canadian scientific community. Preceding years’ topics include: Probability and Stochastic Control (1992-93); Dynamical Systems (1993-94); Geometry and Topology (1994-95); Applied and Numerical Analysis (1995-96); Combinatorics and Group Theory (1996-97), Statistics (1997-98), Number Theory and Arithmetic Geometry (1998-99). A year’s activities can combine a good number of workshops and conferences, one or two Aisenstadt chairs, a certain number of visiting scientists in residence, and some post-doctoral fellowships. Typically, there is some coordination with Montréal universities to offer appropriate graduate courses in order to help graduate students participate in the activities. The reports are presented in the language in which they were submitted. Theme Year 1999-2000: Mathematical Physics

Overview CRM 804 participants including 89 postdoctoral Many sectors of mathematics and physics have fellows and 238 graduate students. been tightly interwoven in the last decades. The 9th CRM Summer School: Theoretical interactions have triggered some important th developments that turned out to be fruitful for Physics at the End of the XX Century both disciplines: to name only a few, conformal June 27 – July 10, 1999, Banff, Alberta Org. : Yvan Saint-Aubin and Luc Vinet (UdeM and CRM) field theory, vertex operators and representation theory; string theory, duality, non-commutative When organizing a summer school at the end of geometry and mirror symmetry; classical and the most fruitful century in the history of physics quantum integrable systems and quantum one must carefully consider the question of groups. topics. We decided to avoid a retrospective of These links make a theme year in mathematical problems solved during the last century and we physics particularly appealing. Several other shied away from a prediction of which ones reasons make it compelling. Canada can boast of might be settled during the next. We opted for a an impressive number of first-class snapshot of what theoretical physics is at the end mathematical physicists, a number which is even of this century (or, should we say, the last larger if one includes theoretical physicists century), namely problems actively researched whose research interests have been influenced in the last few years of the nineteen nineties. by mathematical developments. Through its This choice led to twelve courses that were various events and minicourses, it will also timely, diverse and exciting. And the response provide excellent opportunities for (pure) from the participants was extremely positive. mathematicians to learn how recent developments in some of their disciplines are Main Lectures • being used in physical theories. The summer Ian Affleck (UBC), Boundary CFT Approach to school, the longer workshops, and the winter Quantum Impurity Problems in Condensed concentration period are designed to welcome Matter Physics. • advanced graduate students and postdoctoral Gilles Brassard (Montréal), Quantum fellows in both mathematics and physics and Information Processing. • give them a chance to interact among themselves Eric D'Hoker (UCLA), Supersymmetric Yang- and with the leaders of these disciplines. Two of Mills Theory and Integrable Systems.* • the workshops draw not only from mathematics Michael Duff (Texas A&M), Branes, Black and physics but from yet a third discipline Holes and anti-De Sitter Space.* • (finance and computer science, respectively). Krzysztof Gawedzki (IHES), Easy Finally the theme year will enhance links Turbulence.* • between the mathematics and theoretical physics Brian R. Greene (Columbia), Geometry and communities in Canada. It will have brought to Quantum Gravity. • Allan Griffin (Toronto), Bose-Einstein Condensation.*

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• Satoru Odake (Shinsu Univ.), Integrability, aspects purement théoriques de ce problème. Deformed Virasoro and Elliptic Algebras.* De l'avis des conférenciers, cet atelier a été une • José Onuchic (UCSD), Exploring the Protein première. Il a mis en contact des experts de Folding Funnel Landscape: Connection Between différentes approches, réunis autour d'un même Theory and Experiments.* problème, soit la solution de modèles de type • Marc Potters (Science & Finance, Paris) Hubbard (contenant à la fois les aspects localisé Statistical Finance - New Problems for et délocalisé) en basse dimension. Des Physicists, présentations pédagogiques longues (une heure • Ben Simons (Cambridge), Mesoscopic et demie) le matin ont permis à chacun Physics.* d'apprécier les forces, les faiblesses ainsi que les • Frank Wilczek (IAS, Princeton), QCD in problèmes ouverts pour chacune des méthodes Extreme Conditions.* théoriques importantes. Des présentations plus The courses with an asterisk will appear in the year 2001 in courtes l'après-midi ont permis de faire le point the collection Mathematical and Theoretical Physics sur des problèmes d'actualité. Une heure et published jointly by Springer and CRM. demie par jour a été réservée aux affiches, qui ont été exposées durant toute la durée de Workshop on Theoretical Methods for l'atelier, ce qui a permis plusieurs discussions Strongly Correlated Fermions informelles, entre autres durant les pauses café May 26 - 30, 1999 ou le matin à l'arrivée. L'atelier a attiré 57 Org. : André-Marie Tremblay (Sherbrooke) and Andrei Ruckenstein (Rutgers) participants dont 28 étudiants et boursiers Cet atelier a permis de confronter différentes postdoctoraux. approches théoriques pour les modèles La première journée a été consacrée aux d'électrons fortement corrélés, c'est-à-dire pour méthodes numériques. S. White a présenté une les systèmes d'électrons où les énergies introduction à la méthode de renormalisation cinétiques et potentielles sont comparables. On par la matrice densité alors que K. Hallberg nous rencontre ces problèmes entre autre dans le a fait part des tous derniers développements. contexte de la supraconductivité à haute L'exposé de M. Imada a permis de faire le point température. Ces matériaux sont fortement sur les résultats pour un grand nombre de anisotropes, plus spécifiquement quasi- modèles. S. Zhang avait préparé un exposé très bidimensionnels, et les électrons ne sont ni pédagogique sur les méthodes Monte Carlo complètement localisés ni complètement quantique et sur une nouvelle méthode pour délocalisés, ce qui implique encore une fois que éliminer le problème du signe fermionique. les méthodes traditionnelles ne sont pas Ce sont les méthodes de bosonisation qui ont été utilisables. au cœur de la deuxième journée. Après une Parmi les méthodes théoriques développées introduction magistrale de D. Sénéchal, les récemment, on compte les développements conférenciers T. Giamarchi, I. Affleck et M.P.A. autour de la dimension infinie, la bosonisation, Fisher ont décrit comment ces méthodes l'invariance conforme, le groupe de permettent de comprendre, respectivement, renormalisation, les bosons esclaves et diverses l'effet du désordre sur les systèmes quasi- autres méthodes non-perturbatives. Chacune de unidimensionnels désordonnés, la résonance de ces méthodes ayant ses limites et chacune d'elle spin dans les chaînes de spin unidimensionnelles étant suffisamment complexe, il est rare qu'une et les fermions fortement corrélés en deux personne puisse en maîtriser plusieurs. Les dimensions. La présentation pédagogique de G. approches numériques jouent un rôle essentiel Kotliar sur la transition de Mott s'inscrivait dans puisqu'on ne peut pour le moment étudier que un cadre méthodologique différent mais des Hamiltoniens qui sont des caricatures des soulevait un problème de fond. En effet, des systèmes accessibles expérimentalement. Ainsi, résultats récents sont venus contester le fait que les approches numériques permettent de tester la transition de Mott soit du premier ordre à la validité des autres méthodes de nature plus température nulle, comme le suggère la méthode analytique. de développement en dimension infinie. Ce problème a été discuté en profondeur par les Malgré les nombreuses conférences et ateliers deux groupes impliqués lors d'une des deux sur les fermions fortement corrélés, on ne séances de discussion de samedi après-midi et il retrouve pas d'atelier consacré uniquement aux

CRM Annual Report 1999-2000 15 S c i e n t i f i c A c t i v i t i e s a été conclu que la méthode de calcul en longueur de corrélation à une particule devient dimension infinie devait pour le moment être plus petite que la longueur de corrélation des considérée plus fiable. modes collectifs. La journée de vendredi a commencé par un tour V. Dobrosavljevic a montré le dimanche d'horizon des applications de la méthode de comment traiter l'effet combiné du désordre et renormalisation de Wilson aux fermions. C. des interactions grâce aux méthodes de Bourbonnais y a introduit le sujet et expliqué ses dimension infinie. A. Chubukov a terminé applications aux systèmes quasi- l'atelier par un exposé plus spéculatif sur l'effet unidimensionnels. Il a exposé une nouvelle de l'antiferromagnétisme sur la supra- méthode qui donne de meilleurs résultats que la conductivité, terminant sur une note stimulante. bosonisation lorsqu'elle est appliquée aux systèmes de spins avec interactions aux premiers AARMS-CRM Workshop on Bäcklund et deuxième voisins. La plupart des experts du & Darboux Transformations: The domaine étaient dans la salle. Des questions Geometry of Soliton Theory assez techniques sur l'applicabilité de la June 5 - 9, 1999, Halifax, Nova Scotia méthode de Wilson aux ordres supérieurs ont Org. : Mark J. Aablowitz (Colorado), Alan Coley (AARMS, Dalhousie), Athanassios S. Fokas (Imperial College), Decio été débattues et éclaircies. Les unidimensionnels Levi (Roma 3), Peter J. Olver (Minnesota), Colin Rogers ont en général des lignes de points critiques à (New South Wales), and Pavel Winternitz (CRM) température nulle et S. Sachdev a enchaîné avec L'objectif de l'atelier était de regrouper un grand des explications très physiques sur les points nombre de chercheurs actifs dans la théorie des critiques quantiques. L'effet du désordre près solitons. Ce fut un succès puisque 62 chercheurs, des points critiques quantiques a été discuté par dont 7 étudiants et chercheurs postdoctoraux, A. Rosch. S. Zhang a présenté un nouveau ont participé à l'atelier. L'accent a été mis sur le développement de sa théorie de la développement et les applications des supraconductivité de type SO(5). Il a en effet transformations de Bäcklund et de Darboux. Il y expliqué pourquoi les calculs numériques ne a eu un total de 51 présentations de la part de montrent qu'une partie du spectre des états en conférenciers invités. établissant une analogie avec l'effet chiral du champ magnétique. P. Wölfle, quant à lui, a Astrophysics and Cosmology montré comment on peut utiliser les méthodes June 6 - 12, 1999 conservatrices pour développer de nouveaux This large conference will group two major types d'approximation avec les bosons esclaves. workshops covering closely related subjects that Samedi, N. Bickers a présenté une introduction are usually isolated. très claire aux équations parquet et expliqué les nouvelles approches numériques qu'il a Black Holes II: développées pour résoudre ces équations. Une Theory and Mathematical Aspects nouvelle approche hamiltonienne à l'effet Hall June 6 - 9, 1999, Fall Hills Inn, Val Morin Co-sponsors : Canadian Institute for Advanced Research quantique fractionnaire a ensuite été présentée (CIAR) and Canadian Institute for Theoretical par R. Shankar. Nous avons déjà parlé d'une des Astrophysics (CITA) deux tables rondes de l'après-midi sur la Org. : Valeri Frolov (Alberta), Werner Israel (Victoria), Robert Myers (McGill), Don Page (Alberta), and Eric transition de Mott avec G. Kotliar et S. Kehrein. Poisson (Guelph) Des discussions en petit groupe suite à l'autre table ronde menée par R. Frésard et B. Kyung The focus of this workshop was the many recent sur de nouvelles méthodes non-perturbatives developments in the statistical mechanical ont permis de faire le point sur les contradictions description of black holes. The workshop apparentes dans la littérature antérieure entre brought together some 66 researchers, including différentes approches au problème à N-corps. 37 graduate students and postdoctoral fellows, Les méthodes auto-cohérentes et les simulations in general relativity and string theory who are Monte Carlo semblaient indiquer l'absence de interested in these developments. It was the pseudogap dans le poids spectral à une particule second instalment in a series of similar alors que de nouvelles méthodes et de nouvelles workshops; the first one was held in Banff simulations indiquent plutôt qu'il y a un (Alberta) in June, 1997. Black Holes II was held pseudogap à basse température lorsque la in conjunction with the Eighth Canadian Conference on General Relativity and

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Relativistic Astrophysics (McGill University, theory, which are amenable to examining and June 10-12), organized by Rob Myers and Cliff counting the underlying microscopic states. Burgess. The early nineteen seventies produced Hence a precise statistical mechanical account of remarkable advances in our understanding of the black hole entropy could be given in these black holes. A set of four basic laws governing particular cases. Motivated by the string theory the evolution of classical black holes were results, complementary calculations were later formulated. While these laws bore a striking made using spacetime loop variables, and also resemblance to the four laws of using an infinite conformal symmetry which thermodynamics, such a comparison remained a apparently characterizes the spacetime geometry formal analogy until 1974. At that time, near an event horizon. The extent to which any Hawking made the astounding discovery that of these calculations hold in general, and how quantum processes occurring near the event the different approaches might be related, are horizon give rise to a thermal flux of radiation important open questions that were discussed far from the black hole, with a temperature during the workshop. proportional to the surface gravity of the There were 16 invited speakers at the workshop, horizon. Thus Hawking's discovery showed that and 15 additional speakers contributed talks. black holes do indeed behave as thermodynamic The invited lectures were held in the mornings systems, and confirmed a suggestion by and evenings, and the afternoons were devoted Bekenstein that they must possess an entropy to the contributed lectures. We now present a proportional to the surface area of the event brief overview of the invited lectures. horizon. This realization revealed a profound Sunday morning started out with reviews of the connection between three different branches of mostly classical aspects of black hole physics: general relativity, quantum mechanics, thermodynamics, presented by Robert Wald and thermodynamics, and there is a widely held (Chicago), Abhay Ashtekar (Penn State), and belief that this connection will provide insights Werner Israel (Victoria). The evening's lecture into the elusive problem of quantizing gravity. was given by Leonard Susskind (Stanford), who While the first law of black hole talked about the holographic principle, and the thermodynamics provides a formula for black anti-de Sitter/conformal field theory hole entropy in terms of the area of the event correspondence. On Monday morning, the talks horizon, it also presents us with a were mostly concerned with quantum-gravity thermodynamic understanding of the entropy - aspects of black hole thermodynamics; these namely, it is associated with energy unavailable were given by Steve Carlip (UC Davis), Gabor for work, or energy that cannot be extracted Kunstatter (Winnipeg), and Emil Martinec from the black hole through classical processes. (Chicago). In particular, Steve Carlip reviewed For ordinary thermal systems, statistical the calculations of black hole entropy using the mechanics provides a complementary conformal symmetry of the near-horizon description of entropy in terms of our geometry, and Emil Martinec gave an overview uncertainty about the precise state of the of the many different microscopic descriptions microscopic degrees of freedom. Constructing that string theory provides in various cases. The such a microphysical description of black holes evening lecture was given by Don Page has been an unresolved problem in gravitational (Alberta), whose topic was the thermodynamics physics which, despite numerous attempts, of very cold (near extreme) black holes. The yielded no progress until very recently. The past discussion of quantum aspects continued on few years have produced many breakthroughs Tuesday morning, with talks by Ted Jacobson in our understanding of the statistical origin of (Maryland), Valeri Frolov (Alberta), and Robert the black hole entropy. The main purpose of this Mann (Waterloo). Bill Unruh (UBC) gave the workshop was to take stock of this progress, evening lecture, and talked on his sonic identify the remaining open issues, and map out analogue of black holes. Finally, Wednesday future research directions. String theory, morning was devoted specifically to string currently the favoured candidate for a theory of theoretic aspects of black hole thermodynamics, quantum gravity, is largely responsible for much with talks by Juan Maldacena (Harvard), Finn of this recent progress. Certain black holes can Larsen (Chicago), David Lowe (Brown), and be associated with configurations in string Steve Gubser (Harvard).

CRM Annual Report 1999-2000 17 S c i e n t i f i c A c t i v i t i e s

There were also thirty-four contributed talks Eighth Canadian Conference on (including eleven by graduate students) and General Relativity and Relativistic fourteen poster presentations. A brief sampling Astrophysics of the wide variety of topics covered in these June 10 - 12, 1999, McGill Univ, Montréal contributions is: the dynamics of Brill-wave Co-sponsor: Canadian Institute for Theoretical Astrophysics (CITA) spacetimes, algebraic computing in general Org. : C.P. Burgess (McGill), J. Gegenberg (New relativity, detection of gravitational waves from Brunswick), D. Hobill (Calgary), G. Kunstatter (Winnipeg), coalescing binaries, the Hamiltonian description R.G. McLenaghan (Waterloo), and R.C. Myers (McGill) of isolated black holes, topological censorship, This conference was the eighth in an ongoing and the scattering cosmic strings from black series of biannual meetings, which bring holes. together Canadian researchers working on various aspects of gravitational physics, as well Frontiers of Mathematical Physics: as experts in this field from around the world. At Summer Workshop on Particles, Fields the present time, the study of general relativity and Strings 99 and relativistic astrophysics is progressing August 2 - 20 1999, Univ. of British Columbia, Vancouver, rapidly in several different directions. Two British Columbia Co-sponsors : Pacific Institute for Mathematical Sciences prime examples are: the explosion of research (PIms) and Asia Pacific Center for Theoretical Physics activity in the statistical mechanical properties of (APCTP) black holes, stimulated by recent developments Org. : Taejin Lee (Kangwon National Univ.), Yuri Makeenko (ITEP, Moscow & NBI, Copenhagen), John Ng in superstring theory, and the intense study of (TRIUMF), Soonkeon Nam (APCTP, Seoul), Chaiho Rim gravitational waves, stimulated by the advent of (APCTP, Seoul), Alexander Rutherford (PIms), Gordon Semenoff (UBC), K.S. Viswanathan (Simon Fraser), and large-scale experiments (LIGO) which should be Ariel Zhitnitsky (UBC) able to detect these waves in the near future. Partly as a result of the sense of excitement The main scientific topic of this workshop, which this activity has created, we were able to which took place at the Pacific Institute for attract a hundred participants from nine Mathematical Sciences site at the University of different countries (Canada, England, France, British Columbia, was recent developments in Israel, Singapore, South Korea, Sweden, superstring theory. The two main themes were Switzerland and the United States), including 53 the IKKT matrix model of type IIB strings and graduate students and postdoctoral fellows. the AdS/CFT correspondence. Other topics, Many of the participants came to McGill after such as the role of K-theory in string theory, the attending the workshop, "Black Holes II: Theory structure of supersymmetric Yang-Mills theory and Mathematical Aspects", which was held in and some general questions about the solutions Val Morin (in the Laurentians, north of of supergravity were also discussed. Igor Montréal) on June 6-9, 1999. Klebanov (Princeton University) presented a The list of invited talks included: Abhay series of three review lectures on the AdS/CFT Ashtekar, Quantum Geometry and Black Hole correspondence. Joe Polchinski (ITP Santa Entropy; Gilles Fontaine, White Dwarf Stars as Barbara) gave a series of two lectures discussing Potential Contributors to Baryonic Dark Matter; Ted some more advanced issues in that subject. Jacobson, Entropy and Gravity: Horizons, There were 68 participants. Of these, 16 were Entanglement and the Holographic Bound; Vicky postdoctoral fellows, 14 were graduate students Kaspi, Binary Radio Pulsar Timing and General and the remainder were more senior scientists. Relativity; Lev Kofman, Preheating After Inflation; Most were theoretical and mathematical Sharon Morsink, Surprises from Rotating Neutron physicists. Three were mathematicians. Stars; Don Page, Can Quantum Cosmology Give Participants came from Russia, Korea, Japan, Observational Consequences of Many-Worlds Taiwan, USA, Canada, Italy, France, England, Quantum Theory?; Peter Saulson, What Will We Spain, Denmark, and Ireland. Learn from Gravitational Wave Detection?; Lennie There were two seminars per day during the Susskind,The Holographic Principle; Bill Unruh, workshop. The schedule provided a significant The Effect of Second Order Perturbations on the amount of time for discussions and scientific Expansion of the Universe; Jeff Winicour: The work. Collaborations were encouraged. The Characteristics of Colliding Black Holes. seminar speakers were a combination of invited speakers and other participants. The presence of

18 Annual Report 1999-2000 CRM S c i e n t i f i c A c t i v i t i e s invited speakers provided a scientific focus to recently. To begin with, it is mathematical rather the workshop and strengthened the quality of than physical. On one hand, a renormalization the seminars. group can be considered as an infinite The invited speakers were Peter Horava dimensional dynamical system and the methods (Caltech), Seungjoon Hyun (Seoul), Hikaru of non-linear differential equations play an Kawai (Kyoto), Igor Klebanov (Princeton), essential role here. On the other hand, the Kimyeong Lee (Seoul National U.), Amanda Peet method of renormalization group turned out to (Santa Barbara), Joe Polchinski (Santa Barbara), be very effective in understanding long time and S. Rajeev (Rochester). behaviour of rather complicated evolution equations. Workshop on Non-linear Dynamics Though the development described above first and the Renormalization Group appeared in physics, the problems addressed August 22 - 27, 1999 there are of key interest in other fields, such as Org. : Israel Michael Sigal (Toronto) and Catherine Sulem biology, economics, chemistry, and engineering. (Toronto) So far these problems have been attacked mostly This workshop was devoted to two relatively with heuristic arguments, justified by computer young and fast developing areas of simulations and costly experiments. Developing mathematical physics - non-linear dynamics and mathematical techniques, as well as introducing the renormalization group, the former being logical clarity in these areas, is one of the main understood as a qualitative theory of non-linear challenges facing mathematicians. This evolution partial differential equations. Some of workshop has brought together mathematicians the questions addressed were: the dynamics of and physicists working on non-linear differential particle-like structures (e.g. solitons and equations and renormalization group methods. vortices) and interface boundaries, blow-up It has contributed to the exchange of ideas in profiles, universal features of large-time these fields. behaviour, and the application of The workshop attracted 56 participants, renormalization group methods to quantum including 9 graduate students and postdoctoral field theory, statistical mechanics and in non- fellows, from Canada, USA, France, Switzerland, linear partial differential equations (in Germany, Japan, Taiwan, and Greece. The list of particular, in general relativity). speakers included: S. Alama (McMaster), N. The workshop had review talks summarizing Alikakos (Athens), F. Bethuel (Paris VI), P. Bizon recent advances, talks on current progress and (Warsaw), O. Bogoyavlenski (Queen's), L. discussions on promising directions. We Bronsard (McMaster), P. Deift (Courant), J.P. describe in more detail the subject matter of the Eckmann (Geneva), J. Feldman (UBC), J.M. Graf workshop. Non-linear dynamics and (Zurich), S. Gustafson (Toronto), T. Hurd renormalization group theory, which are among (McMaster), V. Jaksic (Ottawa), R. Jerrard the most active areas of research in physics in (Illinois), L. Kapitansky (Kansas), N. Kevlahan the last 25 years, have rather disparate origins, at (McMaster), M. Kiessling (Rutgers), J. Lebowitz least at first sight. The non-linear evolution (Rutgers), R. McCann (Toronto), M. Merkli equations describe usually macroscopic objects (Toronto), H. Nawa (Nagoya), D. Pelinowsky whose characteristics undergo changes in space (Toronto), G. Perelman (EP, Paris), R. Pyke and time. The renormalization group theory, on (Ryerson), Y. Saint-Aubin (Montréal), S. Serfaty the other hand, was invented to investigate the (ENS, Paris), J. Shatah (Courant), T. Spencer microscopic systems of enormous number, say (IAS, Princeton), A. Soffer (Rutgers), B. 23 10 , of degrees of freedom, which are in a state Vasiljevic (Toronto). of equilibrium. However, these areas are closely related. It has been known for a long time that The general feeling among participants was that states of macro-objects, whose evolution is given the workshop was a great success, that it made a through non-linear evolution equations, valuable contribution to the fields in question describe large scale, collective characteristics of and that it helped to ease the entry of new microsystems of a large number of degrees of researchers, and most importantly graduate freedom. However, the interaction of these two students and postdoctoral fellows, into these areas, of interest to us, was discovered only fascinating fields. The participants were

CRM Annual Report 1999-2000 19 S c i e n t i f i c A c t i v i t i e s impressed by CRM facilities, the helpfulness of Transform and Canonical Transformations for the staff and the lively atmosphere of the city. Spheres; P. Paradan, Localisation of the Riemann- Roch Character; A. Uribe, Semiclassical Properties of Workshop on Aspects of Quantization Almost-Kaehlerr and Spin-c Quantizations; L. September 23 - 29, 1999 Jeffrey, The Verlinde Formula for Moduli Spaces of Org. : Lisa Jeffrey (Toronto) Parabolic Bundles; J. Sniatycki, Commutativity of Quantization originates in theoretical physics (in Quantization and Reduction and Decomposition of the passage from the classical phase space which Representations; M. Gotay, On Quantizing parametrizes the position and momentum of a Nilpotent and Solvable Basic Algebras; B. Hall, classical particle, to the Hilbert space of wave Unitarity in Quantization Commutes with functions whose norm squared describes the Reduction; S. Berceanu, Symplectic Area of Geodesic probability distribution of the particle). It has Triangles and Coherent states; C. Duval, been incorporated into various disciplines in Equivariant Quantization; H. Fuehr, Coherent pure mathematics including algebraic and States from Cyclic Representations; S.T. Ali, symplectic geometry. This workshop brought Coherent State Quantization and a Generalized together researchers with interests in three Wigner Function. different areas of mathematics related to the theory of quantization: QIP 2000 : Workshop on Quantum • quantization by coherent states; Information Processing • geometric quantization; December 5 - 11, 1999 • Org. : Gilles Brassard (Montréal) and Richard Cleve the behaviour of quantization under (Calgary) symplectic reduction, in particular the conjecture of Guillemin and Sternberg that L'informatique quantique est un domaine de "quantization commutes with reduction". recherches en pleine ébullition qui étudie les nouvelles avenues pour le traitement de The portion of the conference devoted to l'information que rend possibles la mécanique coherent state quantization was organized by quantique. Nous nous intéressons en particulier Prof. S.T. Ali (Concordia Univ.). au calcul quantique, à la cryptographie The workshop brought together 46 participants quantique, à la téléportation quantique et aux including 18 postdoctoral fellows and graduate autres formes de communication quantique qui students. The list of invited speakers included mettent en oeuvre le phénomène de l'intrication researchers from Canada, France, Mexico and quantique. the USA. To the best of the organizer's QIP 2000 était le troisième d'une série d'ateliers knowledge, this was the first time a meeting internationaux dont le but est de réunir une fois devoted exclusively to the theme of quantization l'an les chercheurs qui s'intéressent had been held in Canada. particulièrement aux aspect informatiques du The list of invited talks included: traitement quantique de l'information. Les E. Meinrenken, A Fixed Point Formula for Loop conférenciers invités provenaient du Canada, du Group Actions; R. Sjamaar, Imploded Cross Danemark, des États-Unis, d'Israël, de la Sections; C. Woodward, Quantization of the Lettonie, des Pays-Bas et du Royaume-Uni. Moduli Space of Flat Connections for non Simply- Une centaine de participants, dont 47 étudiants Connected Groups A Cubic Dirac ; B. Kostant, et boursiers postdoctoraux, ont rendu cet Operator and a Generalization of Bott-Borel-Weil ; J. événement particulièrement enrichissant. Afin The Duflo Isomorphism and Weitsman, M. Vergne, de favoriser les discussions informelles, le the Campbell-Hausdorff Formula The ; M. Brion, programme contenait des conférences le matin et General Faces of the Moment Polytope ; A. Szenes, en fin d'après-midi, mais trois heures de temps Deformation Quantization of Moduli Spaces of libre étaient prévues chaque jour en début Vector Bundles A Non-Abelian ; E. Lerman, d'après-midi. Une photo de groupe est Duistermaat-Heckman Formula ; J. Hurtubise, disponible à l'URL suivant: Framed Parabolic Bundles and Representations with http://www.crm.umontreal.ca/act/theme/1999/Q Weighted Frames; C. Teleman, Quantization of the IP2KNS.jpg Hitchin System; Equivariant and Y.-H. Kiem, Un cahier des résumés des conférences a été Intersection Cohomology of Moduli Spaces of Vector distribué lors de l'inscription. Bundles; C. Villegas Blas, The Segal-Bargmann

20 Annual Report 1999-2000 CRM S c i e n t i f i c A c t i v i t i e s

La journée initiale de l'atelier a été consacrée à Wolf, Log-Rank Lower Bound for Entanglement- une série de mini-cours (tutorials) dont le but Assisted Quantum Communication Complexity; était de permettre à des chercheurs n'ayant pas Harry Buhrman, Quantum Communication déjà les connaissances préalables dans le Complexity Bounds by Polynomials; Classical domaine de pouvoir suivre les conférences des Communication Cost in Quantum Information jours suivants. Au programme de cette journée Processing; Hoi-Kwong Lo, A Generalization of du 6 décembre 1999, les cours suivants ont été Quantum Communication Complexity. donnés: La sixième et dernière journée, 11 décembre Gilles Brassard, Introduction to Quantum Infor- 1999, a été consacrée à la théorie de la complexité mation Processing; Richard Cleve, Fundamental quantique (derechef) et à la théorie de Quantum Algorithms; Isaac Chuang, Quantum l'information quantique (derechef): John Computers: Physical Implementation; Daniel Watrous, Space-Efficient Simulation of Quantum Gottesman, Introduction to Quantum Error Processes; Raymond Laflamme, Quantum Correction and Fault-Tolerance et Charles H. Computation, the Power of one bit of Quantum Bennett, Quantum Information Theory Tutorial . Information and Quadratically Signed Weight La seconde journée, 7 décembre 1999, a été Enumerators; Andris Ambainis, Quantum Lower consacrée au stockage et à l'extraction de Bounds by Quantum Adversaries; Michael Nielsen, l'information quantique, ainsi qu'à l'autotest: The Structure of the Entangled States; Christopher Lov K. Grover, Amplitude Amplification with A. Fuchs, On Unknown Quantum States et Multiple Targets; John P. Preskill, Topological Richard Jozsa, Distinguishability of States and von Storage of Quantum Information; Michele Mosca, Neumann Entropy. Self-Testing of Universal Sets of Quantum Gates et Dominic Mayers, Violation of Locality and Self- Workshop on Strings, Duality and Testing Quantum Apparatus. Geometry La troisième journée, 8 décembre 1999, a été March 22 - 25, 2000 Org. : Eric D'Hoker (UCLA) and Duong H. Phong consacrée à la théorie de l'information quantique (Columbia) et des algorithmes quantiques: Peter W. Shor, The workshop on “Strings, Duality, and EPR Assisted Capacity of a Quantum Channel; Geometry” was centered on recent advances in David DiVincenzo, Algebraic and Graph Theoretic this fast evolving area of interface between Aspects of Unextendible Product Bases and Bound geometry and physics. Particular attention was Entanglement; Umesh Vazirani, Quantum devoted to mirror symmetry and Calabi-Yau Computation with Highly Mixed States et Tal Mor, manifolds, construction of Lagrangian fibrations Algorithmic Cooling for Ensemble Computers. of tori and symplectic geometry, Seiberg-Witten Le matin de la quatrième journée, 9 décembre theory and integrable models, holographic 1999, a été consacrée à la cryptographie duals, Eisenstein series and exact thresholds, quantique: Claude Crépeau, Bit Commitment and non-commutative geometry and non- Zero-Knowledge: Classical vs Quantum; Louis commutative quantum field theory, and Salvail, Perfectly Concealing Quantum bit differential geometric problems related to the Commitment from any Quantum One-Way AdS/CFT correspondence. Permutation A Proof of et Vwani Roychowdhury, The workshop attracted 58 participants Security of Quantum key Distribution . L'après-midi including 19 graduate students and postdoctoral de cette journée était libre afin de favoriser fellows. There was an ideally balanced group of encore davantage les discussions informelles et mathematicians and physicists, and the de démontrer l'adage de Erdos selon lequel le workshop led to many fruitful exchanges. The mathématicien est une machine destinée à workshop also benefited from the presence of transformer la caféine en théorèmes. Roman Jackiw, Aisenstadt Chair, whose lectures La cinquième journée, 10 décembre 1999, a été were included in the programme. consacrée aux algorithmes quantiques (derechef) The list of invited speakers included: Brian et à la théorie de la complexité quantique: Dorit Greene, Boris Pioline, Shing-Tung Yau, Eric Aharonov, A Quantum to Classical Phase Zaslow, Samir Mathur, Rob Myers, Dan Freed, Transition in Noisy Quantum Computers; Eli Mark Gross, Albrecht Klemm, Michael Faux, Biham, Exact Solution of Grover's Search Algorithm Bong Lian, Kefeng Liu, Bernard Julia, Dan Using any Unitary Transformations; Ronald de

CRM Annual Report 1999-2000 21 S c i e n t i f i c A c t i v i t i e s

Kabat, Steve Naculich, Howard Schnitzer, intégrables en matière de l'état solide et la François Lalonde, Wei-Dong Ruan, Massimo physique hors-équilibre. Tous les participants, Porratti, Philippe Pouliot, Jean-Loup Gervais, dont certains reconnus internationalement, Frederik Denef, Anatoly Libgober, Konstantin furent en résidence pour des périodes d'au Savvidy, and Andrei Todorov. moins deux semaines et allant parfois jusqu'à deux mois et demi. Onze personnes ont participé Workshop on Mathematical Physicists à toutes les activités du trimestre, incluant sept in Finance and Industry étudiants et boursiers postdoctoraux dont cinq June 12 - 17, 2000 provenant d'institutions de l'extérieur. Le Org. : Luis Seco (Toronto) and Stathis Tompaidis (Texas) sentiment général est celui d'un événement The workshop consisted of two distinct parts. excitant et extrêmement productif. The first part was a series of mini-courses given by the organizers and John Chadam Quantum Algebras and Integrability (Pittsburgh). Participants in the course consisted April 2 - 30, 2000 Org. : André LeClair (Cornell) and Nicolai Reshetikhin mainly of graduate students, with a small (Berkeley) number of professional scientists who had an interest in a quick introduction to the subject. Cette première période de concentration était The format of the courses was that of case consacrée aux aspects plus mathématiques sous- studies, mixed with the fundamental elements of jacents aux modèles intégrables quantiques. Des the theory. They were very well attended, and résultats récents y ont été présentés sur les sujets the audience participated eagerly. suivants: algèbres affines quantiques pour les modèles sur réseau et en théorie des champs Part II was a traditional conference, that hosted quantiques; opérateurs vertex et facteurs de visitors from North America and Europe mainly. forme; équations de Kniznick-Zamolodchikov Of special interest was a joint talk given by déformées et autres équations aux différences; Fields Medalist Charles Fefferman and Allan Ho, facteurs elliptiques; algèbres de Virasoro from Princeton University, a talk with the format déformées; résultats exacts sur les fonctions de of a "duet" rarely seen in mathematical talks. The corrélation; température finie; théorie des topics covered were very varied, from stochastic champs avec frontière; perturbations intégrables volatility to transactions costs, from pricing of des théories des champs conformes; algèbres American options to risk management in non- affines quantiques et matrices S exactes. gaussian markets. Of special interest was the fact Les activités de ce premier mois du Trimestre that several talks were given by students and sur l'intégrabilité quantique ont attiré 62 young scientists, as well as by noted scientists chercheurs dont 26 étudiants et boursiers established in their fields. Altogether, there were postdoctoraux. 40 participants including 11 graduate students and postdoctoral fellows. Workshop on Isomonodromic Defor- Part II ended with an "Industry Day", which mations and Applications in Physics included the participation of CIRANO and May 1 - 6, 2000 Banque Nationale. Personnel from Hydro Org. : John Harnad (Concordia, CRM) and Alexander Its Québec also participated in the workshop. (IUPUI, Indianapolis) This was the first international workshop Concentration Period organized solely on the theme of Quantum Integrability 2000 Isomonodromic Deformations and Applications April 2 - June 11, 2000 in Physics. The study of isomonodromic Org. : Philippe Di Francesco (North Carolina), André deformation equations is currently in very active LeClair (Cornell), Nicolai Reshetikhin (Berkeley) and Hubert Saleur (USC) development, motivated in part by the central role of such equations in a number of areas of D'avril à juin, le CRM a été l'hôte d'un trimestre quantum and statistical physics. The main de concentration lors de l'hiver 2000 avec domains in physics to which this approach is plusieurs chercheurs en résidence. Le applicable are: programme fut constitué de deux périodes de • Computation of correlation functions in quatre semaines et d'un atelier. La première quantum integrable systems and lattice période a porté sur les Algèbres quantiques et models of statistical physics; l'intégrabilité et la seconde sur les Modèles

22 Annual Report 1999-2000 CRM S c i e n t i f i c A c t i v i t i e s

• The spectral theory of random matrices, random polynomials; Frobenius manifolds; with applications to quantum gravity; relations to classical integrable systems; • Topological field theory, with applications perturbations of infinite dimensional integrable to solution of the DVVW equations through systems. the theory of Frobenius manifolds; The list of speakers and further details may be • Scaling reductions of classical integrable found at the workshop web site: systems. http://www.crm.umontreal.ca/~harnad/home. There was a certain overlap in participation with dir/ISOMON.dir/isomon-workshop.html and at the preceding CRM period of concentration on http://www.crm.umontreal.ca/~harnad/home. Quantum Algebras and Integrability. Also, dir/ISOMON.dir/isomon-sched.html. during the first three days of the six-day The proceedings will be published by the AMS workshop, the Aisenstadt Chair lectures by Prof. in the CRM Proceedings and Lecture Notes Joel Feldman, on Fermi Surfaces and Infinite series. Genus Riemann Surfaces, were integrated into the schedule. Integrable Models in Condensed The speakers at the workshop included some of Matter and Non-Equilibrium Physics the foremost experts in the field, together with a May 14 - June 11, 2000 number of active younger researchers. There Org. : Philippe Di Francesco (North Carolina), André were a total of about 40 participants, including LeClair (Cornell) and Hubert Saleur (USC) 11 graduate students and postdoctoral fellows, Le second mois du Trimestre sur l'intégrabilité coming from the U.S., Canada, Japan, Russia, quantique se concentrait sur la matière Ukraine, Germany, Spain, United Kingdom, condensée, avec une emphase sur le désordre. Belgium, Italy, and Australia. The programme Ceci était particulièrement heureux puisque consisted of a total of 24 one hour talks, mainly plusieurs résultats importants apparaissaient à by invited speakers. The specific topics covered ce moment-là et plusieurs furent présentés et included: Inverse monodromy problems for discutés au CRM. Parmi les sujets traités se differential operators with meromorphic trouvent : les systèmes désordonnés; les matrices coefficients, and monodromy preserving aléatoires; les problèmes d'impureté; les deformations; isomonodromic tau functions as systèmes de Hall quantiques; les matériaux Fredholm determinants; matrix Riemann-Hilbert tubulaires et les plateaux de magnétisation; les problems, non-linear WKB and applications to théories conformes des champs avec frontière; asymptotics; vertex operators, Darboux and l'intégrabilité des processus stochastiques; le Backlund transformations; applications to scaling dans les systèmes loin de l'équilibre; la computation of correlation functions in quantum turbulence; la criticalité auto-organisée. Cette integrable systems and lattice models of activité a réuni 63 chercheurs dont 18 étudiants statistical mechanics; applications to the spectral et boursiers postdoctoraux. theory of random matrices, random word and random permutation problems, and zeros of

CRM Annual Report 1999-2000 23 S c i e n t i f i c A c t i v i t i e s

Aisenstadt Chair

The Aisenstadt Chair was endowed by Montréal philanthropist Dr. André Aisenstadt. Under its auspices, one or two distinguished mathematicians are invited each year for a period of at least one week, ideally one or two months. During their stay the lecturers present a series of courses on a specialized subject. They are also invited to prepare a monograph. At the request of Dr. Aisenstadt, the first of their lectures should be accessible to a wide audience. Previous holders of the Aisenstadt Chair are: Marc Kac, Eduardo Zarantonello, Robert Hermann, Marcos Moshinsky, Sybren de Groot, Donald Knuth, Jacques-Louis Lions, R. Tyrell Rockafellar, Yuval Ne’eman, Gian-Carlo Rota, Laurent Schwartz, Gérard Debreu, Philip Holmes, Ronald Graham, Robert Langlands, Yuri Manin, Jerrold Marsden, Dan Voiculescu, James Arthur, Eugene B. Dynkin, David P. Ruelle, Robert Bryant, Blaine Lawson, Yves Meyer, Ioannis Karatzas, László Babai, Efim I. Zelmanov, Peter Hall, David Cox, and Frans Oort. The CRM was honoured to have as Aisenstadt chairholder, during the 1999-2000 theme year in Mathematical Physics, Professors Joel Feldman of the University of British Columbia, Roman Jackiw of the Massachusetts Institute of Technology, and Duong H. Phong of Colombia University.

Professor Joel S. Feldman work led to the first example of the Wightman University of British Columbia axioms in 3-dimensional spacetime, a tour de Joel S. Feldman, force. His accomplishments in the areas of Professor of constructive quantum field theory, Mathematics at the renormalization theory, Schroedinger operators, University of British many body theory, and the theory of Riemann Columbia obtained his surfaces have been characterized by great B.Sc. in Mathematics technical power and clarity of thought. He has and Physics at the had fruitful collaborations with various co- University of Toronto, workers such as V. Rivasseau, H. Knörrer, E. and went on to obtain Trubowitz, J. Magnen, D. Lehmann, M. his A.M. and his Ph.D. Salmhofer, J. Feldman, etc. in some 30 papers, in Physics at Harvard University. He became a studying systems of interacting electrons, in research Fellow at the same university in 1974 particular Fermi liquids and superconductivity. and proceeded to become a CLE Moore During his visit to the CRM in the summer of Instructor at the Massachusetts Institute of 1999, Professor Feldman gave a series of lectures Technology from 1975 to 1977. He has been on the Renormalization Group and Fermionic professor of mathematics at the University of Functional Integrals. The Renormalization British Columbia since 1977. Group is the name given to a technique for He has since widely participated in organizing analyzing the qualitative behaviour of a class of mathematical workshops and has been a physical systems by iterating a map on the keynote speaker at several international vector space of interactions for the class. In a meetings including Canadian Mathematical typical non-rigorous application of this Society meetings in St.John's (1986), Vancouver technique one assumes, based on one's physical (1993) and Toronto (1995), the International intuition, that only a certain finite-dimensional Association of Mathematical Physicists subspace (usually of dimension three or less) is Congress (Swansea, 1988) and the International important. Congress of Mathematicians (Kyoto, 1990). His From August 22 to 25, 1999, Professor Feldman honours and distinctions include the James gave a series of lectures that covered the Loudon Gold Medal in Mathematics and definition of Grassmann algebras, the definition Physics, The Woodrow Wilson Fellowship, the and basic algebraic properties of Gaussian Charles Bayne Aiken Fellowship and the UBC integrals over these algebras, a statement of Killam Research Prize. how one formulates Fermionic models of Dr. Feldman is recognized as one of the leading quantum field theory and many-body physics in mathematical physicist in the world. He has terms of integrals over Grassmann algebras, always worked on hard problems in modern some basic bounds on Gaussian integrals over a physics involving deep mathematics. His early Grassmann algebra, an expansion for non- Gaussian Grassmann integrals that converges

24 Annual Report 1999-2000 CRM S c i e n t i f i c A c t i v i t i e s when a covariance for the Gaussian part of the charge and spin in these theories. He is measure is really nice, and finally, the use of the recognized for his imaginative use of quantum renormalization group to prove convergence of field theory which throws light on physical non-Gaussian Grassmann integrals when the problems, including his work on topological covariance for the Gaussian part of the measure solitons, field theory at high temperatures, and is not so nice. the existence of anomalies and their role in particle physics. During a second visit from April 28 to May 3, He gave a first series of lectures at the CRM on 2000, Professor Feldman presented a series of March 22 through 24, 2000 on Non-linear (Fluid lectures on Fermi Surfaces and Infinite Genus Dynamical) Equations and d-Branes. He Riemann Surfaces. He introduced a class of explored relationships among various non-linear infinite genus Riemann surfaces to which much differential equations on the basis of their of the classical theory extends. He concentrated relation to the Nambu-Goto action for extended on a family of examples that arise in the study of objects. Some of these equations describe fluid the spectrum of Schoedinger operators, which motion and they are generalized by the inclusion are differential operators that play a central role of Grassmann variables to build models of in modeling crystals. supersymmetric fluid dynamics. From June 7 through 9, 2000, he gave a second Professor Roman Jackiw series of lectures on Non-linear (Fluid Massachusetts Institute of Technology Dynamical) Equations, Complete Integrability Roman Jackiw and Non-Abelian Generalization. Non-linear obtained his B.A. in equations suggested by fluid mechanics were 1961 from the described and their complete integrability was Swarthmore College demonstrated. Ordinary fluid dynamical models and continued his were generalized to accommodate invariance studies at Cornell against global non-Abelian transformation University where he groups. received his Ph.D. in 1966. From 1966 to Professor Duong H. Phong 1969, he was at Columbia University Harvard University as a Junior Fellow. He joined MIT in 1969. He was an invited professor at Professor Duong H. several prominent institutions among them, the Phong obtained his Institute for Theoretical Physics, the University B.A. (1973) and Ph.D. of California and Columbia University. in mathematics (1977) from Princeton He is a fellow of the American Academy of Arts University. He went and Sciences, the American Physical Society and on to become L.E. the National Academy of Sciences. He is also a Dickson Instructor of recipient of the Alfred P. Sloan Research Mathematics at the Fellowship as well as the John Simon University of Chicago, Guggenheim Memorial Fellowship. His career and was a member of the Institute for Advanced has extended into scientific publications such as Study in 1977. In 1978 he became a Ritt Assistant the Annals of Physics where he became an Professor of Mathematics at Columbia assistant editor in 1973. He also is a University. Now full professor, he has also correspondent for Comments on Nuclear and served as chair of the Department of Particle Physics since 1984 and has remained on Mathematics. the editorial board of the Ukrainian Journal of Physics since 1991. He has published over 30 His awards include the Alfred P. Sloan books, book reviews and non-technical papers in Fellowship (1982-84). He is also Fellow of the his field. American Mathematical Society. In 1994, he was an invited speaker at the Zürich International Professor Jackiw has made major contributions Congress of Mathematicians. Throughout his to field theories relevant to condensed matter career Professor Phong has been involved in a physics, notably with his discovery of fractional variety of scientific activities. He became a

CRM Annual Report 1999-2000 25 S c i e n t i f i c A c t i v i t i e s member of the Editorial Board of the proceedings of a Conference on String, Duality Mathematical Physics Series of World Scientific, and Geometry, both held at the University of the Asian Journal of Mathematics and a member Montréal. of the Scientific Committee of the International During his stay at CRM from May 17 to May 26, Congress of the Chinese Mathematicians in 2000, Professor Phong delivered a series of Beijing in 1998. In 1986 and 1991, he was a lectures entitled Symplectic Forms, Soliton visiting professor at the Université de Paris-Sud Equations, and Supersymmetric Gauge Theories. He and at Princeton University, respectively. provided a self-contained introduction to Furthermore from 1993 to 1996, he was part of symplectic forms in soliton theory and the scientific advisory committee of CRM where supersymmetric gauge theories. He discussed he jointly organized two workshops, Strings, constructions of symplectic forms in terms of Duality and Geometry and Mirror Symmetry and Lax pairs, new integrable models of Calogero- Complex Geometry. Moser and spin chain types, and their relations In the past 10 years, he has been a major speaker with Seiberg-Witten solutions of in numerous scientific meetings in Europe, the supersymmetric gauge theories. Finally, he United States, and China. He also has supervised discussed methods for extracting the numerous Ph.D. theses. He has contributed to prepotential from the Seiberg-Witten spectral over 76 scientific publications and was involved curves. as an editor in two books: Mirror Symmetry III, proceedings of a conference on Complex Geometry and Mirror Symmetry and Mirror Symmetry IV,

26 Annual Report 1999-2000 CRM S c i e n t i f i c A c t i v i t i e s

General Programme

The CRM’s general programme funds a wide variety of scientific events, both on-site and around the world. Whether it be for specialized workshops for a small number of researchers, large meetings for hundreds of participants or activities for high school or undergraduate students, the general programme promotes research in mathematical sciences at all levels. The programme is quite flexible, to allow for opportunities as they arise.

The Cartan Equivalence Method, and Michael AARMS Combinatorics Workshop Wong Singular Plane Curves and ODEs. May 24 - 28, 1999, Memorial Univ., Saint-John’s, Newfoundland Org.: Jason Brown (Dalhousie), Richard Nowakowski CMS Summer Meeting: Special Session (Dalhousie), Abraham Punnen (New Brunswick), and in Harmonic Analysis Nabil Shalaby (Memorial) May 29- June 1, 1999 Memorial Univ., Saint-John’s, Newfoundland The scope of the workshop was combinatorics Org.: Kathryn Hare (Waterloo) with emphasis on combinatorial designs, their constructions, and related open problems. The This special session brought together 15 invited The Role of programme started with a short introduction of speakers: J. Benedetto (Maryland) Tiling in Sampling and Wavelet Theory the concepts and constructions of combinatorial , T. Chen Generalized Hardy Operators and designs by Nabil Shalaby (Memorial). The (UWO) Normalizing Measures Transfer topics presented by the main speakers included , C. Finet (Belgium) Principles in Orlicz Spaces a survey of colouring problems in combinatorial , B. Forrest (Waterloo) Operator Spaces in Noncommutative Harmonic designs (Alexander Rosa, McMaster), Analysis decomposing complete graphs of cycles of fixed , Jean-Paul Gabardo (McMaster) Determinacy in Truncated Trigonometric Moment length (Brian Alspach, Simon Fraser), and edge Problems and the Extension Property colourings and their uses (Chris Rodger, , E. Granirer Some Functional Analytic Properties of Auburn). The other invited speakers included (UBC) Quotients of the Fourier Algebra as Reflected by Anthony Bonato (Mount Allison), Hadi Some Subsets of the Real Line Kharaghani (Lethbridge), David Pike , H. Heinig Modular Inequalities for the Calderón (Memorial), Rolf Reese (Memorial), and (McMaster) Operator Isomorphism and Ruizhong Wei (Waterloo). Attendance was 36, , Z. Hu (Windsor) Homomorphism Results on the von Neumann including 10 senior researchers and 23 graduate Algebra VN(G) Weighted students. This workshop was well appreciated , R. Kerman (Brock) Inequalities for Semigroups of Operators and the by all participants. Norm Convergence of the Abel Means of Certain Canadian Undergraduate Mathematics Eigenfunction Expansions, T. Lau (Alberta) On the Conference Centre of Some Banach Algebras Associated to a May 26 - 30, 1999, Memorial Univ., Saint-John’s, Locally Compact Group, D. Oberlin (Florida) Newfoundland Convolution With Affine Arclength Measures in the The Canadian Undergraduate Mathematics Plane, J.-O. Ronning (Skovde) Generalized Perron Conference is organized by and for Trees – What and why, G. Sinnamon (UWO) From undergraduate mathematics students. CRM Nörlund Matrices to Laplace Representations, subsidized the participation of a group of Nicolaas Spronk (Waterloo) Diagonal Type students from McGill University. The following Conditions on Group C*-Algebras, and S. Wainger students gave talks: Shabnam Beheshti, Some (Wisconsin) Some Discrete Problems in Harmonic Basics of Hyperbolic Geometry; Madeline Pool, Analysis. Modeling Infectious Disease; Alexandru Ghitza, Counting Lattice Points; Patrick Lam, The Prime Number Theorem; Gabriel Holmes, Nets and Filters; Brian Kudlow, Equivalences of Automata and Monoids, Jean-Sabin McEwen, A Possible Explanation of the Solar Neutrino Problem; Peter Green, Locale Theory; Pierre-Alexandre Tremblay,

CRM Annual Report 1999-2000 27 S c i e n t i f i c A c t i v i t i e s

1999 Math Camp système de caméra pour l'étude de la May 31 - June 9, 1999, Université du Québec à Trois- cinématique humaine. Rivières, Trois-Rivières Org. : Harry White (Université du Québec à Trois-Rivières) 20th Annual Meeting of the Canadian Le camp mathématique est une activité Applied and Industrial Mathematics parrainée par l'Association mathématique du Society Québec (AMQ) dans le but de mettre en contact June 11 - 13, 1999, Univ. Laval, Québec des étudiants doués pour les mathématiques Org.: Michel Fortin (Laval) avec des mathématiciens professionnels. Les Le département de mathématiques et de campeurs sont sélectionnés parmi ceux qui ont le statistique de l'Université Laval et le GIREF mieux réussi au concours de l'AMQ (niveau (Groupe interdisciplinaire de recherche en collégial). En 1999, il y a eu 23 participants. Le éléments finis) ont été les hôtes de la rencontre premier prix du Concours est allé à Sol Moreno annuelle de la SSCMAI, tenue conjointement du Collège Brébeuf. Les deuxième et troisième avec la dixième Journée de Éléments Finis (JEF). prix sont allés à Pierre Levan du Petit Séminaire Le but de cette rencontre étant de faire le point de Québec, campus de l'Outaouais et à Pascal sur les activités de recherche en mathématiques Turbis du Cégep de Baie-Comeau. appliquées au Canada, le programme se devait d'être vaste et de fournir au plus grand nombre Annual Meeting of the Statistical possible de chercheurs la possibilité de présenter Society of Canada: Special Session on leurs travaux. Directional Statistics Les sujets suivants ont été approfondis dans un June 3 - 6, 1999, Univ. of Regina, Regina, Saskatchewan Org.: Louis-Paul Rivest (Laval) minisymposium et couvert par une conférence plénière donnée par un éminent chercheur. Le CRM a commandité une session spéciale sur Suivant chaque titre, vous trouverez entre la statistique directionnelle dans le cadre du parenthèses le nom de l'organisateur et celui du congrès annuel de la Société statistique du conférencier invité : Cryptographie quantique (C. Canada. Les conférenciers invités de la session Crépeau, McGill et R. Cleve, Alberta), Dynamique étaient Nick Fisher du CSIRO en Australie, un des populations (S. Rhuan, Dalhousie et O. chercheur établi dans le domaine, de même que Diekmann, Utrecht), Interfaces en sciences des deux chercheurs canadiens, Peter Kim de matériaux (L. Bronsard, McMaster et G. Milton, l'Université Guelph et Duncan Murdoch de Utah), Méthodes numériques pour les EDP non l'Université Western Ontario. Environ 40 linéaires (M. Gunzberger, SIAM et Iowa), personnes ont assisté à la session. Arithmétique par intervalles (G. Alefeld, GAMM et La session a débuté par la présentation de N. Karlsruhe), Théorie de la bifurcation (B. Dionne, Fisher qui a traité de la détection des modes Ottawa et M. Golubitsky, Houston), dans un échantillon d'angles. L'auteur a présenté Biomécanique numérique (H. Manouzi, Laval et M. plusieurs façons de traiter ce problème tout en Thiriet, INRIA) et Mathématiques et physiologie (J. soulignant la nécessité de poursuivre la Bélair, Montréal et L. Glass, McGill). recherche dans ce domaine car il ne possède pas En plus de ces minisymposia, il y eut neuf encore de solution satisfaisante. La deuxième séances de communications d'une vingtaine de présentation, par Peter Kim, a traité de la minutes pour un total de plus de 80 modélisation statistique d'un échantillon de présentations. La rencontre a été un franc succès vecteurs-unités en trois dimensions. L'auteur a attirant pas moins de 132 personnes parmi mis de l'avant une méthode générale lesquels on retrouvait une trentaine d'étudiants d'estimation qu'il a ensuite utilisée pour et 35 chercheurs en provenance de l'extérieur du modéliser les directions orthogonales aux plans pays. de rotation des comètes dans le système solaire. Il a terminé son exposé en faisant une brève interprétation physique des résultats de l'analyse statistique. M. Murdoch a ensuite traité d'un modèle de régression pour des matrices de rotations 3x3. Il a ensuite appliqué sa méthode pour calibrer les orientations fournies par un

28 Annual Report 1999-2000 CRM S c i e n t i f i c A c t i v i t i e s

13th High Performance Computing Le Forum a attiré environ 120 participants. La Symposium, HPCS'99 première journée a été consacrée à des tutoriaux. June 13 – 16, 1999, Queen's Univ., Kingston, Ontario La seconde journée a débuté avec la présentation Org. : Andrew Pollard (Queen's) du conférencier principal, Ahmed Jerraya The symposium brought together over 125 (CNRS, Grenoble), intitulée Hardware Software leading researchers from academic and Co-design from SDL. Le reste de la conférence a government research laboratories in nine été consacrée aux résultats des conférenciers countries. The Symposium included all-day dont les articles avaient été acceptés. Les tutorials (on HPC Java, Tools for IBM SP, Cluster principaux conférenciers invités étaient Yair Computing, and Open MP) and three days filled Lahav, Oystein Haugen, Rick Reed, Uwe with papers that expounded exciting advances Glässer, Reinhard Gotzhein, A. Prinz et in HPC from the medical, pharmaceutical and Claudine Simson. Les comptes-rendus de la engineering industries, as well as novel conférence ont été publiés chez Elsevier. contributions from researchers in HPC systems and architectures. The proceedings from this CNTA'99 conference were published by Kluwer Academic June 20 – 24, 1999, Univ. of Manitoba, Winnipeg, Manitoba Org.: J. Borwein (SFU), D. Boyd (UBC), C. David Publishers. (Concordia), R. Murty (Queen's), C. Stewart (Waterloo), Posters that highlight recent work were set up local organizer; H. Williams (Manitoba) during the symposium. A Jobs Fair was held and The purpose of the Canadian Number Theory a number of graduate students had the Association (CNTA) is to enhance and promote opportunity to interview and be interviewed by learning and research in Number Theory, the many agencies present. Ample time was particularly in Canada where we already have a made available for discussion, either around the great deal of strength in this area. To advance extended lunchtime periods or during the many these goals the CNTA organizes major social events. international conferences. The focus of CNTA is mainly on the following areas: SDL FORUM'99: The next Millenium combinatorial/computational number theory, June 21 - 25, 1999 analytic number theory, diophantine problems Org.: Rachida Dssouli (Montréal), Gregor von Bochmann (Ottawa), Yair Lahav (SDL Forum Society, ECI Telecom and arithmetic geometry. All of these areas have LDT) and Nortel Networks seen rapid development in recent years, both in Le Forum'99 LDS porte sur le SDL, soit Canada and internationally. They are also well Specification and Description Language. Ce forum represented among the interests of the members se tient à tous les deux ans et celui-ci était le 9e of the scientific committee for this conference. de la série. Le langage normalisé LDS permet la For CNTA'99 there were 8 plenary one-hour spécification et la description des systèmes talks and 17 invited 40-minute talks. The communicants. Il a évolué sur une vingtaine plenary speakers were: H. Darmon (McGill), J. d'années à travers des versions successives du Friedlander (Toronto), E. Goren (McGill) A. standard émanant de l'organisation de Granville (Georgia), P. Sarnak (Princeton), W. normalisation ITU-T. LDS est connu sous le nom Schmidt (Colorado), C. Skinner (Princeton), and "norme Z.100". La première version, apparue en T. Wooley (Michigan). These were chosen on the 1980, contenait déjà une représentation basis of the importance of their recent and past graphique en plus de représentation textuelle. La work and their stature as internationally dernière version est appelée SDL 2000. recognized number theorists. They presented Une particularité importante du forum est qu'il knowledgeable survey lectures concerning réunit des participants de l'industrie et des recent progress in their respective fields. The 17 universités dans des proportions de 2/3 et 1/3, invited speakers were selected to represent the respectivement. Les thèmes du forum étaient : themes of the conference and did so very les applications du langage LDS, la dérivation effectively. To mention just a few of these talks, systématique de LDS et la génération de code, A. Odlyzko gave a very nice survey of his recent les extensions au langage, la convergence avec work in computing the zeros of the Riemann UML et, finalement, test, performance et zeta function, D. Bressoud gave a very nice simulations fondés sur LDS. account of the alternating sign matrix conjecture, A. Bremner gave a beautiful presentation of his

CRM Annual Report 1999-2000 29 S c i e n t i f i c A c t i v i t i e s work on magic squares and elliptic curves, C. Calogero-like Systems: Physics and Mathematics; N. Greither provided a lovely account of his work Reshetikhin, Quantization of Integrable Systems; S. on generalizing the Redei-Reichardt theorem Ruijsenaars, Special Functions Associated With and M. Harper gave the first proof of a very Integrable Quantum Systems; E. Sklyanin, Bäcklund important result: Z[√14] is Euclidean. There were Transformations, Baxter's Q-Operators and also 40 contributed talks organized in 8 sessions Separation of Variables; C.A. Tracy, Random Matrix each representing a particular theme of the Models and Integrable Systems; P. Winternitz, conference. These talks were very strong and, in Integrable Systems, Symmetries, and Lie Algebra some cases, outstanding. In particular, the talk Contractions. of K. Williams on bounding the size of the least solutions of diagonal quadratic equations and International Conference and Work- the talk of Chan on new approximations to π shop on Valuation Theory come to mind, but there were many others. The July 26 - August 11, 1999 Univ. of Saskatchewan, Saskatoon, Saskatchewan talks were all very well attended. Org.: Andrew Carson (Saskatchewan), Murray Marshall Andrew Granville, a former Ph.D. student of P. (Saskatchewan), Franz-Viktor Kuhlmann (Saskatchewan), Deirdre Haskell (College of the Holy Cross), Salma Ribenboim from 1984-87, received the first Kuhlmann (Saskatchewan), Hans Schoutens (Wesleyan Ribenboim medal. He also presented the Univ.). Ribenboim Lecture. This was an account of his Co-sponsors : Fields Institute and PIms joint work with Soundararajan on how large or This conference is dedicated to Paulo small character sums can be, both conjecturally Ribenboim, in recognition of his extensive and unconditionally, and how their values are contributions to the subject. Tutorials were given distributed in the complex plane. on July 26 and 27. The conference was held from July 28 through August 4. A special session in Séminaire de mathématiques supé- honor of Paulo Ribenboim was held on July 31, rieures: Integrable Systems: From while the informal workshop was held from Classical to Quantum August 5 through August 11. July 26 - August 6, 1999, Université de Montréal, Montréal Org. : A. Daigneault (Montréal), J. Harnad (Concordia and The intent of the conference was to cover recent CRM), P. Winternitz (Montréal and CRM), S. Lessard developments in valuation theory and its (Montréal), W. Miller (Minnesota-Minneapolis), A. applications: algebraic geometry (especially local Polychronakos (Ioannina, Greece and Uppsala, Sweden), and G. Sabidussi (Montréal) uniformization), real algebraic geometry (and quadratic forms), Galois theory, rigid analysis The topic of the 1999 SMS was quantum and curves over valuation rings, model theory of integrable systems, with special emphasis on the valued fields (especially in positive passage from classical to quantum integrability, characteristic), o-minimal expansions of the reals as well as the relation to exactly solvable models (and Hardy fields), ultrametric spaces and in statistical mechanics. Although this area has spherically complete fields, p-adic numbers, seen much progress in recent years, there have non-commutative valuation theory. been few occasions where young researchers are given a systematic overview that would permit The main topics of the Workshop were: Local them to enter the field. This was one of the main uniformization and resolution of singularities, objectives of this activity. Other than the main model theory of valued fields in positive speakers, there were 40 participants. characteristic and its connections with resolution of singularities, the theory of valued function Loop The main lectures were given by J. Harnad, fields, approximate roots and related subjects, o- Groups, R-Matrices, and Separation of Variables ; J. minimal expansions of the reals and Hardy Hitchin Systems, Spectral Curves, and Hurtubise, fields. In addition to these subjects, the Surfaces A Riemann-Hilbert Approach in the ; A. Its, workshop offered an opportunity to discuss Exactly Solvable Quantum Field and Statistical other recent developments and open problems Physics Models Determinant ; V. Korepin, which are connected to the scientific programme Representations for Quantum Correlation Functions of the conference. for Exactly Solvable Models; W. Miller, Multiseparability and Superintegrability for Classical The list of invited speakers included: Shreeram and Quantum Systems; T. Miwa, Algebraic Analysis Abhyankar (Purdue), Francois Loeser (Paris), of Solvable Lattice Models; A. Polychronakis, Carlos Andradas (Madrid), James Madden

30 Annual Report 1999-2000 CRM S c i e n t i f i c A c t i v i t i e s

(Baton Rouge), Ron Brown (Hawaii), Jan Minac The Future of Mathematical (Western Ontario), Alexandru Buium (Urbana), Communication Freddy van Oystayen (Antwerpen), Gilles December 1 - 5, 1999, MSRI, Berkeley, California Org. : François Bergeron (UQAM), Jonathan Borwein Christol (Paris), Olivier Piltant (Paris), Vincent (Simon Fraser), Joe Buhler (MSRI, Berkeley), Bradd Hart Cossart (Versailles), Florian Pop (Bonn), Michel (Fields), Martin Groetschel (IMU), Peter Michor (EMS), Coste (Rennes), Patrick Popescu-Pampu (Paris), and Andrew Odlyzko. Tom Craven (Hawaii), Victoria Powers (Emory), This workshop explored the probable evolution Dale Cutkosky (Missouri), Ana Reguera of mathematical communication in coming years (Valladolid), Nikolai Dubrovin (Vladimir), Paulo and follows a similar workshop held five years Ribenboim (Kingston), Yuri Ershov earlier, also at MSRI. The conference had several (Novosibirsk), Peter Roquette (Heidelberg), Jose disparate associated events, including a half-day Engler (Campinas), Mohamed Saidi (Bonn), training workshop on the use of streaming Joachim Graeter (Potsdam), Thomas Scanlon video, a one-day workshop on electronic (Berkeley), Urs Hartl (Ulm), Claus Scheiderer publishing in the sciences aimed at attracting a (Regensburg/Duisburg), Roland Huber broader audience, and a session of talks and (Wuppertal), Erwin Schoerner (Munich), Sudesh discussion sponsored by the IMU's Committee Khanduja (Chandigarh), Niels Schwartz on Electronic Information and Communication. (Passau), Hagen Knaf (Heidelberg), John Among the major issues covered by the Shackell (Canterbury), Jochen Koenigsmann workshop, we note preprint servers, journals, (Konstanz), Patrick Speissegger (Toronto), books, intellectual property, protocols and Leung Ka Hin (Singapore), Michel Vaquie languages for scientific communication, (Paris), Quing Liu (Bordeaux), Adrian metadata and search mechanisms, multi-media Wadsworth (San Diego). and interactive tools.

First Canada-China Math Congress Canadian Mathematical Society Winter August 23 - 28, 1999, Tsinghua University, China Meeting 1999: Org. : N. Ghoussoub (PIMS), K.C. Chang (Chinese Math Society), L. Peng (Beijing), D. Cai (Tsinghua), X.-W. Zhou Special Sessions on Algebraic and (Nankai), S. Halperin (MITACS), D. Dawson (Fields), R. Geometric Methods in Differential Kane (Canadian Math Society), and L. Vinet (CRM) Equations and Algebraic Combinatorics, This was the first joint mathematical congress Group Representations, and Macdonald with China. Organized jointly by the three Polynomials mathematical institutes, it provided an December 11 – 13, 1999, Montréal important opportunity to establish future Org.: Michel Delfour (Montréal) Local org.: Véronique Hussin (Montréal) scientific projects with Chinese mathematicians. It was an unqualified success with more than The Département de mathématiques et de sixty Canadian participants. statistique of Université de Montréal was the host of the CMS Winter Meeting 1999. The First Meeting of Chairs of Winter Meeting and the First CMS Job Fair Mathematics/Statistics Departments in attracted a record number of 439 registered Canada participants. CRM sponsored two symposia. November 20 - 21, 1999, CRM The first, entitled Algebraic and Geometric th This activity brought together 25 Chairs of Methods in Differential Equations: The 20 Mathematics/Statistics Departments from Century in Celestial Mechanics and one Century th Canada, as well as six representatives from the of Work on Hilbert's 16 Problem, was mathematical institutes, MITACS, the ISM, and organized by Angelo Mingarelli (Carleton) and the CMS, to discuss common problems. Among Christiane Rousseau (Montréal). The themes of the items of the agenda that were discussed, the session cover major developments in the th were the recruitment of students at all levels, mathematics of the 20 century. It brought links with the mathematical institutes, data and together people using algebraic, geometric, resources, and outreach to schools. The meeting algebro-geometric and bifurcation methods in was such a success that a new meeting is being differential equations (mostly ordinary planned for 2000. differential equations, but also differential delay equations) in the spirit of Poincaré's work. The

CRM Annual Report 1999-2000 31 S c i e n t i f i c A c t i v i t i e s invited speakers were Kenneth Meyer problèmes informatiques tels ceux qui sont (Cincinnati), Florin Diacu (Victoria), Dan Offin posés par la spécification et la dérivation de (Queen's) Tadashi Tokieda (UQAM), J. Chalmers programmes, la production de démonstrateurs (Carleton), Ernesto Perez-Chavela (UNAM – de théorèmes, la conception de bases de Mexico), Philip Holmes (Princeton), John données, la tolérance aux fautes et le codage de Guckenheimer (Cornell), Sue Campbell l'information. Malgré sa base axiomatique (Waterloo), Jacques Bélair (Montréal), Freddy simple, l'algèbre des relations a montré qu'elle Dumortier (Limburgs Universitair Centrum – peut être appliquée à une grande variété de Diepenbeek, Belgium), Yulij Il'yashenko structures d'information. (Moscou and Cornell), Sergey Yakovenko Le but de ce séminaire et de toute la série (Weizmann Institute, Israel), Jean-Pierre RelMiCS est de regrouper des chercheurs venant Françoise (Paris VI), Dana Schlomiuk (Montréal), de différentes sous-disciplines des mathé- Robert Roussarie (Bourgogne, France), matiques et de l'informatique, qui utilisent le Christiane Rousseau (Montréal), and Pietro- calcul des relations comme outil conceptuel et Luciano Buono (Warwick, United Kingdom). méthodologique dans leur travail. Nous The second symposium was called Algebraic cherchons à mieux comprendre les problèmes Combinatorics, Group Representations, and informatiques tels que la spécification et la Macdonald Polynomials. It was organized by conception de programmes, la vérification du François Bergeron (UQAM), Nantel Bergeron logiciel et du matériel, la décomposition des (York), and Mike Zabrocki (UQAM and CRM). bases de données relationnelles, etc. À travers un The invited speakers were Adriano Garsia (UC outil commun, plusieurs domaines de l'informa- San Diego), François Bergeron (UQAM), Victor tique sont touchés. Les articles présentés dans Ginzburg (Chicago), Siddhartha Sahi (Rutgers), ces séminaires contribuent à la fois au Ed Allen (Wake Forest), Carol Chang développement de la théorie et des applications. (Northeastern), Mark Haiman (UC San Diego), Des comptes rendus des présentations ont été Mike Zabrocki (UQAM), Jean-Christophe Aval publiés. Les principales conférences invitées (Bordeaux I), Alain Lascoux (Marne La Vallée), étaient Security by Typing de Mourad Debbabi Jennifer Morse (UC San Diego), Tudose Geanina (Laval), Certification of Compiler Optimizations (York), and Luc Vinet (McGill). using Kleene Algebra with Tests de Dexetr Kozen

th (Cornell) et A Retrospective View on RelMiCS and 5 International Seminar on Relational some Promising Directions de Gunther Schmidt Methods in Computer Science (Universität des Bundeswehr München). January 9 - 14, 2000, Valcartier, Québec Org. : Jules Desharnais (Laval), Marc Frappier (Sherbrooke), and Wendy MacCaull (St.Francis Xavier) Workshop CRM - MITACS - IRIS Data Mining and Machine Learning : Depuis le milieu des années 70, il est devenu Selecting and Combining Models with clair que le calcul des relations est un outil Machine Learning Algorithms conceptuel fondamental en informatique tout April 11 -14, 2000 autant qu'en logique. Alors que les applications Org.: Yoshua Bengio (Montréal) and Dale Schuurmans informatiques évoluent rapidement, la nécessité (Waterloo) de faire appel aux sciences exactes pour The workshop was held April 11-14, 2000, at the comprendre les méthodes existantes se fait CRM. Its objective was to bring together experts sentir. Il est de plus en plus approprié d'utiliser and neophytes, senior researchers, students and les approches formelles pour faire face à la practitioners in the field of model selection and complexité de l'information, des algorithmes et model combination for machine learning des designs. En effet, on considère maintenant algorithms. que les approches formelles sont nécessaires au A central objective of machine learning research développement futur de plusieurs zones de is to develop algorithms that learn predictive l'informatique, comme par exemple la relationships from data. This is a central spécification et la vérification des systèmes component of data mining and knowledge distribués. Parmi les approches formelles, on discovery tasks, which are becoming retrouve celles qui sont basées sur l'algèbre des commonplace applications in the realm of e- relations. Celle-ci a été utilisée pour l'analyse, la commerce. This is a difficult task, however, modélisation et la résolution de plusieurs

32 Annual Report 1999-2000 CRM S c i e n t i f i c A c t i v i t i e s because inferring a predictive function from data Minimization, Support Vector Machines, various is in fact an "ill-posed" problem; that is, many Boosting algorithms, and the Bagging algorithm. functions can often "fit" a given finite data set, These new approaches suggest that better and yet these functions might generalize very generalization performance can be obtained differently on new data drawn from the same using new, broadly applicable procedures. distribution. Progress in this area has not only been important for improving our understanding of how More than 130 participants (from 4 continents) machine learning algorithms generalize; it has have contributed to make this workshop a already been demonstrated to be very useful for success and a noted international event. The practical applications of machine learning and workshop started with a tutorial on data-mining data analysis. by Hugh Chipman on the 11th. In the following three days, leaders in the field, along with The workshop brought together several key promising graduate students, presented some researchers in the fields of machine learning and thought-provoking contributions, some of which statistics to present their recent results and sparked animated arguments in the audience. debate the controversial issues that have been Although most of the presentations were dividing them in recent machine learning and focused on algorithms and mathematical neural network conferences. analyses, several speakers presented important The list of invited speakers includes Peter applications (e.g. in handwriting recognition and Bartlett (Australia National Univ.), Leo Breiman in bio-informatics). The speakers contributed (Berkeley), Huch Chipman (Waterloo), Tom papers or slides, in electronic form, and these Dietterich (Oregon State Univ.), Yoav Freund have been posted on the workshop web page (AT&T Labs-Research), Christian Léger (www.iro.umontreal.ca/~bengioy/crmworkshop2000) (Montréal), Michael Perrone (IBM T.J. Watson Furthermore, the organizers are putting together Research Center), Robert Schapire (AT&T Labs- a special issue of the Machine Learning Journal Research), Dale Schuurmans (Waterloo), Peter (on model selection and model combination) in Sollich (King's College, Univ. of London), and which the best papers of the workshop will be Grace Wahba (Wisconsin at Madison). published. But what is model selection? To make the Special Functions 2000 : learning problem well-posed, one needs to Current Perspective and Future somehow "calibrate" the complexity of the Directions proposed function class to the amount and May 29–June 9, 2000, Arizona State University, Tempe, Arizona quality of available sample data. A classical Org. : Sergei Suslov (Arizona State), Vyacheslav approach is to perform "model selection" where Spiridonov (Joint Institute for Nuclear Research, Dubna, one imposes a preference structure over function Russia), Tom Koornwinder (Amsterdam), and Luc Vinet (CRM) classes and then optimizes a combined objective of class preference and data fit. In doing so, Special function theory and its applications is however, it would be useful to have an accurate currently enjoying enormous interest, due in estimate of the expected generalization part to meetings organized in the last few years performance at each preference level; one could by the Canadian mathematical institutes. The then pick the function class that obtained the topics of the workshop included orthogonal lowest expected error, or combine functions polynomials and special functions in one and from the functions classes with the lowest several variables, asymptotics, continued expected error, and so on. Many approaches fractions, applications to number theory, have been proposed in the past for this purpose, combinatorics and mathematical physics, both in the statistics and the machine learning integrable systems, harmonic analysis and research communities. quantum groups, Painlevé classification. Among the Canadian participants, M. Rahman Recently in machine learning there has been (Carleton) and L. Vinet (CRM) were lecturers. significant interest in new techniques for This workshop was part of the NATO Science evaluating generalization error, for optimizing Programme. generalization error, and for combining and selecting models. This is exemplified, for example, by recent work on Structural Risk

CRM Annual Report 1999-2000 33 S c i e n t i f i c A c t i v i t i e s

CRM Prizes CRM/Fields Prizes André-Aisenstadt Prize In 1994 the Centre de recherches Created in 1991, the André-Aisenstadt mathématiques (CRM) and the Fields Institute Mathematics Prize is intended to recognize and announced the creation of a new prize to be reward talented young Canadian awarded for exceptional contributions to the mathematicians. The Prize, which is given for mathematical sciences. The recipient of the prize is chosen by the Comité consultatif of the research achievement in pure and applied CRM and the Scientific Advisory Committee mathematics, consists of a $3000 award. The of the Fields Institute according to the criterion recipient is chosen by the CRM Advisory of excellence in research. The prize consists of Committee. At the time of nomination, both a $5 000 award and a medal, and the candidates must be Canadian citizens or winner is required to give a lecture at the CRM permanent residents of Canada, and no more and the Fields Institute. The past recipients are: than seven years from their Ph.D. The previous H.S.M. Coxeter, G.A. Elliot, J. Arthur, R.V. winners of the André-Aisenstadt Prize were: Moody, and Stephen A. Cook. Niky Kamran (1991); Ian Putnam (1992); The CRM-Fields Michael Ward and Nigel Higson (1994); Adrian Institute 2000 Prize is S. Lewis (1995); Henri Darmon and Lisa Jeffrey awarded to Israel (1996); Boris Khesin (1997); John Toth (1998). Michael Sigal. One of CRM was delighted to the outstanding award the André- mathematical Aisenstadt Prize to physicists active in Professor Changgeng Canada today, Gui of the University Professor Israel of British Columbia Michael Sigal was and the University of born in Russia. He obtained his bachelor’s Connecticut. Dr. Gui degree at Gorky University in 1968 and his Ph.D. completed his at Tel-Aviv University (1976). He is currently undergraduate Professor at the University of Toronto. studies at the University of Beijing and obtained Apart from being a worldwide leader in his area his Ph.D. at the University of Minnesota in 1991. of quantum theory, he is the leading expert on From 1993 to 1995, he was a Postdoctoral Fellow the analysis of the Schroedinger equation, which at McMaster University and became Assistant is at the heart of mathematical models of atoms Professor at the University of British Columbia and molecules. He also made groundbreaking in 1997. His main research interests are in contributions to the theory of interaction qualitative properties of solutions to non-linear between light and matter, known as Quantum partial differential equations, such as existence, Electrodynamics. He has been rewarded with multiplicities, symmetry, and stability. many honors. He is a Fellow of the Royal Society When Professor Gui came to receive his prize, he of Canada and received, in 1993, the John L. gave a lecture entitled Some Mathematical Synge Award for being an outstanding Problems Related to Phase Transitions. Gradient Canadian mathematician. These honours include theory of phase transitions has been studied several invited lectures at the International extensively in the last thirty years, particularly in Congress of Mathematical Physics and the connection with minimal surfaces and motions, International Congress of Mathematics, and by mean curvature. In this talk, he discussed editorships of the following journals: Reviews in some progress in answering some fundamental Mathematical Physics and the Duke questions related to this theory, including Mathematical Journal. He received his prize on solutions to the Gibbons conjecture and the De November 10, 1999 in Montréal. Giorgi conjecture. These conjectures concern the basic configurations of states near plane interfaces.

34 Annual Report 1999-2000 CRM S c i e n t i f i c A c t i v i t i e s

CRM-CAP Prize background field. He discovered an important Awarded for the first time in 1995, the CRM- extra-local gauge symmetry in the Kazakov- CAP Prize is given for outstanding Migdal model which is a lattice gauge theory of contributions to theoretical and mathematical induced quantum chromo-dynamics. Finally he physics. It consists of a $2000 award and a obtained an exact solution of a variety of matrix medal. Previous winners were Werner Israel of models that resemble Coulomb gas models of the University of Alberta (1995), William G. quarks. Unruh of the University of British Columbia (1996), Ian Affleck of the University of British CRM-SSC Prize Columbia (1997), J. Richard Bond of CITA of In 1999, the Centre de recherches the University of Toronto (1998), and David mathématiques (CRM) and the Statistical J. Rowe of the University of Toronto (1999). Society of Canada created the CRM-SSC Prize The 2000 CRM-CAP prize has been awarded to in statistics in recognition of outstanding Dr. Gordon Semenoff. contributions to the Statistical Sciences during Dr. Semenoff attended the recipient’s first 15 years after earning a the University of doctorate. The CRM-SSC Prize in Statistics Alberta where he consists of a $3000 award and a medal. The received his B.Sc. with recipient is chosen by a joint CRM/SSC first class honors in advisory committee, consisting of three Physics in 1976 and a members named by the SSC and two, Ph.D. in theoretical including a president, by the CRM. In 1999, the physics in 1981. After Prize went to Christian Genest of Université a Postdoctoral Laval. Fellowship at MIT, he This year, the Centre joined the faculty of the University of British de recherches Columbia where he has been Professor of mathématiques and Physics since. He was a member of the Institute the Statistical Society for Advanced Study in Princeton in the years of Canada have 1985 and 2000 and a visiting professor at the awarded the CRM- Niels Bohr Institute in Copenhagen in 1999. Dr. SSC 2000 Prize in Semenoff has received a number of honors Statistics to Dr. including a Killam Research Prize (1989), the Robert Tibshirani of MacDowell Medal for Achievement in Physics Stanford University. (1991), and the National Bank of Denmark Rob Tibshirani grew up in the Niagara Falls Award (1999). area. He completed his Bachelor's degree in Dr. Semenoff is a theoretical physicist who has statistics and computer science at the University made contributions to quantum field theory, of Waterloo in 1979 and a Master's degree in statistical mechanics and string theory. He is Statistics at the University of Toronto in 1980. He best known for his the first use of index obtained his Ph.D. in 1984 from Stanford theorems to compute the quantum numbers of University. He then joined the Department of topological solitons in field theory. He published Biostatistics and Preventive Medicine and the this work in 1982 and 1983, and an authoritative Department of Statistics of the University of review of the subject in 1984. Toronto in 1985. In 1998, he accepted a joint position in the Department of Health Research Dr. Semenoff is also an authority on quantum and Policy and the Department of Statistics at field theory in unusual environments such as Stanford University. He has received numerous high temperature and density. He has made awards, including the COPSS award given to the many subsequent contributions to theoretical best statistician under 40 years of age in the and mathematical physics and he has done well world (1996), the E.W.R. Steacie Memorial known work in the field-theoretical realization Fellowship of NSERC (1997), as well as a of particles with exotic spin and statistics called fellowship of the J. Guggenheim Foundation anyons. He also obtained one of the first (1994). He is a fellow of the American Statistical solutions of the unitary matrix model in a

CRM Annual Report 1999-2000 35 S c i e n t i f i c A c t i v i t i e s

Association and of the Institute of Mathematical Professor Tibshirani is a world leader in the Statistics. He has served as Associate Editor of development of computer-intensive statistical the Annals of Statistics, Statistical Science, Journal modeling and analysis for applications in of the American Statistical Association, and of the genetics, medicine and public health. One of his Canadian Journal of Statistics. He gives numerous papers which has had a large impact was conferences and has supervised many Ph.D. published in the New England Journal of Medicine students. He is particularly well known for his and studied the risks of car accidents when books on generalized additive models and on using a cellular phone. the bootstrap.

36 Annual Report 1999-2000 CRM S c i e n t i f i c A c t i v i t i e s

Members’ Seminars & Special Events

The members of the CRM are encouraged to organize seminars and other scientific activities during their stay at the CRM. These activities take the form of courses, workshops and research seminars

Seminar of the Physnum Group June 17, 1999 January 13, 2000 André Boivin, Univ. of Western Ontario Cécile Amblard, CRM Théorème(s) de Muntz dans C Résolution de problèmes inverses mal posés par la July 8, 1999 méthode du maximum d’entropie sur la moyenne Edouardo Santillan Zeron, CRM February 10, 2000 Low Dimensional Singularities and Polynomial Alin Andrei Carsteanu, INRS-EAU Convexity Statistique bivariées dans les cascades multiplicatives July 15, 1999 et génératrices de mesures multifractales Paul Gauthier, CRM & Univ. de Montréal Transformations quasirégulières et régulières Special Lectures July 29, 1999 June 8, 1999 Marc Thiriet, INRIA Yacine Rebahi Modèles numériqiues en mécaniques des fluides. Irrégularité des D-modules algébriques holonomes Illustration à l’aide de quelques exemples October 1, 1999 Thomas Ransford, Univ. Laval April 14, 2000 Théorème de Bloch pour les multifonctions Adi Ben-Israel, Rutgers Univ. The Matrix Volume and its Applications in Analysis algébroides January 14, 2000 Seminar in Non-linear Analysis Mohamad Pouryayevali, Univ. de Montréal Org.: Andrej Granas (CRM & Univ. de Montréal) Injective Holomorphic Mappings November 22, 1999 January 28, 2000 Alberto Abbondandolo, Scuola Normale di Pisa Lev Abramovich Aizenberg, Univ. Bar-Ilan Morse Theory for Strongly Indefinite Functionals Duality in Complex Analysis November 23, 1999 February 4, 2000 Alberto Abbondandolo, Scuola Normale di Pisa Petr Paramonov, Univ. de Moskva Applications to Hamiltonian Systems Uniform Approximation of and by Gravitational Fields November 29, 1999 Andrej Granas, CRM & Univ. de Montréal February 18, 2000 Extension of Compact Homotopies and the Leray- Wolhfard Hansen, Univ. Bielefeld Schauder Principle Harnack Inequalities for Schrödinger Operators November 30, 1999 February 25, 2000 Donald O’Regan, National Univ. of Ireland Richard Fournier, CRM Multiplicity Results in Fixed Point Theory and Un principe de continuation analytique hyperbolique Applications March 10, 2000 Richard Fournier, CRM Analysis Seminar CRM-ISM Un principe de continuation analytique hyperbolique Org.: Paul Gauthier (CRM & Univ. de Montréal) II June 3, 1999 March 17, 2000 Richard Duncan, Univ. de Montréal Alexandre Erëmenko, Purdue Univ. Théorème ergodique et groupes unitaires Meromorphic Functions, Negative Curvature and June 10, 1999 Spherical Geometry Galia Dafni, Concordia Univ. March 24, 2000 H1 and CMOs Fabian Todor Intération des polynômes complexes et l’équation fractale avec applications

CRM Annual Report 1999-2000 37 S c i e n t i f i c A c t i v i t i e s

April 28, 2000 Theta Functions, Isomonodromic Deformations and André Boivin, Univ. of Western Ontario Applications, V Sur les séries de Fourier non-harmoniques March 2, 2000 May 12, 2000 Dmitri Korotkin, CRM & Concordia Univ. Sebastien Manka, Univ. de Montréal Theta Functions, Isomonodromic Deformations and Le problème de Dirichlet dans le demi-plan Applications, VI May 19, 2000 Pierre-Olivier Rathé, Univ. de Montréal The Langlands Geometric Programme Le problème de Dirichlet dans le disque Org.: Jacques Hurtubise (McGill) January 13, 2000 Study Workshop: Inverse Monodromy Eyal Z. Goren, CRM & McGill Univ. Problems Vector Bundles Org.: John Harnad (Concordia) January 27, 2000 November 4, 1999 Eyal Z. Goren, CRM & McGill Univ. Yousuke Ohyama, CRM & Osaka Univ. Moduli of Vector Bundles Special Solutions of Schlesinger Equations February 10, 2000 November 18, 1999 Jacques Hurtubise, CRM & McGill Univ. John McKay, CRM & Concordia Univ. Hitchin's Integrable Systems on the Moduli of Stable Moonshine - What it is about Pairs November 25, 1999 March 9, 2000 Marco Bertola, CRM Jacques Hurtubise, CRM & McGill Univ. Frobenius Manifolds I: Introduction Quantification des systèmes de Hitchin December 2, 1999 March 28, 2000 Yousuke Ohyama, CRM & Osaka Univ. Henri Darmon, CRM & McGill Univ. Special Solutions of Schlesinger Equations (Part II) Correspondance Fonctions-faisceaux December 9, 1999 April 20, 2000 Yousuke Ohyama, CRM & Osaka Univ. Edward Frenkel, Univ. of California Special Solutions of Schlesinger Equations (Part III) Introduction to the Geometric Langlands Programme December 16, 1999 Marco Bertola, CRM Seminar in Mathematical Physics Frobenius Structures on Hurwitz Spaces of Org.: Jiri Patera & Pavel Winternitz (CRM & Univ. Functions de Montréal) January 20, 2000 September 21, 1999 Dmitri Korotkin, CRM & Concordia Univ. Hubert de Guise, CRM Theta Functions, Isomonodromic Deformations and Des représentations indécomposables de dimension Applications I finie du groupe E(2) January 27, 2000 September 28, 1999 Dmitri Korotkin, CRM & Concordia Univ. Louis-Sébastien Guimond, CRM Theta Functions, Isomonodromic Deformations and Les quasicrystaux utilisés pour éliminer la Applications II périodicité des générateurs de nombres pseudo- aléatoires February 3, 2000 Dmitri Korotkin, CRM & Concordia Univ. October 19, 1999 Theta Functions, Isomonodromic Deformations and Pierre Valin, CRM & Lockheed Martin Canada Applications III DND / LM Canada / University Collaborations Developing Technologies for Airbone Mission February 10, 2000 Management Systems Dmitri Korotkin, CRM & Concordia Univ. Theta Functions, Isomonodromic Deformations and October 26, 1999 Applications IV Marco Bertola, CRM Jacobi Groups, Jacobi Forms and their Applications March 2, 2000 Dmitri Korotkin, CRM & Concordia Univ.

38 Annual Report 1999-2000 CRM S c i e n t i f i c A c t i v i t i e s

November 9, 1999 CRM Statistics Seminar Faruk Güngör , Istantul Technical Univ. Org.: Christian Léger (CRM & Univ. de Montréal) Symmetries and Solutions of the Generalized June 17, 1999 Boussinesq Equation Ian McLeod, Univ. of Western Ontario Louis Michel, Institut des hautes études Time Series Forecasting with Feed-Forward Neural scientifiques (IHES) Nets La symétrie d’un crystal impose la connexité de September 16, 1999 l’ensemble des branches d’une bande d’énergie Gilles Ducharme, Univ. Montpellier II & Univ. élémentaire de Montréal November 23, 1999 1900-2000, cent ans de tests d’adéquation Alexei Zhedanov, Donetsk Institute for Physics September 23, 1999 and Technology, Ukraine David Tyler, Univ. Rutgers Orthogonal Polynomials and Krall-Sheffer Duality On the Uniqueness of the Multivariate S-functionals November 30, 1999 and M-functionals under Non-Elliptical Stéphane Lafortune, CRM Distributions Point Symmetries of Generalized Toda Field Theories September 30, 1999 December 7, 1999 Jean-Michel Zakoian, CREST, Paris & Univ. de Jean-Pierre Gazeau, Univ. Paris 7 Lille 1 États cohérents pour le puit infini de potentiel Least-Squares and Autocorrelation Based Estimators December 14, 1999 of Weak ARMA Model Decio Levi, Univ. di Roma Tre October 14, 1999 Lie Algebras, Contractions and Symmetries of the Jack Kalbfleisch, Univ. of Waterloo, President of Toda Hierarchy the Statistical Society of Canada December 21, 1999 Methods for Response-Selective and Missing Data Yuriy Korenyak , Kharkiv Univ., Ukraine Problems A new Point of View to the Modeling of Fields on October 25, 1999 Surfaces Roger Lafosse, Univ. Paul-Sabatier January 11, 2000 Proposition de SVD généralisée : application en Jamil Daboul, Ben Gurion Univ. sélection de variables et reconnaissance de structure Kac-Moody Algebras and the Hydrogen Atom January 27, 2000 January 18, 2000 Christian Léger, CRM & Univ. de Montréal Igor Loutsenko, CRM & Princeton Univ. Intervalles de confiance basés sur le rééchantillonnage Soliton Solutions of Integrable Hierarchies and après la sélection de modèle en régression linéaire Coulomb Plasma multiple January 25, 2000 February 3, 2000 Richard L. Hall, CRM & Concordia Univ. Jean-François Angers, CRM & Univ. de Montréal Geometric Spectral Inversion Identificateur d’une densité et les valeurs aberrantes February 4, 2000 February 17, 2000 Jan Derezinsk, Univ. of Warsaw François Bellavance, HEC Hypergeometric Type Functions and Lie Algebras Méta-analyse d’une variable dépendante multinomiale à l’aide de modèles linéaires à effets February 8, 2000 fixes et mixtes Oleg I. Bogoyavlenskÿ, CRM & Queen’s Univ. Exact Global Plasma Equilibria February 24, 2000 M'hamed Mesfioui, Univ. Laval February 15, 2000 Nouvelles classes d'ordres stochastiques bivariés, avec George Pogosyan, Joint Institute for Nuclear applications en actuariat et épidémie Research, Dubna, Russia Superintegrability on Spaces wth Constant March 9, 2000 Curvature Denis Larocque, Univ. du Québec à Trois- Rivières Un test du signe multidimensionnel affine-invariant pour données corrélées en grappes

CRM Annual Report 1999-2000 39 S c i e n t i f i c A c t i v i t i e s

March 16, 2000 Partial Regression and Correlation Curves François Perron, CRM & Univ. de Montréal April 13, 2000 Sur l'échantillonnage selon l'algorithme acceptation- Peter Mueller, Univ. Duke rejet en simulation Hierarchical Meta-Analysis over Related Non- April 6, 2000 parametric Models Kjell Doksum, Univ. of California, Berkeley

40 Annual Report 1999-2000 CRM S c i e n t i f i c A c t i v i t i e s

CRM-ISM Colloquium The CRM, together with the Institut des sciences mathématiques (the Québec university graduate mathematics consortium), runs the Montréal mathematics colloquium, which, during the university year, organises survey talks by distinguished mathematicians on topics of current interest.

Autumn 1999 Winter 2000 September 17 ,1999 January 14, 2000 Nicole Tomczak-Jaegermann, Univ. of Alberta Andrew Majda, Courant Institute The Mathematics of Closure for Turbulent Reaction Geometry, Linear Structure and Random Phenomena in Finite-dimensional Normed Spaces Diffusion Equations September 24, 1999 January 21, 2000 Troy Day, Univ. of Toronto Lou Van den Dries, Univ. of Illinois at Urbana- Champaign A Generalization of Pontryagin's Maximum Principle for Modeling Dynamic Evolutionary Games Between Logarithmic-Exponential Series Relatives October 8, 1999 Victor Kac, MIT January 28, 2000 Mark Goresky, Institute for Advanced Study (IAS) Classification of Infinite-Dimensional Groups of Supersymmetries and the Standard Model Shift Registers, Finite Fields, and Elliptic Curves October 15, 1999 February 4, 2000 Niky Kamran, McGill Univ. Pierre Cartier, École Normale Supérieure Le comportement étrange des solutions classiques de l' Algèbre et combinatoire des graphes (d'Euler à Feynman) opérateur de Dirac au voisinage d'un trou noir February 11, 2000 October 22, 1999 Olga Kharlampovich, McGill Univ. Algebraic Geometry over Groups and the Tarski's Problem Christian Genest, Univ. Laval Modéliser la dépendance et mesurer ses effets en tthéorie du February 18, 2000 risque Victor Havin, St. Petersburg State Univ. On Some Non-Local Shift Invariant Operators October 29, 1999 Richard P. Stanley, MIT March 10, 2000 The Volume and Ehrhart Polynomial of Convex Polytopes Jeffrey S. Rosenthal, Univ. of Toronto November 5, 1999 Markov Chain Convergence Times and Pseudo-Small Sets Laurent Lafforgue, CNRS, Univ. d’Orsay March 24, 2000 La correspondance de Langlands sur les courbes Terry Gannon, Univ. of Alberta November 12, 1999 The Classification of Conformal Field Theories Peter Kronheimer, Harvard Univ. March 31, 2000 Gauge Theory and Topology Jean-Paul Allouche, Univ. Paris-Sud, Centre d’Orsay November 25, 1999 Transcendance de nombre réels trop « réguliers » Harry Kesten, Cornell Univ. April 7, 2000 Percolation of Arbitrary Words in {0,1}N Steven Boyer, UQAM Linear Representations of the Fundamental Groups of 3- December 3, 1999 Alain Lascoux, Univ. Paris 7 manifolds Les polynômes harmoniques April 14, 2000 Helmut Koch, Humboldt-Univ. of Berlin Cubic Number Fields April 19, 2000 Klauss Fleischmann, Weierstrass Institute for Applied and Stochastics, Bertin (Germany) Catalytic, Mutually Catalytic, and Cyclically Catalytic Branching April 28, 2000 Joel Feldman, Univ. of British Columbia Fermi Surfaces and Infinite Genus Riemann Surfaces

CRM Annual Report 1999-2000 41 World Mathematical Year

Sponsored by the International Mathematical Union and UNESCO, the year 2000 was declared the World Mathematical Year. On this occasion, many special activities were held all year long throughout the country. Many of them were organized by CRM members.

Mathematical Posters Operation Subway 2000 Stéphane Durand, a CRM member, was awarded One of the activities of the World Mathematical first prize in the international poster contest Year was a series of exhibits of mathematical organized by the European Mathematical posters in the subways of the world's biggest Society. His entry consisted of a series of seven cities. In January 2000, Montréal's subway was posters on the links between mathematics and the first to display these mathematical posters. nature. These posters have been used and The campaign was organized by Christiane adapted in many countries in different ways Rousseau, a CRM member. (posters in the subway, postcards, CD-ROM, etc.): Public Lectures • Montréal (posters in the subway) Les Belles Soirées of the Université de Montréal • France (posters and postcards) consist of lectures for a wide audience on a • Denmark (postcards) variety of topics. To mark the World • Belgium and Holland (posters) Mathematical Year, three lectures on • Italy (Archimède journal) mathematics were given in October 2000. The • UK and Portugal (CD-M) lecturers were Adrien Douady of Paris-Sud XI • Germany (CD-ROM) University at Orsay (La dimension fractale) and Three of the posters were printed in Québec. Stéphane Durand of CRM (Structure universelle... Besides their use in Montréal's subway, they vraiment? Les mathématiques dans la nature: du have also been widely circulated in the schools. and léopard au tournesol...).

What do a Why do snail and the sunflower number seeds show a √ (1+ 5)/2 pattern of 34 have in clockwise curves common? and 21 counterclockwise curves?

Why do buttercups have 5 petals? Why do pineapples have 8 The number (1+√5)/2 is the golden mean which is found in diagonals in one direction and 13 in the other? Why do daisies many parts of nature. The spiral shell of the nautilus is an generally have 34, 55, or 89 petals? All these numbers are part example of a geometric construction based on this number. of the Fibonacci sequence (1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,…) Even Stradivarius used it when constructing his famous related to the golden mean, and where each number is violins. obtained by adding the two previous ones. Only recently have we understood why these numbers are important in nature.

42 Annual Report 1999-2000 CRM W o r l d M a t h e m a t i c a l Y e a r

Mathematical Insert Exhibition To show the general public the importance and An exhibition called 1, 2, 3 Math. was prepared the presence of mathematics in modern life, jointly by the Museum of the séminaire de CRM has prepared a popular document on the Sherbrooke, the Association mathématique du mathematical sciences in Québec. Entitled Québec, and Université de Montréal. It was Math2000, it was published in the magazine inaugurated in May 2000 and since then has Québec Science in May 2000. This document was travelled in Québec and the rest of Canada. This edited by Stéphane Durand in collaboration with animated and interactive travelling exhibition is Québec Science and 40,000 copies were printed. intended for the general public and school- The document has also been widely distributed children. Some CRM members participated in its in schools, colleges, and university departments development, including Stéphane Durand, Jean- of mathematics education. Marc Lina, and Christiane Rousseau. When it came to the Exhibit Centre of Université de Montréal from October 3rd through November 10th 2000, guided tours were offered to schoolchildren. They were led by students from the Department of Mathematics and Statistics.

Mega-Congress of Year 2000 Mathematics educators, from grade school to university, met during a mega-congress sponsored by the Ministry of Education of the Province of Québec. It was held last May at the Université Laval. Seven associations dedicated to the promotion of mathematics in Québec hosted this meeting.

Television Programmes Hosted by Jean-Marie De Koninck of Université Laval, the television series, C'est mathématique, of 16 half-hour programmes was produced by Productions Téléfiction and shown on Canal Z during Winter 2000. The following CRM members participated: Jacques Bélair, Stéphane Durand, Jean-Marc Lina, Christiane Rousseau, and Yvan Saint-Aubin. Following its release, the Another document, entitled Mathématiques An series was bought by many schools. A sequel is 2000, was prepared jointly by the Institut des being planned. sciences mathématiques and by the Association mathématique du Québec. Giving a brief survey of Radio shows research in mathematics, it was distributed with Interface, the magazine of the Association As part of the radio programme Les nourritures canadienne-française pour l'avancement des sciences terrestres of the French CBC Radio 2, a half-hour (ACFAS). interview with Stéphane Durand on mathematics was broadcast on October 26, 2000. A paper called Décoder la nature was also published in the magazine Quatre-temps of the Montréal Botanical Garden (vol 24, no 4, december 2000).

CRM Annual Report 1999-2000 43 Coming Events

Theme Year 2000-2001: Mathematical Methods in Biology and Medicine Organizing Committee International Annual Meetings Jacques Bélair (Montréal) Combinatorial Pattern Matching (CPM Leon Glass (McGill) 2000) Brian Golding (McMaster) June 21 – 23, 2000 Org. : Raffaele Giancarlo (Univ. of Palermo), David Leah Keshet (UBC) Sankoff (Montréal) David Sankoff (Montréal) Invited speakers : A. Broder (Altavista), F. Major (Montréal), Keith Worsley (McGill) F. Pereira (AT&T Labs), I. Witten (Waikato, New Zealand). This meeting has a major computational biology Overview component and includes fields which share a The year 2000-2001 at the CRM will be devoted common focus on the formulation, algorithmic to the rapidly developing field of mathematical recognition, analysis, communication, and methods in biology and medicine. The storage of patterns in diverse kinds of data. application of mathematics contributes to the understanding of natural processes both through 5th Annual International Conference on mathematical models and their analysis, and Computational Molecular Biology through the development and application of (RECOMB 01) mathematical methods of inference. The year April 22 – 25, 2001 emphasizes both aspects, with workshops Org. : David Sankoff (Montréal) covering various applications of nonlinear The premier annual meeting in computational dynamics in biology and medicine, as well as molecular biology, featuring a highly genomics, and medical imaging. competitive selection of the best research papers th from cutting edge projects whose subjects are 10 CRM Summer School: Nonlinear computational and mathematical in nature. Dynamics in Biology and Medecine May 22 - June 2, 2000 Org. : Jacques Bélair (Montréal) Workshop on Novel Approaches in RNA Instructors : L. Glass (McGill), M. Guevara (McGill), A. Informatics (NARI) Longtin (Ottawa), M. C. Mackey (McGill), J. Milton May 18 – 19, 2000 (Chicago), A. Vinet (Montréal), J. Bélair (Montréal). Org. : François Major (Montréal) Invited speakers : C. Duarte (Columbia), E. Rivas Offered jointly with the “Centre for Nonlinear (Washington), B. Shapiro (NCI), M. Venkantraman (Isis Dynamics in Physiology and Medicine”, this is Pharmaceuticals Inc.), C. Wilson (UCSC), M. Zuker an intensive introduction to the applications of (Washington). nonlinear dynamics to biology and medicine, The goal of this symposium is to explore the with computer exercises and an introduction to current state of the art in RNA informatics and numerical techniques. to look towards the future of the field. The NARI symposium will provide a general forum for Aisenstadt Chair Lecture Series disseminating the latest developments, and will • Vortices in Motionless Media bring together scientists from biochemistry, Arthur T. Winfree (Arizona) molecular biology, computer science, September 2000 mathematics, and statistics who will present an • Mathematics for Reading and Understanding overview of novel approaches. Genetic Sequences Michael S. Waterman (USC) March 2001

44 Annual Report 1999-2000 CRM C o m i n g E v e n t s

Workshop on Bioinformatics plant, other eukaryote, prokaryote, organellar, May 17, 2000 and viral genomes. Org. : Nadia El-Mabrouk (Montréal) Invited speakers: I. Barrette (Montréal), G. Butler (Concordia), G. Drouin (Ottawa), N. El-Mabrouk (Montréal), Workshop on Nonlinear Dynamics and D. Forsdyke (Queen's), A. Kusalik (Saskatoon), M. Li Biomathematics (Waterloo), A. Nip (Montréal), G. Poisson (Montréal), P. October 3 – 6, 2000 Rouzé (Ghent), D. Sankoff (Montréal). Org.: Pierre Auger (Lyon), Jacques Bélair (Montréal), Jacques Demongeot (Grenoble), Christiane Rousseau A workshop on problem areas in bioinformatics (Montréal) was held, as part of the annual meeting of the Invited speakers: O. Arino (Pau), P. Auger (Lyon), J. Bélair Association canadienne-française pour (Montréal), H. Benali (CHU Pitié Salpêtrière), A. Bourdou l'avancement des sciences (ACFAS). (INSERM), R. Bravo de la Parra (Alacala), S.A. Campbell (Waterloo), C. Chevalet (Toulouse), F. Clarke (Lyon), J.-L. Coatrieux (Rennes I), M. Courtemanche (Montréal), J. Workshop on Molecular, Metabolic, Demongeot (Grenoble), L. Glass (McGill), A. Goldbeter (UL Bruxelles), B. Goulard (Montréal), J.-M. Lina (Montréal), S. and Gene Control Networks Lessard (Montréal), A. Longtin (Ottawa), N. Raissi September 9 – 13, 2000 (Morocco), D. Salahub (Institut Steacie), P. Tracqui Org. : Michael C. Mackey (McGill) (Grenoble), B. A. Vinet (Hôpital du Sacré-Coeur), G. Invited speakers: D. Bray (Cambridge), G. Church (Harvard), Wolkowicz (McMaster). J. Collins (Boston), J. Ferrell (Stanford), L. Glass (McGill), A. Goldbeter (UL Bruxelles), H. Herzel (Berlin), K. Kohn (NIH), The state of the art in the application of R. Larter (Purdue), J. Mahaffy (San Diego State), J. Paulsson techniques from nonlinear dynamics to diverse (Uppsala), J. Ross (Stanford), M. Roussel (Lethbridge), M. fields of biology (biochemistry, physiology, Santillan (Mexico City), P. Smolen (Houston), R. Somogyi (Incyte), D. Thieffry (ULB), J. Tyson (Virginia). resources management, medical imaging) will be covered. This workshop is part of the Entretiens Recently in this field modeling has been done of du Centre Jacques-Cartier. regulation of progression through the cell cycle as mediated by check points, control in the Workshop on Memory, Delays, and lactose and tryptophan operons, and the Multistability integrated behaviour of large coupled October 12 – 15, 2000 molecular/metabolic/gene networks. This Org. : André Longtin (Ottawa) workshop brings together both experimentalists Invited speakers: K. Aihara (Tokyo), T. Aonishi (RIKEN, and modelers to examine the current state of the Japon), S. Becker (McMaster), J. Bélair (Montréal), F. Buarque de Lima Neto (Imperial College), J.-L. Cabrera (Chicago), field and the exciting future prospects. S.A. Campbell (Waterloo), C. Canavier (New Orleans), G. Carpenter (Boston), M. Chacron (Ottawa), G. Deco (Siemens), Workshop on Gene Order Dynamics, A. Destexhe (Laval), M. Ding (Florida Atlantic), B. Doiron (Ottawa), R. Engbert (Postdam), U. Ernst (Bremen), J. Freund Comparative Mapping and Multigene (Humboldt), W. Gerster (Lausanne), L. Glass (McGill), S. Families (DCAF) Guillouzic (Ottawa), R. Hahnloser (MIT), S.K. Han September 22 – 25, 2000, Ste-Adèle (Chungbuk Nat. Univ.), A. Herz (Humboldt-Bremen), E. Org. : David Sankoff (Montréal), Joseph H. Nadeau (Case Izhikevich (Neurosciences Inst.), J. Jeong (Yale), R. Kuske Western Reserve University) (Minnesota), C. Laing (Pittsburgh), J. Lewis (Ottawa), W. Mass (Tech. U. Graz), M. Menzinger (Toronto), J. Milton Invited speakers: S. Anderson (Uppsala), V. Barriel (Paris) & (Chicago), K. Pakdaman (INSERM), A. Potapov (Lethbridge), C. Gallut (Paris), B. Bed'Hom (Paris), J. Boore (Michigan), P. M. Titcombe (UQAM), R. Wackerbauer (West Virginia), H. Bork (Heidelberg), D. Bryant (Montpellier), A. Caprara Wilson (York), J. Wu (York). (Bologna) & G. Lancia (Padua), O. Cohen (Grenoble), J. Demongeot (Joseph Fourier de Grenoble), K. Devos (UK), J. This workshop will focus on important current Dicks (Norwich Research Park), E. Eichler (Case Western Reserve), N. El-Mabrouk (Montréal), A. Hughes (South issues in the modeling of neural activity in Carolina), B. Koop (Victoria), F. Lang (Montréal), D. Liben- recurrent circuitry, such as recurrent activity Nowell (Cornell), L.A. Lyons (NIH), B. McAllister (Texas), thought to lie at the core of sensory information S.R. McCouch (Cornell), A. McLysaght (Dublin), J. Meidanis (Sao Paolo), I. Parkin (Saskatoon Research Centre), A. processing. The emphasis will be on the Paterson (Georgia), P.A. Pevzner (USC), D. Schoen (McGill), mathematical issues which arise in the modeling R. Shamir & I. Pe'er (Tel Aviv), B. Trask (Seattle), M. Turmel of such activity in real biological systems. (Laval), D. Waddington (UK), T. Warnow (Austin), J. Womack (Texas A&M). This meeting will bring together scholars in the biological and mathematical sciences working on genome rearrangement, mapping, and the evolution of gene families in human, animal,

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Workshop on Mapping and Control of geometry, topology, statistics, and random Complex Arrhythmia fields. This workshop is intended to bring October 29– November 1, 2000 together mathematicians and statisticians Org. : Leon Glass (McGill) interested in brain mapping, and medical Invited speakers: J. Beaumont (SUNY Syracuse), A. Beuter (UQAM), D. Christini (New York), J. Collins (Boston), F. researchers interested in mathematical and Fenton (Northeastern), A. Garfinkel (Los Angeles), D. statistical methods for the analysis of brain Gauthier (Duke), M. Guevara (McGill), V. Hakim mapping data. (Laboratoire de physique statistique), H. Hastings (Hofstra), R. Ideker (Alabama), A. Karma (Boston), V. Krinsky (Nice), J. Leon (Montréal), S. Nattel (Montréal), A. Panfilov (Holland), Workshop on Population Genetics at G. Rousseau (Paris 7), Y. Rudy (Cleveland), A. Shrier the Molecular Level (McGill), K. Stein (NY Presbyterian Hospital), N. Trayanova (New Orleans), A. Vinet (Montréal). March 8 – 11, 2001 Org. : Brian Golding (McMaster) This workshop will bring together Invited speakers : M. Gouy (Lyon), J. Huelsenbeck mathematicians, experimentalists, physicians, (Rochester), S. Kumar (Arizona State), S. Muse (NCSU), R. Nielsen (Cornell), B. Rannala (Stony Brook), A. Rzhetsky and industrial representatives to present papers (Columbia), D. Schoen (McGill), J. Thorne (NCSU), Z. Yang and discuss approaches to mapping and control (U.C.London). of complex arrhythmias. There will be a strong The genes and alleles of classical genetics are focus on novel interdisciplinary approaches to abstract notions. Now that these are increasingly control atrial fibrillation. understood in terms of particular sequences of DNA and protein, the mathematical foundations Workshop on Fractal and Modeling in of the field must be revisited and expanded, Structural and Dynamical Analysis which is the object of this workshop. November 11 – 14, 2000 Org. : Jacques Bélair (Montréal), Fahima Nekka (Montréal) Invited speakers: A. Arnéodo (C.N.R.S.), Y. Ashkenazy Workshop on Mathematical (Boston), D.R. Bickel (Texas), Q. Cheng (York), S. Dubuc Formalisms for RNA Structure (Montréal), A. Einstein (Mt. Sinaï), A. Khalil (Laval), A.P. April 25 – 26, 2001 Kirilyuk (Institute of Metal Physics, Kiev), H. Kitaoka Org. : François Major (Montréal) (Osaka), L.S. Liebovitch (Florida Atlantic), S. Lovejoy (McGill), S. Lubkin (North Carolina), B. Sapoval Invited speakers: R. Altman (Stanford), J. Brown (NCSU), J. (Polytechnique), C. Tricot (Clermont-Ferrand), M.J. Turner Burke (Vermont), D. Case (Scripps), D. Gautheret (CNRS- Marseille), S. Harvey (Alabama), P. Legault (Georgia), J.-P. (De Montfort). Perreault (Sherbrooke), E. Westhof (CNRS-Strasbourg), M. Classical problems in material sciences (surface Zuker (St. Louis). characterization, description of branching This symposium will explore the current state of networks) have been given new impetus by the the art in computational RNA structures, and introduction of fractal concepts. This workshop provide a look towards the future of the field. will cover the latest theoretical developments, their contributions in the biomedical field and Courses and Seminars future directions of investigations. Combinatorial Pattern Matching June 19 – 20, 2000 Workshop on Mathematical Methods Org. : David Sankoff (Montréal) in Brain Mapping Invited speakers: D. Bryant (Montpellier), N. El-Mabrouk (Montréal), R. Giancarlo (Palermo), C. Lam (Concordia), L. December 10 – 11, 2000 Parida (IBM T.J. Watson Research Center), I. Witten Org. : Keith Worsley (McGill) (Waikato, New Zealand). Invited speakers: J. Ashburner (Inst. of Neurology Funct. Imaging Lab.), J. Aston (London), E. Brown (Harvard), M. Preceding CPM2000, this is a two-day tutorial on Chung (McGill), A. Dale (Harvard), K. Friston (Inst. of sequence analysis and other topics in Neurology Funct. Imaging Lab.), G. Glover (Stanford), N. V. Hartvig (Aarhus), M. Hurdal (Florida Atlantic), S. Kiebel computational biology and pattern matching. (Inst. of Neurology Funct. Imaging Lab.), J.-F. Mangin (Service Hospitalier Frédéric Joliot, Orsay), T. Ozaki (Tokyo), Developing the Tools: A Canadian J.-B. Poline (CEA), J. Polzehl (Weierstrass Inst.), J. Riera Bioinformatics Workshop (Cuban Neuroscience Center), S. Smith (Oxford), J. Taylor (McGill), P. Valdes (Cuban Neuroscience Center). June 26– July 1, 2000 Org. : Christopher Hogue (Toronto), François Major Brain mapping is a rapidly growing research (Montréal) field that tries to understand human brain One of a series of training workshops directed function and anatomy using 3D images from by the Canadian Genetic Diseases Network and MRI, fMRI, PET, EEG and MEG and applying the Biotechnology Human Resources Council.

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Visitors Techniques in Brain Mapping Support is available for short- and long-term December 5 - 8, 2000 visits. Preference will be given to junior Org. : Keith Worsley (McGill), Bernard Goulard (Montréal) investigators. Invited speakers: R. Adler (TECHNION), N. Lange (Harvard), P. Valdes (Cuban Neuroscience Center). Those wishing to participate in the above activities are invited to write to: In preparation for the workshop on brain mapping, four series of introductory lectures Louis Pelletier will be given, covering the geometry of random Centre de recherches mathématiques (CRM) field, methods in functional magnetic resonance E-mail: [email protected] imaging and methods for EEG analysis. World Wide Web: http://www.CRM.UMontreal.CA/biomath Fractals and Wavelets in Medical Imaging February 23 – 24, 2001 Org. : Jean-Marc Lina (Montréal), Fahima Nekka (Montréal) Invited speakers: M. Unser (Swiss Federal Institute of Technology, Lausanne) Preceding the workshop, this tutorial will introduce the subject to non-specialists.

Showcase for Competing Technologies for Phylogenetics (SCOPH) April 19 – 21, 2001 Org.: David Bryant (Montréal), David Sankoff (Montréal) Invited speakers: D. Bryant (Montréal), A. Dress (Bielefeld), J. Felsenstein (Seattle), O. Gascuel (Montpellier), T. Hagedorn (College of New Jersey), J. Huelsenbeck (Rochester), K. Nixon (Cornell), D. Sankoff (Montréal), M. Steel (Canterbury), D. Swofford (Cornell), T. Warnow (Texas, Austin) This seminar is aimed at researchers, teachers and students interested in current developments in phylogenetic analysis. The speakers will each address one or two major areas and there will be ample time for comparison, debate, and discussion. Some of the themes will be: efficient methods for very large phylogenies, model- based versus model-free approaches, tree inference with and without ancestor reconstruction, generalizations of trees. Software packages will be available on-line and there will be facilities for demonstrations and hands-on experimentation.

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General Programme 2000-2001

Canadian Journal of Statistics Read methods have recently come to the fore in the Paper Session area. These new developments provide ample June 4, 2000, Ottawa, Ontario motivation for organizing a mini-programme in Org. : Christian Genest (Laval) this area of research. During the Annual Meeting of the Statistical The aim is to get specialists together from these Society of Canada, a major scientific contribution different fields and have them talk. Plenty of will be read and discussed publicly. The paper is time will be reserved for discussion, and the The Estimating Function Bootstrap of John D. whole event will last three weeks, starting with a Kalbfleisch (Waterloo) and Heifang Hu week of mini-courses, and followed by an (Singapore). The paper will be discussed by Jim extended two week workshop-working session. Zidek (British Columbia), Tom Diccicio (Cornell) and Rob Tibshirani (Stanford), Christian Léger There will be four mini-courses aimed at (Montréal), and Angelo Canty (Concordia). This graduate students and potential researchers: • Asymptotic series and differential event, inspired by a similar activity of the Royal Bolibruch equations. Statistical Society of the United Kingdom, is a • Differential Algebraic Geometry and first for the Canadian Journal of Statistics. Buium, Diophantine Geometry. • Québec Math Camp 2000 L. Van den Dries, Logarithmic-Exponential June 2000, Université du Québec à Trois-Rivières, Trois- Series and o-Minimality. Rivières • V.Y. Kaloshin, Finiteness Theorems in Dyna- Org. : Harry White (Université du Québec à Trois-Rivières) mical Systems. Le camp mathématique est une activité A workshop built around four themes : parrainée par l'Association mathématique du • Algebras of quasi-analytic terms, Québec (AMQ) dans le but de mettre en contact Weierstrass-type preparation theorems and des étudiants doués pour les mathématiques finiteness results with applications to global avec des mathématiciens professionnels. Les problems in analytic vector fields, campeurs sont sélectionnés parmi ceux qui ont le • Finiteness theorems in non-linear dynamical mieux réussi au concours de l'AMQ (niveau systems, collégial). • Ecalle's theory and applications, • Model theory - finiteness theorems in Mini-programme: Asymptotic series, -o-minimality. differential algebra and finiteness There will also be several colloquium style problems in non-linear dynamical lectures. systems June 19 - July 7, 2000 Org. : Dana Schlomiuk (Montréal) , Luc Bélair (UQAM) Séminaire de mathématiques supéri- eures: Approximation, Complex Invited participants : A. Buium (New Mexico), A. Bolibrukh (Steklov Institute), L. Van den Dries (Illinois), F. Dumortier Analysis, and Potential Theory (Limburgs Universitair Centrum), J.P. Françoise (Paris VI), Y. July 3 - 14 , 2000, Université de Montréal, Montréal Ilyashenko (Steklov Institute), V. Kaloshin (Princeton), J. Org. : A. Daigneault (Montréal), N. Arakelian (Armenian Llibre (Universitat Autonoma de Barcelona), C. Miller (Ohio National Academy of Sciences), P. Gauthier (Montréal), D. State), R. Moosa (Illinois at Urbana-Champaign), A. Armitage (Queen's University of Belfast), D. Drasin Mourtada (Bourgogne), J.-P. Rolin (Bourgogne), C. Rousseau (Purdue), A. Gonchar (Steklov), S. Lessard (Montréal), G. (Montréal), P. Speissegger (Wisconsin, Madison), S. Sabidussi (Montréal) Yakovenko (Wiezmann Institute of Science), H. Zhu (Waterloo). The 2000 SMS will focus on the interplay between complex analysis and potential theory. While the relationship between asymptotic Complex analysis relies heavily on potential analysis and differential algebra has long been theory, since the absolute value (as well as the useful in linear differential equations, the merger logarithm) of a holomorphic function is a of tools and the opening of a wider scope of subharmonic function. In the other direction, investigations in both the areas of non-linear much research in potential theory has been dynamics and differential algebraic geometry is inspired by the attempt to seek analogues to more recent. In particular, model theoretical complex phenomena. This is especially true in

48 Annual Report 1999-2000 CRM C o m i n g E v e n t s approximation theory, a central theme of this Colloque LACIM 2000 SMS. September 7 – 10, 2000, UQAM, Montréal Org.: Pierre Leroux (UQAM), Robert Bédard (UQAM), The main lectures will be given by A. Ancona Srecko Brlek (UQAM) , Manon Blais (UQAM). (Paris-Sud), Topics on Martin Boundaries, Positive Co-sponsors: Université du Québec à Montréal (UQAM), le Harmonic Functions and Green's Functions; N. Ministère de la Recherche, de la Science et de la Arakelian (Armenian National Academy of Technologie (Québec). Sciences), Approximation and Value Distribution; Invited speakers: Jean Berstel (Marne-la-Vallée), Richard Ehrenborg (KTH), Nadia El-Mabrouk (Montréal), Dominique D. Armitage (Queen's University of Belfast), Foata (Strasbourg), Adriano Garsia (UCSD), Pierre Lalonde, Uniform and Tangential Harmonic Approximation; Christophe Reutenauer (Strasbourg), Richard Stanley T. Bagby (Indiana), Sobolev Spaces and (Massacchusetts Institute of Technology), Xavier Viennot (LaBRI, Bordeaux I), Doron Zeilberger (Temple). Approximation Problems for Differential Operators; M. Bonk (Michigan), Negative Curvature in Real L'année 2000, année mondiale des and Complex Analysis; H. Chen (Nanjing Normal mathématiques sous l'égide de l'UNESCO, University, China) The Bloch Constant for One and marque, parmi tant d'autres anniversaires, les Several Variables, Holomorphic and Harmonic dix ans du Laboratoire de combinatoire et Mappings; D. Drasin (Purdue), Approximation d'informatique mathématique de l'UQAM. Les Theorem, Normal Families, and Meromorphic disciplines couvertes par le LaCIM ont connu Functions; S. Gardiner (University College, des développements remarquables au cours des Dublin), Harmonic Approximation and its dix dernières années, que ce soit sur le plan Applications; P. Gauthier (Montréal), théorique, en combinatoire énumérative ou Approximation on Riemann Surfaces and Complex algébrique, ou au niveau des applications, en Manifolds; T. Ransford (Laval), Jensen Measures; analyse classique, en calcul formel, en géométrie and A. Stray (Bergen), Simultaneous algorithmique, en chimie combinatoire, en Approximation in Various Function Spaces. physique statistique, et, plus récemment, en bio- informatique. Fête en l'honneur de Walter Hengartner Le but du colloque est de faire le point sur «Hengartnerfest» quelques-uns de ces développements en July 7 – 8, 2000 réunissant des experts internationaux de ces Org. : Richard Fournier (CRM), Paul Gauthier (Montréal) , Thomas Ransford (Laval) domaines. Nous souhaitons également donner la chance aux chercheurs jeunes ou plus Cette conférence vise à honorer la carrière du expérimentés de faire connaître leurs résultats professeur Walter Hengartner à l'occasion de sa récents. Le programme comprend dix retraite de l'Université Laval. Les conférences conférences plénières ainsi que des porteront sur divers sujets de la théorie des communications sélectionnées par le comité fonctions reliés à ses travaux, notamment sur scientifique. Afin de favoriser une plus grande l'analyse complexe. La fête aura lieu durant le interaction, ces communications sont regroupées Séminaire de Mathématiques Supérieures dont à l'intérieur d'une séance d'affichage. Un numéro le sujet est Approximation, analyse complexe et spécial de la revue Discrete Mathematics sera théorie du potentiel. Les conférenciers invités sont consacré aux actes du Colloque sous la direction Daoud Bshouty (Technion-Israel), Ted Suffridge de Gilbert Labelle et Pierre Leroux. (Kentucky), Peter Duren (Michigan), Walter Hayman (Imperial College), Line Baribeau (Laval), Tom Bagby (Indiana) et Paul Gauthier (Montréal).

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XIIth Meeting on the Representation A Series of Conferences by Professor Theory of Algebras Alexei Miasnikov September 29 – 30, 2000, Bishop’s University, Lennoxville March 2 – 30, 2001, McGill Univ. , Montréal Org. : Ibrahim Assem (Sherbrooke), Andrew Dean Org. : O. Kharlampovich (McGill) (Bishop’s), François Huard (Bishop’s), Pierre-Yves Leduc (Sherbrooke), Shiping Liu (Sherbrooke) This is a series of lectures on equations over free groups and free semigroups. In theoretical This is the 12th of a series of annual meetings computer science, this topic is known as the held each autumn, alternately at the Université unification problem. Professor Miasnikov will de Sherbrooke and at Bishop's University. These discuss recent developments in this area related meetings are devoted to the Representation to algebraic geometry over groups, Tarski's Theory of Associative Algebras, an area of problems, and complexity of the unification mathematics which is presently very well problem. Lectures will be given every Friday in developed, and connected to many other areas March. (such as, for instance, commutative algebra, algebraic geometry, algebraic topology, Symplectic and Contact Topology, singularity theory and Lie theory). Quantum Cohomology, Symplectic This year's programme includes invited talks of Field Theory and Higher-Dimensional 45-50 minutes given by Luchevar Avramov Gauge Theory (Purdue), Vlastimil Dlab (Carleton), Alex March 26 - April 7, 2001, Fields Institute, Toronto, Ontario, Martsinkovsky (Northeastern), Cristian Novoa & CRM (Catholic University of Goias, Brazil), Claus Org. : S. Donaldson (London), B. Dubrovin (Trieste), Y. Eliashberg (Stanford), A. Givental (Berkeley), B. Khesin Michael Ringel (Bielefeld), Shaobin Tan (Fields), (Toronto), F. Lalonde (Montréal) Dan Zacharia (Syracuse), and Rita Zuazua This two-week workshop will bring together (National Autonomous University of Mexico). researchers from symplectic topology, algebraic Conférence «Adrien Douady» geometry, and mathematical physicists working in gauge theory and quantum field theory. Its October 20 – 21, 2000 Org. : Dana Schlomiuk (Montréal), Norbert Schlomiuk main goal is to discuss recent developments in (Montréal). the construction and computation of invariants Invited speakers: Bodil Branner (Tecnical Univ. of of symplectic and contact manifolds and their Denmark), Welington de Melo (IMPA - Rio de Janeiro), automorphism groups, using methods of the Adrien Douady (Orsay - Paris), Raphael Douady (E.N.S. theory of J-holomorphic curves, as well as those Paris), John Hubbard (Univ. de Marseille), Mikhael Lyubich from gauge theory and dynamical Hamiltonian (SUNY - Stony Brook), Curtis McMullen (Harvard Univ.), systems. The theory of these invariants is tightly John Milnor (SUNY - Stony Brook), Raghavan Narasimhan related to enumerative algebraic geometry, (Univ. of Chicago), Mitsuhiro Shishikura (Hiroshima Univ.). quantum cohomology and mirror symmetry. Recent results, of both mathematicians and A conference to celebrate the 65 years of Adrien physicists, show the existence of surprising Douady and to highlight his numerous correspondences between various gauge theories important contributions to mathematics, most on real and complex manifolds. notably to dynamical systems and to analytic geometry. The first week, to be held at the Fields Institute in Toronto, will emphasize relations of the theory of holomorphic curves with field theories, mirror symmetries, as well as (higher dimensional) gauge theories. The second week at the CRM in Montréal will concentrate more on the geometric, analytic and dynamical aspects of symplectic topology.

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Theme Year 2001-2002: Groups and Geometry

Organizing Committee Workshop on Groups and 3-manifolds A. Broer (Montréal), S. Boyer (UQAM), June 25 – 29, 2001 J. Carrell (UBC), W. Casselman (UBC), This workshop will focus on recent progress on H. Darmon (McGill), I. Hambleton (McMaster), various open topological and geometric J. Hurtubise (CRM), N. Kamran (McGill), classification problems as well as some of the B. Khesin (Toronto), F. Knop (Rutgers), newer research directions. There will be four 50 R. Lee (Yale), D. Wise (Brandeis and McGill). minute talks per day, leaving plenty of time for informal discussions amongst the participants. Overview They include: M. Boileau (Université Paul Sabatier), D. The role of group actions and groups in general Calegari (Harvard), A. Casson (Yale), D. Cooper (California is ubiquitous in geometry, and the year's at Santa Barbara), M. Culler (Illinois at Chicago), D. Gabai, (California Institute of Technology), C. McA. Gordon (Texas programme will concentrate on some areas in at Austin), S. Kerchoff (Stanford), M. Lackenby (Oxford), D. which there has been important recent progress. Long (California at Santa Barbara), J. Luecke (Texas at Austin), Y. Moriah (Technion), J. Porti (Barcelona), A. Reid The year consists of two segments, the first more (Texas at Austin), H. Rubinstein (Melbourne), P. Shalen differential-geometric in flavour, and the other (Illinois at Chicago), Y.-Q. Wu (Iowa), X. Zhang (State one concentrating specifically on the links University of New York at Buffalo). between algebraic geometry, group theory, and representation theory. Mini-courses July 2 – 6, 2001 Groups, Topology and Differential Michel Boileau (Paul Sabatier) Geometry Geometrization of 3-dimensional orbifolds June - December 2001 Martin Bridson (Oxford) Groups and Low-Dimensional Topology Non-positively Curved Spaces and Hyperbolic June - July 2001 Groups Org. : Steven Boyer (UQAM), Dani Wise (Brandeis & McGill) Ruth Charney (Ohio State) The Geometry of Coxeter and Artin Groups Throughout the 20th century there has been a remarkably fruitful interplay between group Benson Farb (Chicago) theory and the geometry and topology of low- A Crash Course on the Geometry of Groups dimensional manifolds. The study of 3- Peter Shalen (Univ. of Illinois at Chicago) manifolds through their fundamental groups Representations of 3-manifold Groups and symmetries has turned out to be a particularly rich vein with applications to such Workshop on Geometric Group Theory topics as the tabulation of knots, geometrization July 9 – 13, 2001 problems, group actions, and surgery theory. The theory of infinite groups was revolutionized Conversely, results of 3-dimensional topology by an infusion of ideas from geometry and have been fundamental in motivating many topology. This has led to the resolution of many exciting developments in geometric group old problems and the formulation of new theory: actions on R-trees, word-hyperbolic problems and methods which have broadened groups, decomposition theorems, the scope of the field. This workshop will focus quasiconvexity, coherence, etc. Our goal is to on these new developments in geometric group bring together students and researchers from theory. There will be four 50 minute talks per these active research areas over a three week day, leaving plenty of time for informal period in order to underline and foster the discussions amongst the participants. connections between them.

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They include: W. Ballmann (Bonn), M. Bestvina (Utah), B. Bowditch (Southampton), M. Bridson (Oxford), R. Charney structures on the manifolds, such as a volume (Ohio State), B. Farb (Chicago), M. Feighn (Rutgers), I. form, a foliation, a contact structure or a Kapovich (University of Illinois at Urbana-Champaign), M. symplectic structure. The study of these infinite- Kapovich (Utah), O. Kharlampovich (McGill), J. McCammond (Texas A & M), A. Myasnikov (CCNY), P. dimensional Lie groups becomes a fundamental Papazoglou (Paris-Sud), M. Sapir (Vanderbilt), M. Sageev problem in areas of mathematics as diverse as (Technion) , Z. Sela (Hebrew University). hydrodynamics and symplectic topology. Another wide class of infinite-dimensional Lie Topology of Manifolds and Group groups is formed by loop groups, Kac-Moody Actions groups, and more generally, by gauge groups on August 20 – 24, 2001 manifolds of arbitrary dimension. The successes Org. : Ian Hambleton (McMaster), Ronnie Lee (Yale) in the study of these groups have been Recently there have been important immensely fruitful both in low-dimensional breakthroughs in the study of the topology of geometry and topology and in quantum field manifolds and related topics on group actions, theory. Infinite-dimensional Lie groups are also especially in the area of 3-and 4-dimensional fundamental in the theory of integrable systems manifolds with new input from the Seiberg- and their hierarchies. In this context, their action Witten theory and symplectic topology. One of becomes quite explicit on spaces of pseudo- the main objects of this workshop is to describe differential and Fourier integral operators. The these new advances on the subject. purpose of this mini-programme will be to In addition, there also have been important review some of the significant recent developments in other areas. For example, there developments in the above areas and to explore are the study of discrete group actions on some of the important open problems. Euclidean space using controlled surgery theory, • Introductory Lectures the generalization of Casson invariants from A.A. Kirillov (Pennsylvania) SU(2) to SU(3), the study of Torelli group actions October 29– November 1, 2001 on the cohomology of moduli spaces, the • Workshop on the Geometry of Infinite- classification of topological group actions on 4- Dimensional Lie Groups manifolds, just to name a few. Not concentrated November 2 – 6, 2001 completely on 4-dimensions, our programme Participants will include: P. Deift (Pennsylvania), P. Etingof will also present these topics for the case of high- (MIT), V. Fock (ITEP), V. Guillemin (MIT), L. Jeffrey dimensional manifolds and related subjects. In (Toronto), M. Kapranov (Toronto), A.A. Kirillov fact, it is the design of the conference to bring (Pennsylvania) , F. Lalonde (Montréal), J. Leslie (Howard), P. Michor (Vienna), E. Meinrenken (Toronto), P. Olver about formal and informal discussion between (Minnesota), H. Omori (Tokyo), V. Ovsienko (CNRS- different perspectives, to compare questions, Luminy), T. Ratiu (EPFL Lausanne), T. Robart (Howard), P. methods and applications. Slodowy (Hamburg), I. Zakharevich (Ohio State). The list of participants includes: R. Cohen (Stanford), S. Cappell (Courant Institute), J. Davis Groups and Algebraic Geometry (Indiana), A. Edmonds (Indiana), T. Farrell (SUNY at January - June 2002 Binghamton), P. Feehan (Max-Planck-Institute für Mathematik, Bonn), R. Fintushel (Michigan State) K. The importance of algebraic geometry in Froyshov (Harvard), R. Gompf (Texas at Austin), C. Herald representation theory, has grown enormously (Nevada at Reno), R. Kirby (UC Berkeley), T. Leness (Florida during the past decades, with the arrival of such International), T. Li (Princeton), M. Marcolli (Max-Planck- Institut für Mathematik, Bonn), M. McCooey (McMaster), E. techniques as D-modules and perverse sheaves. Miller (Polytechnic University of New York), J. Morgan Geometry intervenes in a crucial fashion in the (Columbia), L. Nicolaescu (Notre Dame), P. Ozsvath (Michigan State), E. Pedersen (SUNY at Binghamton), F. proof of such results as the Kazhdan-Lusztig Quinn (Virginia Polytech Inst & State University), D. conjecture, the construction of canonical bases Ruberman (Brandeis), R. Schultz (UCR), D. Wilczynski (Utah for representations, and the work of Beilinson- State University at Logan), B. Williams (Notre Dame). Drinfeld on the Geometric Langlands programme. A number of deep connections have Infinite-Dimensional Lie Groups arisen between the algebraic geometry and October - November 2001 Org. : Niky Kamran (McGill), Boris Khesin (Toronto) algebraic combinatorics, whose ramifications extend all the way to mathematical physics and From a differential-geometric point-of-view, topology. A special emphasis of the programme infinite-dimensional Lie groups arise as will be in graduate training, and a variety of automorphism groups of various geometric short courses will be organized, as well as

52 Annual Report 1999-2000 CRM C o m i n g E v e n t s graduate courses of a more introductory nature. Invariant Theory Funding is available for graduate students April 8 – 19, 2002, Queen's University, Kingston, Ontario wishing to attend. Org. : D. Wehlau (Queen’s), E. Campbell (Queen’s) The first week will be devoted to introductory Aisenstadt Chairs lectures aimed at graduate students by There will be three series of lectures delivered Professors P. Fleischmann (Kent), H. Kraft under the auspices of the Aisenstadt chair, by E. (Basel), G. W. Schwarz (Brandeis), and Harm Frenkel (Berkeley), L. Lafforgue (IHES), and G. Dersksen (MIT). The second week will be Lusztig (MIT). devoted to a workshop on Invariant Theory. The list of invited speaker includes: M. Brion*, B. Broer, C. De Concini*, L. Helminck , M. Hunziker, G. Kemper, N. Graduate courses Kechagias, F. Knop, P. Littelmann , L. Moser-Jauslin, V. January - April 2002 Popov, Y. Sanderson, R J. Shank, N. Thiery, W. van der Abram Broer (Montréal) Kallen*, E. Vinberg*. Hilbert Schemes of Points and their Applications *To be confirmed Henri Darmon (McGill) Automorphic Forms Concentration Period on the Langlands Eyal Goren (McGill) Programme for Function Fields Curves, Vector Bundles on Curves and their Moduli April - May 2002 Yvan Saint-Aubin (Montréal) Org. : H. Darmon (McGill), J. Hurtubise (CRM) Kac-Moody Algebras The last few years have seen spectacular new results in the Langlands programme over Winter School on Computations in function fields, both in characteristic zero and in Coxeter Groups characteristic p. The aim of this period is to January 21 – 28, 2002 provide an overview of some essential Org. : W. Casselman (UBC), R. Bédard (UQAM), F. du techniques in the area, as well as new results. Cloux (Lyon I) April 2002 These short courses are designed to show how Short courses for graduate students on topics techniques from computer algebra can be including the classical Hitchin systems, étale and applied to effective computation in Coxeter l-adic sheaves, as well as a survey of the number groups. The course will be held in the theoretic Langlands programme. Laurentians, outside Montréal.

Group Actions on Rational Varieties The Langlands Programme for February 27 - March 3, 2002 Function Fields Org. : P. Russell (McGill) April 30 - May 17, 2002 The workshop will focus on recent A three week extended workshop, with the first developments in automorphisms of affine spaces two weeks devoted to survey lectures for and related algebraic varieties with simple graduate students: topology, in particular exotic affine spaces Week 1: Survey lectures on preliminary material: (algebraic varieties homeomorphic to an affine stacks, chtoucas, perverse sheaves and D- space). modules, opers. Lectures by D. Ben Zvi The list of invited speakers includes: T. Asanuma (Toyama), (Chicago), D. Goss (Ohio State), A. Polischuk T. Bandman (Bar-Ilan), D. Daigle (Ottawa), A. Van den Essen (Boston), C. Sorger (Nantes), K. Vilonen (Nijmegen), G. Freudenburg (Southern Indiana), M. Gizatullin (UTFSM), R. Gurjar* (Tata), I. Dolgachev* (Northwestern). (Michigan), J. Winkelmann* (Bochum), S. Kaliman (Miami), Week 2: Aisenstadt lectures given by L. K. Masuda (Himeji), F. Knop* (Rutgers), M. Koras, H. Kraft Lafforgue (IHES) and E. Frenkel (Berkeley), (Basel), L. Makar-Limanov (Wayne State), L. Moser-Jauslin* (Bourgogne), M. Miyanishi (Osaka), P. Cassou-Nogues covering recent results in the Langlands (Bordeaux), V. Popov (MIEM), A. Sathaye (Kentucky), G. programme over function fields, in both Schwarz (Brandeis), D. Wright (Washington University), M. characteristic 0 and characteristic p. During the Zaidenberg (Grenoble), D. Zhang (Singapore). first two weeks, R. Langlands will also give a * To be confirmed series of lectures. Week 3: The concentration period is to be followed by the 2002 Canadian Number Theory Association conference.

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Computational Lie Theory Algebraic Transformation Groups May 27 - June 10, 2002 June 10 – 15, 2002 Org. : W. Casselman (UBC), F. Knop (Rutgers) Org. : A. Broer (Montréal), J. Carrell (UBC) This extended workshop is aimed at researchers The purpose of the meeting is to bring together interested in explicit computations in Lie theory, experts in Algebraic Groups, Algebraic in particular Coxeter groups. In addition to the Geometry, Representation Theory and related usual talks, there will also be several series of areas, especially those touching on: geometric survey lectures, suitable for graduate students, methods in representation theory using tools like by M. Brion (Grenoble), M. Geck (Lyon), F. Knop equivariant cohomology and perverse sheaves; (Rutgers), P. Littelmann (Wuppertal), G. the Hilbert scheme of points on a surface and its Olshanskii (*) (IITP), J. Stembridge (Michigan). connection with the n!-conjecture in algebraic Professor G. Lusztig (MIT) will be delivering combinatorics; equivariant versions of some of his Aisenstadt lectures during the cohomology and Chow groups related to flag period of the conference. manifolds and Schubert varieties; quantum Invited participants include: D. L. Alvis (Indiana), A. cohomology and Schubert calculus. Anatolievich Klyachko (Bilkent), R. Bédard (UQAM), R. The list of participants includes: A. Bertram (Utah), M. Brion Bezrukavnikov (Chicago), S. Billey (MIT), M. Brion (Joseph (Grenoble), C. De Concini (Rome), W. Fulton (Michigan), V. Fourier), I. Cherednik (North Carolina), F. du Cloux (Lyon I), Ginzburg (Chicago), M. Haiman (UCSD), M. Kapranov M. J. Dyer (Notre Dame), W. Fulton (Michigan) M. Geck (Toronto), A. Knutson (Berkeley), B. Kostant (MIT), S. Kumar (Lyon), M. Goreski (IAS), M. Haiman (California, San Diego), (North Carolina), L. Manivel (Grenoble), E. Meinrenken G. J. Heckman (Nijmegen), A. G. Helminck (North Carolina (Toronto), I. Mirkovic (Massachusetts), H. Nakajima (Kyoto), State), R.Kottwitz (Chicago), F. Knop (Rutgers), S. Kumar D. Peterson* (UBC), C. Procesi* (Rome), E. Vasserot* (Cergy- (North Carolina at Chapel Hill), P. Littelman (Bergische), R. Pontoise), C. Woodward (Rutgers). MacPherson (IAS), J. McKay (Concordia), M. Noumi (Kobe), * To be confirmed A. Okounkov (Berkeley), M. Olshanetsky (Moscow), G. Olshanski (Moscow), E. M. Opdam (Amsterdam), A. Ram (Wisconsin), Y. B. Sanderson (William Paterson) T. A. Those wishing to participate in the above Springer (Utrech), J. R. Stembridge (Michigan), B. Sturmfels (Berkeley), P. Trapa (Harvard), J. F. van Diejen (Chile), M. activities are invited to write to: van Leeuwen (Poitiers), D. A. Jr Vogan (MIT), N. R. Wallach Louis Pelletier (California, San Diego), G. Saunders Warrington (Harvard), A. Zelevinski (Northeastern). Centre de recherches mathématiques (CRM) * To be confirmed Université de Montréal C.P. 6128, Succ. Centre-ville Montréal (Québec), CANADA H3C3J7 E-mail: [email protected] World Wide Web: http://www.CRM.UMontreal.CA/geometry

54 Annual Report 1999-2000 CRM C o m i n g E v e n t s

General Programme 2001-2002

Second Canadian Journal of Statistics finance, stochastic systems, image processing, Read Paper Session solid mechanics, electrodynamics, combustion, June 2001, Simon Fraser University, Burnaby, British matrix calculation, etc. In-depth coverage of each Columbia Org. : Christian Genest (Laval), Richard Lockhart (Simon theme (including discussion of both numerical, Fraser) modelling and theoretical issues specific to each During the Annual Meeting of the Statistical application) along with hands-on computer Society of Canada, a major scientific contribution experiments will be offered at this SMS 2001. will be read and discussed publicly. The paper is The speakers will be Anne Bourlioux and Flexible Regression Modeling with Adaptive Logistic Panagiotis Souganis, Numerical Combustion : Basis Functions of Peter Hooper (Alberta). The Modelling and Computing Turbulent Flamelets; paper will be discussed by many researchers Gene H. Golub and C. Bai, Matrices, Moments, who have until May 15, 2001 to submit their and Quadratures; Gundolf Haase and Ulrich written discussion. The comments of the selected Langer, Multigrid Methods: Theory, Algorithms, discussants will be published along with the Implementation, Parallelization; Laurence Halpern paper in the September 2001 issue of the One-way Operators, Absorbing Boundary Canadian Journal of Statistics and presented orally Conditions, and Domain Decomposition for during this session. Evolution Operators; Anthony Humphries and Andrew Stuart, Computational Aspects of Eighth Canadian Undergraduate Deterministic and Random Dynamical Systems; Mathematics Conference Karol Mikula and James A. Sethian, Level-set and June 12 – 17, 2001, Université Laval, Québec Diffusion Methods in Image Processing; Frédéric Org. : Pier-André Bouchard St-Amant (Laval), Jean- Nataf, Optimized Domain Decomposition Methods; Philippe Boulet (Laval), Sylvain Hallé (Laval), Jean- François Plante (Laval) George Papanicolaou, Asymptotic Analysis of Stochastic Differential Equations and Applications; This annual conference is aimed at Canadian and Ronnie Sircar, Stochastic Volatility Modelling. undergraduate students whose programme of study involves mathematics. The participants are Statistics 2001 Canada: The Fourth encouraged to present a 20 or 50 minute talk on Canadian Conference in Applied a mathematical subject of their choice. Statistics Furthermore, five invited speakers will enrich July 6 – 8, 2001, Université Concordia, Montréal the participant's knowledge of current Org. : Y. Chaubey (Concordia), F. Nebebe (Concordia) mathematical research. This conference will feature plenary speakers, and contributed and invited papers, with Séminaire de mathématiques emphasis on applied statistics. Areas covered supérieures : Modern Methods in include Bayesian Methods, Biostatistics, Data Scientific Computing and Applications Mining, Demography, Econometrics, July 9 – 20, 2001, Université de Montréal Org. : G. Sabidussi (Montréal), K. Mikula (Slovak Multivariate Analysis, Operations Research, Technical University, Brátislává, Slovakia), A. Bourlioux Probability, Psychometrics, Sampling, Survival (Montréal), M. Gander (McGill), S. Lessard (Montréal), G. Analysis, and Time Series. C. Papanicolaou (Stanford), A. Stuart (Warwick) The conference follows a well established The scientific computing approach to the tradition. The First Canadian Conference in solution of differential equations of all types, Applied Statistics was held in 1971 at Concordia associated with a variety of applications, is a University. Since then, the Department of multi-faceted technique that encompasses not Mathematics and Statistics has organized such a only numerical methods but also more formal conference every tenth year. analysis of the underlying equations, along with The plenary speakers are David Brillinger a good understanding of the practical (Berkeley), Christian Genest (Laval), John D. application being modelled. Recent Kalbfleisch (Waterloo), Jerry Lawless (Waterloo), achievements of this multi-disciplinary approach Jim Ramsay (McGill), C. R. Rao (Penn State), J. will be presented by expert applied N. K. Rao (Carleton), P. K. Sen (North Carolina). mathematicians, together with applications in

CRM Annual Report 1999-2000 55 C o m i n g E v e n t s

FUSION 2001: 4th International Spectral Statistics and High Energy Conference on Information Fusion Eigenstates August 7 – 10, 2001, Montréal August 25 - September 2, 2001, CRM Org. : E. Shahbazian (Lockheed Martin & CRM ) Org. : Dmitry Jakobson (McGill), John Toth (McGill) This conference will provide a forum for the The idea of the workshop is to bring together presentation of research and technological mathematicians and physicists working on advances by scientists and engineers working in issues related to asymptotic eigenstate all aspects of information and data fusion properties, especially as they relate to classical techniques and systems. It will also feature limits and chaos. There are various subjects to be keynote speeches and plenary talks. Topics investigated. These include the asymptotic include various aspects of theoretical and behaviour of individual eigenstates, the role and technical advances in information fusion, utility of random matrix theory in the prediction algorithms and systems, as well as applications. of eigenvalue statistics for the Laplace-Beltrami operator and the role of periodic orbits and Second Gilles Fournier Memorial scars. Conference The list of invited speakers includes: T. Paul* (Paris August 13 – 15, 2001, Université de Sherbrooke Dauphine), S. Zelditch* (Johns Hopkins), V. Jaksic (Ottawa), Org. : Marlène Frigon (Montréal), Andrzej Granas A. Uribe (Michigan), B. Shiffman* (Johns Hopkins), V. (Montréal), Tomasz Kaczynski (Sherbrooke) Guillemin* (MIT), S.T. Yau* (Harvard), M. Zworski (Berkeley), M. Min-Oo (McMaster), W. Craig* (McMaster), Y. Les thèmes principaux de cette seconde Colin De Verdière* (Institut Fourier, Grenoble), P. Deift* conférence dédiée à la mémoire de Gilles (UPenn), G. Olshanski* (Institute for Information Transmission Problems, Moscow, Russia), U. Smilansky Fournier seront la théorie des points fixes et la (Weizman Institute), A. Soshnikov (UC Davis), C. Tracy (UC théorie de points critiques ainsi que leurs Davis), H. Widom (UC Santa Cruz), N. Nadirashvili* applications aux équations différentielles et aux (Chicago), P. Sarnak (Princeton), A. Borodin* (Penn), D. Heijhal* (Minnesota and Uppsala), A. Its* (IUPUI), P. Bleher* systèmes dynamiques. À cette occasion, des (IUPUI), A. Okounkov* (Berkeley), A. Zaharescu* (UIUC), Z. développements récents de ces domaines seront Rudnick (Tel Aviv), K. Soundararajan* (IAS), K. McLaughlin* présentés par des experts canadiens et étrangers (Arizona), X. Zhou* (Duke), A. Eskin* (Chicago), R. Speicher (Queens) afin de stimuler les échanges entre eux et les * to be confirmed étudiants des cycles supérieurs qui participeront. La conférence sera composée de conférences Mathematical Statistics 2002: A principales de 50 minutes, conférences invitées Conference Honouring Constance van de 40 minutes et quelques exposés de 30 minutes Eeden's 75th Birthday données par de jeunes mathématiciens. La May 31– June 1, 2002, CRM participation d'étudiants de cycles supérieurs Org. : Marc Moore (École Polytechnique), Sorana Froda sera fortement encouragée. (UQAM) Les conférenciers principaux seront Massimo This conference will recognize the extraordinary Furi (Florence), Kazimierz Geba (Gdansk), services of Professor Constance van Eeden to the Andrez Granas (Montréal), Antonio Marino Canadian statistical community, and to the (Pise), Mario Martelli (Cal St. Fullerton), Jean Université de Montréal in particular. Five to Mawhin (Université Catholique de Louvain) et eight first-class researchers will be invited to Michel Willem (Université Catholique de give talks in fields in which she has made Louvain). Les conférenciers invités seront A. important contributions, including Abbondandolo (Pise), S. Alama (McMaster), H. nonparametric statistics and decision theory. Ben-El-Mechaiekh (Brock), P. Deguire This conference will precede the Annual (Moncton), M. Lassonde (Université des Antilles Meeting of the Statistical Society of Canada et de la Guyane) et H. Steinlein (Munich). which will be held in Hamilton.

56 Annual Report 1999-2000 CRM C o m i n g E v e n t s

Theme Year 2002-2003 : Mathematical Methods of Computer Science

Organizing Committee More recently, a recurrent theme in many of the Y. Bengio (Montréal) domains examined is probabilistic methods; A. Borodin (Toronto) these have permeated the whole of computer G. Brassard (Montréal) science, and so particular emphasis will be L. Devroye (McGill) placed on the use of these techniques, both in D. Thérien (McGill) theoretical areas and in more applied ones such as simulation and machine learning. Overview The computer has also allowed mathematical The field of computation, formally born only in techniques to be developed and used, in areas in the last century, now constitutes a science in its which the computations were simply too own right, with solid theoretical foundations on daunting. One area, of course, where this is true which its spectacular development is based. The is that of large scale scientific computing. This is CRM thematic year in the mathematical methods not part of the year, as it is being covered of computer science proposes to explore in depth elsewhere. However there are other areas, such a significant spectrum of the many sub-areas as discrete mathematics or optimization, in that are foundational material for modern which the availability of computing power has computer science, that exhibit significant and made an enormous difference. new mathematical content, and that have indeed The main fields to be covered during the influenced the development of mathematics. thematic year are complexity theory and analysis Mathematically, the areas with the earliest of algorithms, quantum computing, influence on computer science were logic and cryptography, stochastic simulation, machine discrete mathematics. Since then, the theory of learning, and discrete computational theoretical computer science has blossomed, and mathematics. ideas from the area (starting with such concepts Along with the usual workshops and courses as the Turing machine) have grown to occupy an being organized during the thematic year, CRM ever more important role in mathematics. will host two of the most important international conferences in theoretical Computer Science, namely the ACM Symposium on Theory of Computing and the IEEE Conference on Computational Complexity.

CRM Annual Report 1999-2000 57 Research Programmes Research reports appear in their original language.

Twareque Ali modèle des observations. Dans ce projet, il est Square-integrable Group Representations, envisagé de généraliser les travaux déjà Wavelets, and Wigner Transforms entrepris sur les paramètres de position aux Twareque Ali's research during the last couple paramètres d’échelle. Une théorie plus globale of years was centred around the theory of sur les modèles de position-échelle sera ensuite square-integrable group representations and the développée. relationship of square-integrability with the Un autre problème important en statistique est Plancherel transform. It has been demonstrated l’estimation d’une fonction basée sur that the Plancherel transform for Type I groups l’observation, avec erreur, de celle-ci à différents is the unifying link between square-integrability, points de son support. En utilisant une the wavelet transform, and the generalized approche bayésienne et une base de fonctions Wigner function. This connection has far- appropriée, il est possible d’estimer une fonction reaching consequences, in the sense that it can be définie sur différents domaines. Dans les mois à used to generate large classes of Wigner venir, il est envisagé d’essayer de développer functions for Type I groups. From the point of une théorie générale qui aura comme cas view of physical applications, Wigner functions particuliers les différents contextes déjà étudiés. are quasi-probability distributions on classical Les propriétés statistiques de ces estimateurs phase spaces (coadjoint orbits of the groups in seront aussi étudiées. question), corresponding to quantum mechanical states, and hence they can be used to Paul Arminjon study the physical states of atomic and Numerical Methods in Fluid Dynamics and quantum-optical systems. They can also be Electrodynamics interpreted as characteristic signatures of signals P. Arminjon works in the area of Computational in image analyses. In this way, the use of the Fluid Dynamics (CFD). With A. Dervieux, he Plancherel transform in connection with square- constructs and analyzes high resolution non integrability unifies the theories of signal oscillatory positivity preserving finite analysis, wavelet transforms, and quantum volume/finite element methods for hyperbolic tomography. On the computational side, a large systems, with applications to compressible number of generalized Wigner distributions flows. have been computed for a special class of group semidirect products admitting open free orbits With M.C. Viallon, he has constructed, for non- under the coadjoint action. These distributions linear hyperbolic systems, a 2-dimensional have been used extensively in atomic and second-order accurate nonoscillatory finite quantum optical calculations. volume method for staggered unstructured triangular grids inspired by the Lax-Friedrichs Jean-François Angers and Nessyahu-Tadmor 1-dimensional difference Modélisation avec des densités a priori à schemes; they also proved the convergence of queues aplaties et estimation de fonction the method for a linear hyperbolic equation. En théorie de la décision bayésienne, en plus With D. Stanescu, he extended these schemes to d’avoir à spécifier un modèle statistique pour les a finite volume method for Cartesian grids, and observations, nous devons spécifier un autre with A. Madrane he developed and applied the modèle, dit a priori, pour les paramètres triangular method to many typical flow décrivant celui des observations. Le choix du problems; comparison with other methods modèle a priori est très important (discontinuous finite elements, etc.) showed the particulièrement lorsque notre échantillon high resolution and sharp shock capture contient des valeurs extrêmes. En effet, le capacities of the method, which also requires comportement des règles de décisions en shorter computing times. With A. Madrane, he présence de telles observations dépend has constructed a mixed finite volume/finite principalement de la différence d’aplatissement element method for the Navier-Stokes equations, entre les queues du modèle a priori avec celles du where the convective terms are treated with the

58 Annual Report 1999-2000 CRM R e s e a r c h P r o g r a m m e s

Arminjon-Viallon finite volume method and the destruction à taux constant. Ce travail incorpore viscous terms with a finite element method. les découvertes les plus récentes sur la With A. St-Cyr and A. Madrane, they have also thrombopoeitine, et permet de suggérer des extended the non-linear hyperbolic method to mécanismes d’induction d’oscillation dans le the 3-dimensional case. Results are excellent niveau des plaquettes sanguines en circulation. both for cartesian grids and for unstructured Un projet de collaboration avec des chercheurs tetrahedric grids. For cartesian grids they have en pharmacie a mené à une co-supervision proved positivity and a maximum principle. d’étudiant, afin de construire des modèles qui incorporent des régimes transients pour la Liliane Beaulieu représentation de mécanismes d’absorption de Bourbaki en son temps relaxant neuromusculaires. Un modèle original a L’objectif central de cette étude est de été mis au point. reconstituer l’histoire de la formation du groupe Enfin, dans le cadre du réseau MaTICS, un de mathématiciens N(icolas) Bourbaki, dans les étudiant a travaillé sur le raffinement d’un années trente, de sa survie durant les années de modèle ionique de myocyte auriculaire. guerre et de la restauration de l’équipe à la fin des années quarante. Ce travail d’historien Habib Benali s’appuie sur une documentation solide, inédite à Modélisation en imagerie neurofonctionnelle ce jour, qui fait elle-même l’objet d’une publication sous la forme d’une base de Notre projet de recherche consiste à développer données. Au plan mathématique, il s’agit de une méthodologie de quantification fiable des retracer les changements de cap pris par processus physiologiques cérébraux à partir de Bourbaki dans ses choix théoriques et de les séquences d'images médicales multimodalité en situer dans le contexte, plus vaste, des IRM fonctionnelle, IRM anatomique, MEG et mathématiques qui étaient en train de se EEG. Les approches utilisées relèvent des développer, notamment en théorie des techniques statistiques multidimensionnelles ensembles, en algèbre et en théorie de ainsi que l'apport des méthodes hiérarchiques et l’intégration. D’autres publications du chercheur multi-échelles pour la localisation des ont porté sur l’histoire de la topologie, de la activations en IRMf et des sources d'activations stochastique et de l’informatique. en EEG/MEG. Nos applications cognitives et cliniques ont pour objectifs de: • Jacques Bélair Caractériser les circuits neuronaux des Équations différentielles non linéaires processus cognitifs correspondant à des retardées et modélisation physiologique ensembles distribués au niveau du cerveau et liés transitoirement pour exécuter une La dynamique non linéaire fournit une tâche. Les liens dynamiques entre ces interprétation de changements complexes du ensembles seront examinés à l'aide des rythme physiologique comme bifurcations modalités d'imagerie IRMf et EEG/MEG. lorsque les valeurs des paramètres de contrôle • sont modifiées. La théorie mène à des Caractériser les invariants anatomiques et prédictions pour les comportements possibles fonctionnels de ces ensembles neuronaux. dans un environnement expérimental et permet Dans des études longitudinales, ces une explication unifiée des divers régimes. Le invariants seront corrélés au processus de travail de Bélair est concentré sur les feed back réorganisation fonctionnelle de l'activité non linéaires à retard en contrôle et dans les cérébrale. L'étude de la plasticité cérébrale systèmes d’oscillations hormonales et chez des patients opérés de Gliomes bas neuromusculaires, en insistant sur le rôle du grades guidera nos développements délai, des boucles multiples de feed back et des méthodologiques. délais variables dans la génération de comportements périodiques (oscillatoires) ou irréguliers. En collaboration avec J. Mahaffy, M. Mackey et M. Santillan, nous avons développé un modèle de thrombopoièse qui inclut un mécanisme de

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Yoshua Bengio multiplicité peut correspondre aux niveaux Algorithmes d’apprentissage atomiques, pour l’algèbre, elle représente une Les algorithmes d’apprentissage automatique dimension, et pour la combinatoire, elle répond permettent à l’ordinateur d’apprendre à partir à un problème d’énumération. Un résultat d’exemples. Ce champ de recherche est à classique de Frobenius rend accessibles ces l’intersection de l’intelligence artificielle, calculs (autrement difficiles) dans le contexte de l’inférence statistique, et l’optimisation la théorie des fonctions symétriques, au prix du numérique. Les algorithmes d’apprentissage développement de formules donnant sont particulièrement utiles dans les situations l’expression de certains polynômes en termes où nous n’avons pas assez de connaissances sur d’une base fixée. Les fonctions de Schur et les un problème pour directement énoncer une fonctions de Hall-Littlewood ont classiquement solution sous la forme d’un programme, mais où joué ce rôle de bases fondamentales, mais, au nous avons des exemples illustrant la tâche à cours des dernières années, de nouvelles bases effectuer. Le problème de l’apprentissage peut ont été introduites pour répondre à de nouvelles s’exprimer comme le choix d’une fonction parmi problématiques. Ces variantes ont été un ensemble de fonctions selon l’espérance d’un synthétisées par Macdonald pour donner critère (la qualité de la solution choisie par naissance à une nouvelle famille de fonctions l’ordinateur pour un exemple particulier). symétriques à deux paramètres contenant toutes Cependant, comme la véritable distribution des les bases précédentes. exemples est inconnue, cette espérance ne peut En utilisant des techniques de la théorie des pas être calculée, seulement estimée par sa représentations, de la combinatoire algébrique et valeur empirique sur les données observées. La des calculs dans l’algèbre des fonctions véritable difficulté de l’apprentissage est donc de symétriques, je cherche à trouver et démontrer généraliser, ou de pouvoir transférer des identités et des propriétés de ces polynômes l’information existante dans les exemples de Macdonald. Ce sujet est particulièrement disponibles à de nouveaux exemples. Les intéressant en ce qu’il fait interagir combinatoire, recherches de Yoshua Bengio se concentrent sur théorie de la représentation, analyse certains types d’algorithmes d’apprentissage (en harmonique, théorie des fonctions spéciales et particulier les réseaux de neurones artificiels et géométrie algébrique. Chaque progrès donne les modèles de Markov cachés) et leurs lieu à de multiples questions et applications applications (en reconnaissance de formes, dans tous ces domaines. reconnaissance de la parole, vision par ordinateur, analyse de processus industriels, et Nantel Bergeron la prédiction et prise de décision à partir de Combinatoire algébrique et application séries chronologiques financières). Cette année Nous nous intéressons à l’étude de structures des résultats très importants ont été obtenus algébriques en utilisant la combinatoire. Deux dans le domaine de la modélisation statistique grandes lignes de recherche se découpent dans du langage, battant les systèmes qui dominent ce nos travaux. problème depuis vingt ans. • L’étude d’espaces de polynômes quasi- François Bergeron harmoniques associés à des diagrammes. • Décomposition de représentations Les algèbres de Hopf associés à des réseaux. Mes recherches concernent divers aspects de En ce qui concerne le premier point, nous avons l’interaction entre la combinatoire et l’algèbre, émis l’hypothèse que ces espaces sont hautement plus particulièrement autour d’un problème symétriques et leur étude a suscité beaucoup central de la théorie de la représentation d’intérêt dans la communauté mathématique et consistant à décomposer une représentation physique. Nous savons maintenant que certains donnée en ses composantes irréductibles. On dit de ces espaces sont liés à des solutions de que le nombre d’occurrences d’une modèles en physique quantique. représentation irréductible au sein d’une En ce qui concerne le second point, nous avons représentation est sa multiplicité. Il appert que le remarqué que pour plusieurs algèbres, les calcul de ces multiplicités est fondamental dans constantes de structure multiplicative sont liées plusieurs domaines de la physique et des à l’énumération de chemins dans des réseaux. mathématiques. Ainsi, pour la physique, cette Nous développons présentement une théorie qui

60 Annual Report 1999-2000 CRM R e s e a r c h P r o g r a m m e s nous permet de mieux comprendre ce lien et fundamental groups. In particular they made d’unifier les constructions existantes. important theoretical advances in this latter area which led to other applications in surgery Anne Bourlioux theory. Simulation numérique de flammes turbulentes This year he began a collaboration with Dale Le régime de flammelettes (applicable par Rolfsen (UBC) and Bert Wiest (PIms) centred on exemple dans les moteurs d’automobiles) est the orderability of the fundamental groups of 3- caractérisé par une épaisseur de flamme très manifolds. mince: le défi en combustion numérique turbulente est de représenter de façon adéquate Abraham Broer l’effet global sur la propagation de la flamme de Les groupes algébriques de transformation et phénomènes (combustion, turbulence) se la théorie des invariants. passant à une échelle trop petite pour être Présentement, il s’intéresse aux variétés représentés de façon précise dans une simulation algébriques qui sont liées à la théorie des numérique. représentations des groupes de Lie semi- Une stratégie de développement et de validation simples. Les liens entre la théorie des systématique de modèles mathématiques pour représentations et la géométrie algébrique sont ces effets sous-grille a été mise en place via une profonds et très intéressants. équation idéalisée. Les effets des petites échelles Quelques exemples typiques de telles variétés sont renormalisés de façon asymptotique sont les variétés nilpotentes dans une algèbre de rigoureuse. Lie, les variétés de décompositions et le fibré Cette stratégie a permis d’élucider dans le cotangent d’une variété de drapeaux. Pour contexte du modèle idéalisé des questions l’étude de ces variétés, on a besoin de la posées par les ingénieurs qui développent des géométrie algébrique, de la topologie algébrique codes de simulation de moteurs à combustion: et la théorie des invariants. • dans le cas de flammes prémélangées: Ces dernières années, il a étudié en particulier la l’identification de deux régimes distincts structure des variétés de décomposition des dans la paramétrisation de l’augmentation algèbres de Lie semi-simples, avec des de la flamme en fonction de l’intensité de la applications dans la théorie des arrangements turbulence (l’effet de «bending»); d’hyperplans associés aux groupes de réflexion. • dans le cas de flammes non-prémélangées (moteurs diesel): la réduction du taux de Francis Clarke convergence asymptotique des modèles Control and Nonsmooth Analysis hybrides utilisés en pratique comparés au taux de convergence idéal des modèles A recent paper [IEEE Transactions on Automatic théoriques. Control 42 (1997) 1394-1407] written in collaboration with Yu. S. Ledyaev, E. Sontag and Steven Boyer A. Subbotin solves a well-known and long- Studies in Low-dimensional Topology standing question in control theory: we give a constructive proof of the fact that any The research efforts of Steven Boyer over the last asymptotically controllable system admits a few years focused on the topology of low- retour d'état which stabilizes it. In general, it is dimensional manifolds, particularly knot theory, necessary that this retour d'état be discontinuous. and the geometric representation theory of 3- One can then prove its robustness by some new manifold groups. His primary interest in the first and apparently very promising techniques, and of these research areas is to study exceptional establish interesting relationships with the phenomena which arise from the geometric regularity of eventual Liapunov functions. operation of Dehn surgery on knots. Together with his collaborator Xingru Zhang (SUNY at Buffalo) they were able to prove definitive results in several cases they studied. The methods they employed involve an interplay between the topology of 3-dimensional manifolds and the representation theory of their

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Henri Darmon • the design of solid vibrating gyroscopes Courbes elliptiques et formes modulaires (Bryan effect), • Mes recherches des dernières années ont visé the stabilization and control of partial tout d'abord à démontrer certaines variantes p- differential equations on submanifolds when adiques de la célèbre conjecture de Birch et the underlying geometry is an integral part Swinnerton-Dyer, projet qui a été mené à bien of the control process (non-cylindrical dans une série d'articles conjoints avec Massimo problems, shells). Bertolini. Plus récemment, mes travaux avec This work has had an impact on the Canadian Bertolini m'ont amené à découvrir une Space Programme for the design of thermal généralisation inattendue de la théorie classique diffusers and radiators to condition the thermal de la multiplication complexe; cette environment of satellites and on the positioning généralisation, si elle pouvait être placée sur des of sensors and actuators for satellites of the third bases mathématiques solides, aurait des generation. The fundamental results of the conséquences importantes pour la théorie des research are also used on current projects on the nombres. C'est désormais le développement de design of planned NEV to be built by cette théorie qui me préoccupe principalement. Bombardier and the design of medical devices (stents for cardiac surgery). Michel Delfour Modeling, Design, and Control of Physical and Rachida Dssouli Technological Systems with Respect to Shapes Ingénierie des logiciels de télécommunication The theme of this programme is the study of the Nos projets de recherche s’inscrivent dans le theoretical and numerical aspects of shapes and cadre de l’ingénierie des logiciels de geometries as variables in the modeling, design, télécommunication. On s’intéresse tout and control of physical and technological particulièrement à la modélisation des systèmes systems. This area of research is becoming very complexes réactifs en temps réel. La majorité de broad, rich and fascinating with an extremely nos travaux utilisent des techniques formelles important potential for applications in many telles que la théorie de contrôle, la théorie des different areas: optimal design of mechanical automates, la théorie des graphes et algorithmes parts for the automotive industry, positioning of de minimisation. Nos projets sont: sensors and actuators, control of the position of • Server and e-commerce testing qui traite des the free boundary in material sciences, active tests des applications type commerce control of noise, image processing, free and électronique et des tests de serveurs. moving boundary problems, design of • Testing Complex Systems qui traite des tests biomedical devices, design and control of thin des systèmes réactifs temps réel et des structures, control of the drag by small changes systèmes communicants avec ou sans files in the shape of the wing of an aircraft, etc... FIFO. There is an urgent need for theory and directions • Spécification incrémentale, analyse et simulation to understand and interpret the increasing de systèmes réactifs fondées sur les langages de number of computational results and the scénario où on s’intéresse à la synthèse et modeling issues encountered in applications. composition de scénarios afin de produire The programme concentrates on the following systématiquement des spécifications five intertwined projects: formelles cohérentes. • • the mathematical analysis, differential Formalisation et test des protocoles de la pile calculus, and optimization for shapes and IPv6. La pile de logiciels de communication geometries, connue sous le vocable IPv6 est la norme qui • the development of appropriate intrinsic va remplacer à long terme la pile IP actuelle. methods for the differential calculus and Ce projet, en collaboration avec un groupe functional analysis on submanifolds of the européen, va fournir des tests de Euclidean space, normalisation dérivés à partir de • the intrinsic modelling and analysis of thin spécifications formelles. and asymptotic shells for C1,1 midsurfaces or curves,

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Stéphane Durand Le deuxième projet consiste à développer un Fractional Generalization of the KdV Equation algorithme, satisfaisant dans un contexte Using supersymmetry it is possible to generalize pratique, qui aide le biologiste à identifier dans in a non-trivial way the Korteweg-de-Vries un génome toutes les parties qui codent pour equation (KdV) to an integrable system of two une famille particulière d'ARN. Cet algorithme coupled differential equations (Mathieu). doit intégrer différentes méthodes efficaces pour Knowing that the supersymmetry can itself be la recherche d'éléments structuraux et de extended (parasupersymmetry and fractional séquences conservées, permettre une définition supersymmetry [Durand, Vinet]), it is natural to souple du ou des motifs, permettre toute sorte look for generalizations to integrable systems of d'erreurs et d'incertitude. Le but de la recherche several coupled differential equations. The est de développer un algorithme qui allie formalism of fractional superspace introduced résultats biologiques pertinents et rapidité by Durand allows such a generalization in a d'exécution. natural way. This result is reached using the fractional extension of supersymmetry, the Isidore Fleischer Hamiltonian structure of the fractional pseudo- Change of Variables in Multiple Integrals classical mechanics and the fractional Change of variables in multiple integrals is very generalization of a superextension of a Virasoro useful both for evaluation of integrals and for algebra (and/or its q-deformations). theoretical purposes. The basic theorem is usually stated by requiring continuous Nadia El-Mabrouk differentiability and injectivity of the Réarrangements génomiques et recherche de transformation. Recent work has succeeded in motifs d'ARN lightening these hypotheses, e.g., by removing Le programme de recherche s'oriente sur deux continuity from the derivative. This study aims aspects différents liés à l'analyse des génomes. to push this cleaning up further. Le premier se situe dans le cadre de la phylogénie et de la génomique comparative, et Richard Fournier le deuxième se rapporte à la recherche de motifs Quelques problèmes d’analyse complexe d'ARN dans le génome. Le domaine de recherche de Richard Fournier Le but ultime de la génomique comparative est est l'analyse complexe, en particulier la théorie de construire l'arbre d'évolution des espèces. géométrique des fonctions d'une variable Cela implique la considération de distances complexe. Ce chercheur s'intéresse plus d'évolution particulières. Une méthode consiste spécialement à certains problèmes sur les à comparer l'ordre des gènes dans les deux transformations conformes, les classes spéciales génomes étudiés. Cette étude sous-entend que de fonctions univalentes et l'extension au plan les espèces ont divergé par des mutations de certaines inégalités classiques (par exemple globales (suppression, duplication, mouvements l'inégalité entre les moyennes arithmétique et de blocs de gènes). Différents problèmes géométrique). L'analyse complexe est un sujet peuvent être abordés, dépendant du type de classique qui s'est récemment renouvelé grâce à mutations, du phénomène d'évolution et de la l'étude des fractals et de la dynamique des complexité biologique considérée. Ces fonctions méromorphes ou entières. problèmes donnent lieu à des études combinatoires, algorithmiques et de théorie des Langis Gagnon graphes variées et complexes. Je me propose de Contours actifs sans contraintes topologiques contribuer au développement du domaine en pour la segmentation d'images bruitées considérant des opérations de réarrangement Le projet consiste à mettre en œuvre et étudier encore non étudiées, comme la duplication de une technique moderne de détection de contours fragments de chromosomes. Je propose dans des images bruitées (e.g., imagerie radar) également de développer des algorithmes qui basée sur une approche de propagation de fronts permettent de prendre en compte différentes d'ondes. Cette technique s'apparente à celle des pondérations pour les opérations de contours actifs (snakes) basée sur une réarrangement en fonction de leur type, leur formulation Lagrangienne de l'évolution d'une position et de leur taille.

CRM Annual Report 1999-2000 63 R e s e a r c h P r o g r a m m e s courbe élastique dans un plan, mais avec deux collaborateurs et étudiants ont amorcé une étude avantages importants : semblable pour les transformations de l’espace. • le contour initial peut être aussi éloigné que Ils continuent aussi leurs recherches en l'on veut de l'objet, ce qui implique approximation. qu'aucune information a priori sur la position ou la forme de l'objet n'est Bernard Goulard nécessaire; Méthodes statistiques et imagerie • le contour final peut être topologiquement Le traitement d'une image revient de plus en différent du contour initial, e.g., un contour plus à reconstruire au mieux un objet à partir fermé peut évoluer en se scindant en d'informations incomplètes et souvent bruitées, plusieurs sous contours pour capturer ce qui amène l'utilisation de connaissances a différent objets. priori et de méthodes statistiques. B. Goulard, La mise en œuvre numérique fait appel à des J.M. Lina et D. Clonda procèdent à une méthodes d'évolution de courbes de niveaux modélisation statistique des images à traiter utilisées dans les simulations de la propagation basée sur les propriétés des ondelettes de des flammes. Daubechies complexes. Leur caractérisation des images passe par une modélisation de la Martin Gander distribution des coefficients en ondelettes par le Parallel Algorithms for High Performance biais d'un modèle en arbre pour un processus de Computing Markov caché. Ce modèle a été perfectionné et appliqué à différents problèmes de traitement Computation is now regarded as an equal and du signal. Ces études sont en phase avec les indispensable partner, along with theory and travaux menés dans le cadre d'une collaboration experiment, in the advance of scientific avec le groupe de Pitié-Salpêtrière (Paris) dans knowledge and engineering practice. Numerical l'analyse des mesures de simulation enables the study of complex systems magnétoencéphalographie (cf J. M. Lina). and natural phenomena that would be too expensive or dangerous, or even impossible, to Par ailleurs, dans un projet subventionné par study by direct experimentation. The quest for Bell-Lube, B.Goulard, J.M.Lina et F. Nekka ever higher levels of detail and realism in such travaillent en collaboration avec B. Johnston simulations requires enormous computational (INRS-Télécommunications) à la mise en oeuvre capacity, and has provided the impetus for d'un système basé sur la technologie intemet. dramatic breakthroughs in computer algorithms L'objectif est de faire circuler des images and architectures. Parallel computers have médicales et des logiciels d'analyse entre des proved to be the only tools with the necessary lieux (hôpitaux, instituts,..) éloignés capacity to satisfy current demands in research géographiquement et ce, dans des conditions and industry. But the development of parallel maximales de confidentialité, intégrité et algorithms specialized for the underlying disponibilité des données. Ce travail implique problems is lagging behind. This is my current notamment une intégration d'analyse des images main area of research. et de leur circulation sur le réseau.

Paul Gauthier Michel Grundland Analyse Symétries et solutions des systèmes non- linéaires en physique Les nombres complexes peuvent être identifiés aux points du plan. Une fonction complexe Au cours des dernières années, les recherches de w=f(z) est donc une fonction qui envoie les Michel Grundland portent sur les méthodes de points du plan des z sur des points du plan des réduction par symétries (MRS) ainsi que sur la w. Le problème principal des nombres méthode des invariants de Riemann (MRI) et complexes est d’estimer la grandeur des disques leurs applications aux équations de la théorie contenus dans l’image de f (constante de Bloch). des champs non-linéaires, à la physique de la Le meilleur estimé à ce jour est celui de Gauthier matière condensée ainsi qu’à la dynamique des et Chen et ils espèrent pouvoir améliorer cet fluides. Le développement de ces méthodes estimé encore. Encouragés par ce succès avec les nous fournit de nouveaux outils pour aborder transformations du plan, Gauthier et ses les phénomènes non-linéaires en physique,

64 Annual Report 1999-2000 CRM R e s e a r c h P r o g r a m m e s spécialement ceux décrits par des systèmes covariantes méromorphes sur la sphère de multidimensionnels d’équations aux dérivées Riemann, et qu’ils satisfont en conséquence des partielles (EDP) et qui n’ont pu être résolus par équations de déformations, équations bilinéaires d’autres méthodes (par exemple la diffusion qui ressemblent à celles de l’hiérarchie KP, mais inverse). Le programme de recherche est où ne figurent que des générateurs de l’algèbre constitué des quatre projets suivants: de Virasoro dans les paramètres de déformation. • Symétries conditionnelles pour les systèmes d’EDP non-linéaires. Jacques Hurtubise • Une comparaison entre les différentes Systèmes intégrables méthodes de groupe de Lie servant à Les travaux de J. Hurtubise pour l'année 99-00 solutionner les EDP. ont porté sur les systèmes intégrables. Un travail • Solutions invariantes et partiellement conjoint avec E. Markman sur les systèmes de invariantes des équations de la dynamique Calogero-Moser, donnant une construction des fluides. naturelle de l'espace de phase, a été terminé et • Les ondes de Riemann multiples pour les soumis. Un autre, portant sur la séparation de systèmes quasilinéaires d’EDP et les variables pour les crochets de Sklyanin, a été relations avec la méthode de réduction par entrepris. Des travaux sont en cours avec L. symétries. Jeffrey pour comprendre les G-fibrés sur une surface de Riemann avec trivialisation John Harnad parabolique. Finalement, conjointement avec H. Systèmes intégrables, déformations Darmon, un séminaire sur la quantification des isomonodromiques et applications systèmes de Hitchin et le programme de Pendant l’année passée (1999-2000), deux Langlands géométrique a été organisé, avec une nouveaux projets ont été développés: dizaine de rencontres. Une relation entre deux approches aux systèmes hamiltoniens complètement intégrables a été Véronique Hussin mise au point. La première approche est fondée Supersymmetry sur les flots hamiltoniens isospectraux dans les During the last twenty years, the theory of Lie groupes et les algèbres de lacets générés par les groups and algebras has been extended in many invariants spectraux avec une structure de directions. One of them deals with the Poisson qui provient d’une matrice R classique. supersymmetric theories and the notions of Lie La seconde approche développée par Magri et supergroups and superalgebras. Since it is ses collaborateurs, est fondée sur la notion de concerned with a unified description of structures multi-hamiltoniennes. On a démontré fermionic and bosonic objects, one has to work que, dans le contexte de flots isospectraux dans with commuting and anticommuting variables. les algèbres et les groupes de lacets, tous les The problem of resolving non-linear differential résultats de la seconde approche, soit l’existence equations with such variables is studied by V. des structures multi-hamiltoniennes, les Hussin with students and collaborators such as invariantes commutatives provenant du P. Winternitz at the CRM. New supersolitonic théorème de Gel’fand-Zakharevich et les solutions have been obtained by generalizing the coordonnées séparatrices associées aux vecteurs method of reduction by symmetries for such propres du tenseur de Nijenhuis, sont des equations. conséquences de la théorie des matrices R associées aux structures de Poisson holomorphes Another aspect of the research of V. Hussin sur les surfaces complexes. deals with the construction of minimal uncertainty states in terms of the so-called Un autre projet a été complété pendant un séjour “coherent” or “squeezed” states for au MSRI à Berkeley. Ceci concerne les supersymmetric systems in quantum mechanics. déterminants de Fredholm de certains We make use of new relations between the opérateurs intégraux qui figurent comme eigenstates of annihilation operators associated fonctions de distributions spectrales de matrices with the harmonic and anharmonic oscillators aléatoires. On a démontré que ces déterminants and the Jaynes-Cummings model important in étaient des “fonctions tau” des systèmes quantum optics. Students, post-doc, and dynamiques qui déterminent des déformations isomonodromiques d’une famille de dérivées

CRM Annual Report 1999-2000 65 R e s e a r c h P r o g r a m m e s collaborators in Mexico and Spain are working type infini. Enfin, il a pour but d’étudier le on this project. comportement global des solutions d’équations d’onde telles que l’équation de Dirac dans les Anatole Joffe variétés pseudo-riemanniennes correspondant Probabilités pures et appliquées aux solutions exactes de type trou noir des Les processus de branchement décrivent équations d’Einstein, un des objectifs étant de l'évolution d'une population d'objets (individus, démontrer la non-existence de fermions en plantes, particules) qui se reproduisent suivant configuration stable au voisinage d’un trou noir un mécanisme aléatoire. Lorsque ces objets se en rotation. déplacent, le modèle est "la promenade aléatoire avec branchement"; ce modèle décrit des choses Paul Koosis aussi différentes que le comportement d'un Amélioration de l’estimation harmonique réacteur nucléaire (une population de neutrons Jusqu’à récemment l’estimation harmonique se reproduisant par les chocs des neutrons sur (c.à.d. l’emploi de la formule généralisée de les atomes) ou la description de la forme d'une Jensen) a été l’un des procédés les plus puissants forêt (une population de graines dispersées par pour trouver des bornes pour une fonction le vent et les oiseaux). analytique dont le comportement précis est Joffe s'intéresse depuis longtemps aux propriétés inconnu. Il est très important en analyse de asymptotiques de ces processus sous des pouvoir établir ces bornes, car elles nous hypothèses minimales. permettent d’augmenter notre connaissance de la fonction en question. Mais l’estimation En collaboration avec A. Fuchs, J.L. Teugels, A. harmonique n’est pas un outil universel et ne Joffe a obtenu des résultats définitifs sur le s’applique pas dans certaines situations; il serait comportement asymptotique du rapport de la donc intéressant de trouver une méthode qui va somme des carrés par le carré de la somme en plus loin. donnant une formule exacte de son espérance. Il s'agit d'études très techniques dont l'origine se On peut parfois obtenir les bornes qu’on cherche trouve dans le problème précédent mais qui pourvu que les intégrales figurant dans présente un intérêt en soi. l’estimation harmonique puissent être remplacées par des sommes de forme semblable, "L'ergodicité forte" dans le domaine des prises sur un ensemble discret de points, et on a mathématiques pures ne peut être décrite dans vu dernièrement que ce remplacement est un langage simple. A. Joffe et I. Fleischer ont parfois possible. Pour cela la plus petite majorante obtenu des résultats dans ce domaine. surharmonique est employée. Le but de ce projet L'impact du développement des mathématiques est de comprendre le rôle, encore mystérieux, pures est complètement imprévisible... mais joué par cet objet dans ce genre de question; on presque toujours inéluctable (it is a tale told by an espère pouvoir de cette façon parvenir à une idiot, full of sound and fury, signifying nothing - méthode générale. De nouveaux résultats ont été Macbeth). obtenus.

Niky Kamran François Lalonde Géométrie des équations aux dérivées Topologie symplectique et systèmes partielles/ Groupes de Lie de dimension hamiltoniens infinie/ Équations d’onde en relativité générale Les travaux les plus récents se rapportent à la Le programme de recherches de Niky Kamran topologie symplectique, à la théorie de jauge et comporte trois axes principaux. D’une part, il aux systèmes hamiltoniens, sujets qui ont fait vise à étudier les rapports géométriques qui l'objet d'un intense développement depuis une existent entre les diverses propriétés quinzaine d'années. d’intégrabilité géométrique et l’existence de lois La topologie (ou géométrie) symplectique est de conservation pour les équations aux dérivées l'étude mathématique des espaces courbes, de ≥ partielles en dimensions m 3. D’autre part, il dimension paire arbitraire, munis d'une forme porte sur l’étude des structures de groupe de Lie symplectique, analogue anti-symétrique d'une de dimension infinie qui sont adaptées à la métrique riemannienne, qui donne à ces espaces théorie des pseudogroupes de Lie analytiques de la structure qu'il faut pour donner un sens aux

66 Annual Report 1999-2000 CRM R e s e a r c h P r o g r a m m e s lois de la physique aussi bien qu'aux procédés Christian Léger de quantification (passage du classique au Resampling Methods and Tuning Parameter quantique). Ce sujet est le versant mathématique Selection de ce que les physiciens appellent la théorie des Christian Léger’s research is on the use of super-cordes. Son développement a attiré resampling methods in statistics. These methods l'attention des physiciens (Witten, Vafa, use the power of the computer to approximate Aspinwal, Greene, ...) aussi bien que celle des the distribution of an estimator to construct, for mathématiciens dont les méthodes ont suivi une instance, a confidence interval for an unknown évolution rapide depuis vingt ans. parameter. To validate these methods, La plupart des travaux portent sur les aspects asymptotic theory as well as computer dits "hard" de la topologie symplectique et des simulations are used. In the last few years, Léger systèmes hamiltoniens, en se servant de has constructed confidence intervals which take techniques topologiques, géométriques et into account the data driven selection of the analytiques, en particulier les méthodes model in multiple linear regression when the d'équations aux dérivées partielles elliptiques et model is chosen using the data. By using the la cohomologie quantique. Ces méthodes sont bootstrap or subsampling to create new data sets fondées sur l'étude du comportement des and by rechoosing the model on each of them, it espaces de modules de courbes is possible to construct confidence intervals pseudoholomorphes, qui sont solutions des which reflect the uncertainty in the model équations de Cauchy-Riemann généralisées selection step. associées à une structure presque complexe. Les résultats que nous avons obtenus au cours des Sabin Lessard deux dernières années incluent l'application de Analysis of Population Genetic Models la cohomologie quantique à l'étude de la Sabin Lessard's research interests include a wide dynamique hamiltonienne qui a mis en évidence variety of population genetic models and the les propriétés de stabilité et de rigidité des concomitant evolutionary dynamics. His systèmes hamiltoniens. Ils contiennent aussi une ultimate goals are: a) to explain the maintenance forte généralisation des travaux de Kirwan et of variability in biological populations, b) to d'Atiyah-Bott sur les fibations symplectiques ou develop mathematical and statistical techniques algébriques, à partir de méthodes tout à fait to analyse population genetic structures, c) to nouvelles. deduce general evolutionary principles, and d) to study populations with complex interactions Robert Langlands, Marc-André Lewis et between individuals. Yvan Saint-Aubin The Ising Model in Domains with Boundary Jean LeTourneux In order to describe the critical behaviour of the q-fonctions spéciales two-dimensional Ising model, this group of La plupart des fonctions spéciales de la physique researchers has introduced a field similar to that mathématique possèdent des q-analogues, c’est- of the free boson whose jump lines delimit the à-dire des déformations faisant intervenir un constant spin clusters. The statistical paramètre q. De même que les algèbres de Lie distribution of this field has been studied by fournissent un cadre unificateur pour l’étude des Monte-Carlo simulations. It satisfies the two fonctions spéciales, les q-déformations de ces hypotheses of universality and conformal algèbres en fournissent un pour celle des q- invariance. Crossings on clusters of positive fonctions spéciales. En collaboration avec Luc spins have also been investigated and some of Vinet (CRM) et Roberto Floreanini (Trieste), Jean their properties are similar to those of crossings LeTourneux étudie systématiquement in percolation models. l’interprétation algébrique des q-polynômes spéciaux contenus dans la hiérarchie des polynômes d’Askey-Wilson.

CRM Annual Report 1999-2000 67 R e s e a r c h P r o g r a m m e s

Jean-Marc Lina of the Haupt modules, and the devices of Ondelettes, statistique et processus complexes symmetrization and desymmetrization, we En collaboration avec le groupe de recherche believe we have a complete list. A consequence PhysNum qu’il codirige avec B. Goulard, Jean- of this is the description of many hundreds of Marc Lina consacre principalement ses activités integrable systems attached to the Haupt scientifiques au traitement du signal. Les modules, generalizing the work of Halphen in différents sujets étudiés ont comme 1881 on the reduction of self-dual Yang-Mills. dénominateurs communs l’analyse statistique, The ADE problem, now called the McKay les techniques d’inférence et, depuis six ans, la correspondence, involves the remarkable fact théorie des ondelettes, qui a donné lieu à une that the fundamental groups of type E8, E7, E6 are recherche active dans le contexte des bases en related to the Monster, Baby, and F24 as Schur ondelettes de Daubechies complexes. Les multipliers. propriétés de ces fonctions ont conduit à des travaux plus appliqués, comme l’estimation de Fahima Nekka signaux dans le domaine de l’industrie nucléaire Vers une nouvelle méthode de classification et et, plus récemment, l’imagerie. Ainsi, la modélisation pharmaco-cinétique des effets modélisation statistique de la représentation spatiaux des médicaments à action rapide. multi-échelle complexe des images (par un En géométrie fractale, il est bien connu qu’on modèle de Markov caché) et la mise au point peut définir différentes dimensions pour le d’un algorithme d’optimisation pour des même objet, ce qui a suscité beaucoup de observations complexes ont débouché au cours recherche autour de la définition et du calcul des de la dernière année sur des algorithmes dimensions fractales. Il est aussi possible d’estimation robustes et sur une technique d’associer la même dimension fractale, voire le originale de classification de textures. La même spectre de dimensions, à différents objets. statistique des signaux complexes est également Ce dernier point est d’importance centrale dans à la base d’une étude d’estimation de phase pour la caractérisation des structures et leur l’imagerie d’interférométrie radar en comparaison en vue de classification. C’est dans collaboration avec l’industrie. Dans le contexte ce but que nous avons entamé notre recherche de l’imagerie cérébrale fonctionnelle, J.M. Lina sur un des indices les plus popularisés par collabore actuellement avec deux unités de Mandelbrot, qui néanmoins a bénéficié de peu recherche à Paris (INSERM et CHU-Pitié- d’études. Nous avons été menés ainsi à étudier Salpêtrière) pour appliquer des techniques un aspect de l’écart par rapport à l’invariance statistiques à la détection des sources par translation. On a démontré que la mesure fonctionnelles à partir de données magnéto- (de Hausdorff) générée par l’intersection des électro-encéphalographiques. Parmi les ensembles étudiés avec leurs translatés vérifie principaux aspects de ce problème, on citera la une loi de conservation de masse avec les prise en compte des informations a priori de échelles. Nous avons aussi trouvé que le spectre l’imagerie de résonance magnétique de mesures associé à ces intersections pouvait fonctionnelle ainsi que la modélisation multi- servir de nouvel outil de classification entre échelle de la surface corticale. deux structures distinctes mais ayant la même dimension. Nous mettons actuellement au point John McKay l’algorithme de calcul de ce spectre de mesure Moonshine and its Haupt Modules and ADE afin de le valider et de l’adapter à des structures We investigate the consequences of the relation réelles. between the Monster sporadic finite group, and Les bloqueurs neuromusculaires sont utilisés the Haupt modules which describe its comme agents anesthésiants à action rapide. Il representations. This research was started in est donc important de bien modéliser la phase 1979 by the author and is known as Monstrous initiale afin de bien évaluer les paramètres Moonshine. Designated by John Thompson pharmacocinétiques et pharmacodynamiques. (Fields medalist) as a ‘problem for the next Les modèles classiques s’avèrent inadéquats century’ it has recently been explained by pour la description de la circulation non- Richard Borchards for which he was awarded a homogène de ces médicaments. Dans ce Fields medal in 1998 at Berlin. By using deuxième projet, nous avons développé un recurrence relations for the Fourier coefficients modèle basé sur l’équation de diffusion qui

68 Annual Report 1999-2000 CRM R e s e a r c h P r o g r a m m e s incorpore l’hétérogénéité spatiale par une donné par la moyenne échantillonnale. Dans meilleure compréhension physiologique de la l’article ‘Improving on the MLE of a Bounded circulation et nous l’avons validé sur une variété Normal Mean’ on montre que le même de données cliniques. phénomène se produit en dimension 1 et 2 lorsque la moyenne est tronquée. De façon Jiri Patera générale, on favorise l’approche bayésienne. On Lie Theory, Quasicrystals, and Image y parvient plus facilement avec l’aide de Processing l’ordinateur en effectuant d’intenses calculs Following is a list of the research interests being numériques. Ceci nous amène à raffiner les pursued by Jiri Patera. méthodes de simulation existantes. Dans l’article Application of Lie theory. Exploitation of our "Beyond Accept-Reject Sampling" on perfectionne most recent results, namely the classification of la méthode d’acceptation-rejet. Un projet en the gradings of classical simple Lie algebras over cours est de la rendre encore plus sophistiquée the real number field. Most important among the en y incorporant des chaînes de Markov. applications is the grading preserving deformations of the algebras. Colin Rogers Study of properties and applications of the cut Deformation of Isothermic Surfaces and K- and project point sets ("quasicrystals"). Nets in Membrane Theory and Nonlinear Completion of a small monograph where the Elasticity : Application of Solitonic Methods properties of the 1-dimensional sets are brought Solitonic pulses with their novel survival together, proven, and explained. properties following interaction have major Specific applications of image processing and technological applications to optimal data fusion motivated mainly by our communication and semi-conducting devices. collaboration with Lockheed Martin, Canada. Materials which allow solitonic propagation are Most intensive efforts will be invested in the of paramount practical importance in nonlinear application of "quasicrystals" in cryptography, optics. This project will provide model and in the exploration of the many possibilities, constitutive laws for smart materials which evaluation of demonstration models, and the admit soliton transmission. In a parallel security questions. investigation, solitonic methods will be used in the engineering design of elastic membrane François Perron structures. Inférence statistique, simulations MCMC We also investigate the synthesis of materials Les intérêts de recherche de F. Perron sont liés à science. Here, recent advances in materials la statistique et portent plus particulièrement sur design and soliton theory are brought together les sujets suivants : théorie de la décision, to synthesize smart solitonic materials. analyse multidimensionnelle, statistique bayésienne et simulations par MCMC (chaînes Ivo Rosenberg de Markov avec Monte-Carlo). Les problèmes Clones and Relations liés à la théorie de la décision visent à améliorer Universal algebra. The main topic is the study of les estimateurs existants. L’approche privilégiée clones, on a finite universe A, which are consiste à produire de meilleurs estimateurs composition closed sets of operations on A. This minimax, l’estimateur minimax étant celui qui is a basic problem for finite algebras. Ideals, performe le mieux dans le pire des cas. Un congruence kernels and discriminator algebras estimateur est meilleur qu’un autre s’il fait were also studied. Algebraic duality, an toujours au moins aussi bien que l’autre en extension of Stone’s duality for boolean algebras, faisant parfois mieux. Dans l’article ‘On a allows topological representations of algebras. It Conjecture of Krishnamoorthy and Gupta’ on was shown that dualizability is invariant under démolit la conjecture qui prétend qu’un certain nilpotent shifts. algorithme améliore plusieurs estimateurs minimax. Dans un autre contexte, celui de The very complex problem of local completeness l’estimation d’une moyenne pour une and of locally maximal clones on infinite distribution de loi normale en plusieurs universes was reduced to a few more dimensions, on sait que lorsque la dimension manageable cases. The completeness problem excède deux, on peut améliorer l’estimateur for uniformly delayed circuits over a finite at-

CRM Annual Report 1999-2000 69 R e s e a r c h P r o g r a m m e s least-four-letter alphabet was advanced. The simplicity of the lattice of clones and the Roch Roy description of all Mal’tsev clones on a finite at- On Time Series Analysis and Modelling least-three-element universe was studied. Roch Roy’s main research interest is time series Hyperalgebras. A hyperalgebra on A is an analysis and modelling. Time series analysis algebraic structure with values in the set P of continues to be a major field of interest in nonvoid subsets of A. I. Rosenberg studied them statistical research as almost scientific discipline as C-isotone algebras on P which allowed a is concerned with data collected over time. His universal algebra approach to hyperalgebras and recent research was mostly concentrated on the lead to interesting problems on C-isotone clones following projects: on P. In particular, hypergroups on A can be • Tests for independence of two possibly studied as C-isotone monoids on P. nonstationnary multivariate time series and application in economic and finance; Christiane Rousseau • Étude qualitative et bifurcations dans les Goodness of fit tests for multivariate time équations différentielles ordinaires series models; • Study of the properties of a class of Un premier aspect porte sur les problèmes de generalized linear regression models for finitude des cycles limites (cyclicité finie) dans describing time series of counts and les bifurcations des champs de vecteurs du plan. application in epidemiology; Ce problème est important dans l’étude des • bifurcations génériques de champs de vecteurs Modelling of non-linear time series using mais aussi pour compléter la partie finitude du weak ARMA representations. 16e problème de Hilbert pour les systèmes During the past year, with the Ph.D. student quadratiques. Un grand programme commencé Pierre Duchesne, he has developed a class of par C. Rousseau, conjointement avec F. consistent tests for the hypothesis of independent Dumortier et R. Roussarie en 1991, montre que la errors against the alternative of serial solution du problème découle de la cyclicité finie dependence of an arbitrary form for the de 121 graphiques du plan. Deux progrès très multivariate autoregressive models with significatifs ont été accomplis: le premier avec la explanatory variables that are also called thèse de H. Zhu (décembre 1999) qui montre la dynamic simultaneous equation models in cyclicité finie de graphiques génériques ayant un econometrics. point nilpotent de type elliptique ou selle, le deuxième avec F. Dumortier et Y. Ilyashenko où Gert Sabidussi un principe de « prolongement analytique » Graphes eulériens et automorphismes de permet de montrer aisément la cyclicité finie de graphes graphiques apparaissant dans des familles Graphes eulériens : Études des graphes 4- continues de graphiques. Des applications de ces réguliers. Inspiré par l'importance de ces théorèmes montrent la cyclicité finie d’environ graphes pour la théorie des nœuds et par le fait 35 graphiques parmi les 121 du programme ci- qu'on connaît peu de choses sur leurs propriétés dessus. combinatoires, nous avons fait une étude Un deuxième aspect porte sur les critères approfondie de deux paramètres combinatoires d’intégrabilité et de linéarisabilité d’un champ importants, le nombre chromatique et le nombre de vecteurs polynomial au voisinage d’un point de stabilité, pour plusieurs classes de graphes 4- de selle. Des travaux préliminaires montrent une réguliers. Pour les deux paramètres il y a des organisation remarquable des strates de champs valeurs « naturelles », et notre recherche porte intégrables et linéarisables. Le travail se poursuit sur l'existence d'algorithmes efficaces pour pour expliquer ce phénomène. La démarche décider si un graphe 4-régulier donné (avec ou consiste à regarder l’influence des invariants de sans contraintes additionnelles) atteint les Martinet-Ramis pour la classification analytique valeurs naturelles. Le résultat principal de des points de selle résonants et des col-nœuds l'étude est que pour les deux paramètres le lorsqu’on perturbe les valeurs propres. Dans ce problème s'avère NP-complet. projet C. Rousseau collabore avec C. Christopher Automorphisme : Pseudo-similarité/similarité. Ici (Plymouth, UK), P. Mardesic et R. Roussarie on étudie des questions découlant de la théorie (Dijon).

70 Annual Report 1999-2000 CRM R e s e a r c h P r o g r a m m e s de reconstruction de graphes. Si en supprimant porte sur la partie finitude du 16e problème de deux arêtes d'un graphe (une à la fois) on obtient Hilbert concernant les cycles limites. deux graphes isomorphes (pseudo-similarité), les deux arêtes sont-elles dans la même orbite Elisa Shahbazian sous l'action du groupe d'automorphismes du Data Fusion graphe (similarité)? En général la réponse est Elisa Shahbazian’s main area of expertise is Data négative, mais elle est affirmative si le nombre Fusion architectures, and how the data fusion d'orbites du graphe est petit. Jusqu'à quel capabilities should be integrated within large nombre d'orbites les deux types de similarité systems. coïncident-ils? Ce qui est important dans ce genre de questions n'est pas nécessairement une Since 1994, she has been responsible for réponse finale mais les méthodes utilisées pour conception, prioritization, and coordination of reconnaître la similarité de deux arêtes (ou all R&D activities at Lockheed Martin Canada. These activities involve development of d'autres éléments) d'un graphe. Plusieurs 4 méthodes puissantes de ce type ont été intelligent decision support technologies for C I développées au cours de notre étude. applications (Data Fusion – levels 1, 2, 3 & 4, Resource Management, Imaging, etc.), and the David Sankoff engineering infrastructure for the establishment Biomathématique et sociolinguistique of these technologies on board the naval and airborne platforms of Canada, and David Sankoff’s research involves the diversification of these capabilities into formulation of mathematical models and the commercial applications such as Intelligent development of analytical methods in the Transportation and Remote Sensing. sciences and humanities. This includes the design of algorithms for problems in Ronald Stern computational biology, applied probability for Nonsmooth Analysis: Theory and Applications phylogenetic analysis of evolution, and statistical methodology for studying R.J. Stern’s general area of interest is nonsmooth grammatical variation and change in speech analysis and control theory. A general goal in communities. Recent work has focused on the control problems is to design a feedback law, evolution of genomes as the result of which achieves some desired behaviour. chromosomal rearrangement processes and on Examples include problems of stabilization in a formal models for bilingual syntax. dynamical system, steering a trajectory to a target set in minimal time, or minimizing a cost Dana Schlomiuk functional subject to some dynamic constraints. Études locales et globales de champs de Even in some very simple models of such vecteurs analytiques problems, however, there is generally no classical (e.g., continuous or smooth) feedback Les travaux de Dana Schlomiuk portent sur des synthesis. The root cause of this is the fact that problèmes locaux (problème de centre) ainsi que in optimal control, the value function is sur la géométrie globale de certaines familles de generally nonsmooth, while in problems of champs de vecteurs polynomiaux ou analytiques stabilization, one only has a generalized dans le plan. Ces travaux visent en particulier à (nonsmooth) Lyapunov function available. Dr. donner une base conceptuelle nouvelle pour les Stern’s present research interests involve champs de vecteurs polynomiaux dans le plan, applying the methods of nonsmooth analysis to permettant d’en dégager des traits such feedback design problems, in order to caractéristiques de la dynamique doublement obtain solutions in a generalized framework. globale (on s’intéresse aux champs dans toute l’étendue du plan et cela pour des familles John Toth dépendant de paramètres) afin d’unifier des résultats épars de la littérature et d’en obtenir I am interested in questions related to spectral des nouveaux. Un trait caractéristique de ces statistics of quantum Hamiltonians and in travaux est l’usage des méthodes problems of quantum chaos for integrable multidisciplinaires : analytiques, algébriques, systems. géométriques (plus particulièrement algébro- géométriques). Un autre volet du projet en cours

CRM Annual Report 1999-2000 71 R e s e a r c h P r o g r a m m e s

Pierre Valin Applications of Lie groups to the study of Fusion de données par raisonnement évidentiel difference equations. Toute application de fusion de données doit Exact solutions of non-linear differential contenir 4 fonctions séquentielles : equations, especially those coming from non- • l’enregistrement spatio-temporel, linear optics. • un mécanisme d’association pour corréler Lie algebra contractions and the separation of les nouvelles données avec des objets variables. existants, Classification of Lie algebras and their • l’estimation de l’identification (ID) (ou subalgebras. fusion d’attributs) obtenue par un raisonnement évidentiel de tous les attributs. Keith Worsley • Les attributs peuvent provenir d’images, de The Geometry of Random Images in Medicine capteurs de type radar, de senseurs and Astrophysics intelligents, ou d’algorithmes. The Euler characteristic of the excursion set of a La présente recherche se concentre sur la random field is a tool that has been used over troisième fonction la plus importante, celle de the last decade to analyse positron emission l’estimation de l’identité, à travers classifieurs tomography (PET) images, functional magnetic (Bayes, réseaux de neurones, etc.) et la logique resonance images (fMRI), galaxy density maps de Dempster-Shafer. and the cosmic microwave background, thought to originate from the creation of the universe. Luc Vinet These images are modelled as a Gaussian Physique théorique et combinatoire algébrique random field, and the excursion set is the set of points where the field exceeds some fixed Les objectifs principaux des projets de recherche threshold value. The Euler characteristic, which de Luc Vinet sont: counts the number of connected components of • de développer les outils théoriques the excursion set minus the number of “holes”, nécessaires à la résolution des modèles is the basis of a proposed estimator of the importants de la physique des systèmes number of “signals” in the image. I have quantiques à plusieurs corps; extended the theory developed by Adler (1981), • d’étendre la théorie algébrique des fonctions The Geometry of Random Fields, to: a) include a spéciales. boundary correction for the expected Euler Deux résultats dignes de mention ont été characteristic, which leads to a highly accurate P obtenus par Luc Vinet et ses collaborateurs en -value for the field maximum; b) χ2, t and F 1999-2000. Il a montré en utilisant les fields; c) searching over smoothing kernel width transformations de Darboux qu’une classe as well as location, so we can estimate the extent importante de polynômes de Koornwinder avec of the signal (joint work with David Siegmund); a b δ δ fonction de poids w(x) = x (1-x) +M0 (x) + M1 d) knots in the excursion set. (1-x) obéissent à des équations différentielles de rang élevé. Jean-Paul Zolézio Il a aussi examiné certains aspects des Coques et dérivabilité polynômes de Krall-Sheffer. Il s’agit de Le premier volet de mes recherches consiste en polynômes à deux variables qui généralisent les la démonstration de la dérivabilité par rapport polynômes orthogonaux classiques à une au domaine dans l’équation des ondes pour des variable. Luc Vinet a montré avec ses seconds membres réguliers. On caractérise la collaborateurs que ces polynômes sont reliés à dérivée comme solution d’un problème des modèles superintégrables sur des espaces à caractéristique au moyen de la dérivée normale courbure constante. de la solution. On établit une condition Pavel Winternitz nécessaire d’optimalité d’un domaine en Group Theoretical Methods in Physics and utilisant la dérivée de forme. Le cas Neumann Non-linear Phenomena in Physics est également étudié. Field of research: Mathematical physics, Les travaux de L. Lasiecka, J-L. Lions et R. symmetries and non-linear phenomena. Triggiani sur l’équation des ondes (1986) donnent une régularité de la dérivée normale,

72 Annual Report 1999-2000 CRM R e s e a r c h P r o g r a m m e s qui ne résulte pas de la régularité de la solution. souhaite dériver les solutions par rapport au Cette régularité cachée permet à l’équation domaine. Pour ce faire, nous utilisons les caractéristique de « survivre » lorsqu’on baisse la méthodes développées pour la dérivabilité par régularité du second membre. On montre que la rapport au domaine dans l’équation des ondes. solution de ce problème est la dérivée par Le problème réside dans l’absence de résultat de rapport au domaine, également dans le cas où le régularité et l’absence de régularité cachée. On second membre est peu régulier. démontre un résultat analogue à la dérivabilité Dans un second volet, je m’intéresse à la cachée de l’équation des ondes par des vibration d’une coque précontrainte. Une coque méthodes de type extracteur, la régularité est contrainte par un grand déplacement et une intérieure étant obtenue par la théorie des semi- petite déformation. On calcule au moyen d’un groupes. logiciel calcul formel-calcul numérique les Parmi les développements futurs, on envisage le positions d’équilibre statique des coques de type modèle exact p(d,∞) pour les coques Adèle et logiciel S3CS. On étudie ensuite la précontraintes. On envisage également de vibration de la coque autour de cette position généraliser les résultats de dérivabilité par d’équilibre stable. La modélisation est effectuée rapport au domaine à une plus grande classe au moyen de la fonction distance orientée. d’équations hyperboliques en extrayant les L’équation obtenue est de type hyperbolique, on hypothèses minimales.

CRM Annual Report 1999-2000 73 Collaborations

Within its general mandate of promoting Programme, described in the next section. mathematical research, the CRM maintains a Another one is the CRM-FI prize awarded in wide network of collaborations at the local, recognition of outstanding accomplishments in national, and international levels. the mathematical sciences in Canada. It was created in 1994. This year's winner is I.M. Sigal of the University of Toronto. The administrative A National Institute responsibility in this matter alternates each year The CRM is strongly committed to its national between the CRM and the FI. Scientific mission. The CRM takes measures to ensure that collaboration continues between the FI and the the largest possible number of scientists across CRM, with a joint workshop in symplectic Canada benefit from its activities and become geometry and topology, during the spring of involved in their planning. For instance, it 2001. appoints to its Advisory Committee eminent Canadian scientists from various parts of the National Programme Committee country; it is present at all important forums The three Canadian Institutes in the where the future directions of the Canadian Mathematical Sciences, CRM, Fields, and PIms, mathematical sciences are discussed; it urges its have initiated a new programme for the support organisers to make efforts to ensure the of joint activities of a national stature in the participation of the Canadian specialists in their mathematical sciences. This programme, funded activities; it organises and supports scientific to the tune of $100,000 per year, is administered events across the country; it collaborates with by a National Programme Committee of Canadian institutes, societies and associations. A members from the three institutes which makes specific budget is set aside each year for the recommendations to the three directors. The participation of Canadian graduate students in programme has many mandates, the first being its programmes. The CRM is the only national to fund conferences and workshops in the institute which operates in the two official mathematical sciences across Canada. These languages of Canada and it is highly visible on funds are essentially allocated to activities that the international scene. In keeping with its fall outside the main purview of the three national role, it co-ordinates its activities with institutes, or that would benefit from joint the Fields Institute, PIms, the Canadian institute funding. The programme also aims to Mathematical Society (CMS), the Canadian support activities that are held at the meetings of Applied and Industrial Mathematics Society the three mathematical science societies: CMS, (CAIMS), the Statistical Society of Canada (SSC), CAIMS, and SSC, as well as to support the the Canadian Association of Physicists (CAP), participation of graduate students at these and other societies as well as with other scientific meetings. Finally, it coordinates institutes abroad. international programmes and other ventures where it is advantageous for the three institutes The Fields Institute (FI) and the Pacific to act as a whole. Institute for the Mathematical Sciences Here is the list of the activities sponsored by the (PIms) National Programme in 1999-2000: Since the early 1990’s two other research institutes have joined the CRM on the Canadian Congrès mathématique de l'an 2000 May 5 – 7, 2000, Univ. Laval, Québec scene: Toronto’s Fields Institute (FI), and the Contact : Frédéric Gourdeau Pacific Institute for Mathematical Sciences Western Canada Linear Algebra Meeting (PIms). As well as co-ordinating their scientific May 26 – 27, 2000, Univ. of Manitoba, Winnipeg, Manitoba activities, the three institutes have worked Contact : Pauline van den Driessche closely on a variety of initiatives, the most Special Functions 2000 important of which has been the Mathematics of May 29 - June 9 2000, Arizona State Univ., Tempe, Arizona Information Technology and Complex Systems, Contact : Luc Vinet of which more is described elsewhere in this Annual Meeting 2000 of the Statistical Society report. of Canada There are several other initiatives worthy of June 4 – 7, 2000, Ottawa, Ontario mention. One of these is the National Contact : Duncan Murdoch

74 Annual Report 1999-2000 CRM C o l l a b o r a t i o n s

Math 2000 publications, the CRM Monograph series and (joint meeting SMC-SCMAI) the CRM Proceedings and Lecture Notes. It also June 10 – 13, 2000, McMaster Univ, Hamilton, Ontario has two series with Springer-Verlag, in statistics Topological and Variational Methods in Non- and in mathematical physics. It has publications linear Analysis exchange agreements with Fields Institute, PIms June 19 – 23, 2000, Warsaw, Poland Contact : Wieslaw Krawcewicz (Pacific Institute for the Mathematical Sciences), M.S.R.I. (Mathematical Sciences Research Séminaire de mathématiques supérieures : Institute), the Institute for Mathematics and its Approximation, Complex Analysis and Applications, École Normale Supérieure Potential Theory (France), and Isaac Newton Institute. July 3 – 7, 2000, Univ. de Montréal, Montréal Contact : Aubert Daigneault First Prairie Industrial Problem Solving A Solid Regional Base Workshop All this activity rests on a solid base of August 7 – 11, 2000, Brandon, Manitoba cooperation with universities in the region, in Contact : Lynn Batten particular the Montréal universities, and most 12th Canadian Conference on Computational particularly the Université de Montréal, whose Geometry support for the CRM has been indefatigable. The August 16 – 19, 2000, Fredericton, New Brunswick Université de Montréal releases each year five of Contact : David Bremner its faculty members to work at the CRM, and the CITA/ICAT Meeting support of these faculty members is an essential August 26 – 30, 2000, Toronto, Ontario asset for the CRM's scientific activities. There is Contact : J. Richard Bond in addition a regular programme of teaching CMS Winter Meeting 2000 release with the other Montréal universities, December 10 – 12, 2000, Vancouver, British Columbia bringing the equivalent of another two positions to the CRM each year. On an ad-hoc basis linked Canadian Associations and to the theme programme, the CRM has also been Professional Societies arranging release of research personnel from The CRM maintains close ties with the different nearby universities such as Laval, Sherbrooke, professional societies in the mathematical Queen’s and Ottawa; some of these sciences: CMS, CAIMS, SSC, and CAP. The arrangements are being put on a more president of the CMS is an ex-officio member of permanent footing. The partnerships of the CRM the CRM advisory committee, and together with with the other research institutes in the Montreal the other institutes, the CRM organises special area have been very profitable. More will be said sessions at CMS meetings. The SSC meetings about these in the next section. have been funded through the national programme; as well, the CRM gives out a prize Institut des sciences mathématiques each year jointly with the SSC; similarly, One important vehicle for collaboration with the together with CAP, it awards a prize each year Québec universities is the Institut des sciences in mathematical and theoretical physics. There mathématiques. This institute, which is a section on this year’s prize-winners encompasses most of Québec’s universities, is elsewhere in this report. principally concerned with co-ordinating graduate training. The links with research are International Collaboration obvious, and indeed, the CRM and the ISM have The CRM has exchange protocols with Osaka a long standing partnership, in particular in University, with Seoul's Asia-Pacific Center for offering postdoctoral fellowships, in organising Theoretical Physics, with the Institute of the CRM-ISM colloquium, and in organising Mathematical Sciences at Nankai University, special courses for the CRM’s thematic with the Technical University of Prague and the programmes. University of Rome. In its publications, the CRM is continuing its partnership with the American Mathematical Society, in particular with its two series of joint

CRM Annual Report 1999-2000 75 Industrial Mathematics

The industrial programme of CRM has grown commercial and industrial applications, considerably in the last year; many important information technology, manufacturing, and initiatives were solidified and others were mathematical finance. Each MITACS project launched. belongs to one of these themes, and theme leaders have organized theme meetings (which MITACS will be repeated next year) where technical This network of centres of excellence on details of the research can be discussed more Mathematics of Information Technology And easily than in the general meeting. Complex Systems (MITACS) is one of 18 such Finally, each of the institutes has organized networks set up by the federal government. special events (workshops, seminars, MITACS was put together by the three Canadian mathematical institutes (CRM, Fields, PIms) in conferences) linked to the MITACS projects. In 1998, and research began in the spring of 1999. the case of the CRM, let us note in particular for This year the network will grow with new 2000 the workshop on Selecting and Combining projects such as those of K. Worsley (McGill) Models with Machine Learning Algorithms, and D. Thérien (McGill) located in Montréal. The which has attracted more than 130 participants, MITACS network covers the whole country, including the majority of the world leaders in with the participation of 26 universities, 200 this research area. This workshop is linked to the researchers, 150 students, and more than 75 MITACS research on data-mining, neural companies. The research areas (essentially in networks, and computational statistics. applied mathematics) also cover a large spectrum. The industrial partners of our On the research side, almost all the groups research projects are: Microcell, National Bank of obtained significant results, which has been Canada, NATCAN, Hydro-Québec, Procter & recognized by the MITACS Board through the Gamble, Heart & Stroke Foundation, Medtronic renewal of the projects for 2000-2001. Among the Inc., DND-Valcartier, and Ad-Opt Technologies. projects linked to the CRM, let us note a few The first general annual meeting of the network really interesting results. For example the group was held in June 2000 in Toronto. This large led by B. Jaumard (Poly) has developed new and scale event brought together most of the more powerful optimization algorithms for researchers in the network, a large number of communication channels allocation, taking students (whose travel fees were mostly paid by advantage of Montréal's expertise in operations MITACS), and many of the industrial research applied to telecommunications collaborators. At the conference, results from the networks. The group led by L. Glass (McGill) research groups were presented, but there were has created new atrial fibrillation models, also very interesting presentations from allowing to classify and detect different types of scientists in industry exhibiting their specific atrial fibrillations. The group led by J. Detemple needs in the areas of applied mathematics (McGill) and R. Garcia (UdeM) has produced an covered by the MITACS researchers, and impressive number of published results showing displaying the links that have been established progress in the areas of asset allocation, between MITACS groups and private partners. statistical models of financial time-series, and Students and postdoctoral fellows played a very statistical inference on these series. The group important role at the conference, with a poster led by F. Soumis (Poly) has created a new session and a study group on the industrial version of the GENCOL software for applications of mathematics held before the mathematical programming based on column main sessions. The best poster presentations generation, and the new system, delivered to AD were selected by a panel and received honorary OPT and GIRO, speeds up the solution (up to a and monetary prizes. factor of 10) of scheduling problems. The group led by Y. Bengio (UdeM) has created a successful The next annual meeting will be held in new paradigm for statistical language modeling Montréal in May 2001. These meetings are which beats the performance of models which essential to create new links and maintain have dominated this area for almost 20 years, cohesion between the different researchers of the thanks to the computation power delivered by network, which work on quite varied aspects of the super-computers of the Réseau Québécois de applied mathematics: biomedical research, Calcul de Haute Performance. New learning

76 Annual Report 1999-2000 CRM I n d u s t r i a l M a t h e m a t i c s algorithms for data-mining of large data sets, centres. In all, the process was quite successful, which interest Bell Canada, have also been with the following new projects being funded: designed. The multi-disciplinary group led by D. • Analyse du risque des flottes de véhicules Thérien (McGill), just added to MITACS, will Georges Dionne, CRT work on modeling biological mechanisms such • Modèles à noyaux et modèles probabilistes pour as the response to medications, based on the l’extraction d’informations utiles de grandes patterns of genetic expression. The group led by bases de données K. Worsley (McGill), also just added to MITACS, Yoshua Bengio, CRM will work on the statistical analysis of 3D images • of the brain, using new results from the areas of Nowcasting and Decision Making for wavelets, functional data analysis, and random Environmental Problems fields. Charles Lin, CERCA • Image Segmentation and Characterization Using Network for Computing and Level Set-Based Curve and Surface Evolution, Mathematical Modelling (ncm2) Boundary Detection and Lie Groups. The CRM is one of seven Montreal-based centres Jiri Patera, CRM which together are the members of the Network • Tarification et gestion du revenu en transport for Computing and Mathematical Modelling, aérien. ncm2 (in French: Réseau de calcul et de Patrice Marcotte, CRT and Gilles Savard, modélisation mathématique, rcm2), a unique GERAD collaboration which allows the network to • respond to the needs of industry in a large Design et contrôle optimal de dispositifs number of fields related to a common area of médicaux. computing and mathematical modelling, mostly Dominique Pelletier, CERCA around three major themes: (1) risk • Algorithme d’optimisation pour les problèmes de management, (2) information processing, tournées et d’horaires. imaging and parallel computing, and (3) François Soumis, GERAD transport and telecommunications. • Quality of Service Mapping as an Optimization The ncm2 is in the third year of a 5-year NSERC Problem grant with an average of $600K per year. The network is managed through the CRM. Odile Marcotte, GERAD and Brigitte Kerhervé, UQAM The other centres of the network at the time of creation were the Centre for Research on • Approche hiérarchique et multi-échelles pour la Computation and its Applications (CERCA), the localisation des sources d’activité en MEG/EEG. Centre for Interuniversity Research and Analysis Bernard Goulard, CRM on Organizations (CIRANO), the Centre for There are in addition 9 ongoing projects, of Research on Transportation (CRT), and the which 3 involve CRM researchers. Overall, the Group for Research in Decision Analysis projects have involved the participation of 50 (GERAD). Since then, two new members joined researchers in the network centres, and 60 the network: the Centre de Recherche postdoctoral fellows and graduate students. The Informatique de Montréal (CRIM) and the total value (cash and in-kind) of the Institut National de la Recherche Scientifique- contributions of our partners in 1999-2000 was Télécommunications (INRS-Télécommunica- $1M. The industrial partners of ncm2's research tions). projects are: Ad Opt, ANIQ R&D Inc., National The year 1999-2000 has been rather active for the Bank of Canada, Centre de sécurité civile du Québec, CHUM (Centre hospitalier de ncm2. The major undertaking of the year was a process of project renewal. Indeed, many of the l’Université de Montréal), CLSC Côte-des- initial projects which were associated to the Neiges, Consultants INRO Inc., Environment network were coming to fruition, and so a call Canada, Bombardier, Prévost Car Inc., ADS for proposals was put out. Proposals were Groupe Composites Inc., Groupe Québec- received, refereed, and adjudicated by a Cartier, Hydro-Québec, HydroSoft, Lockheed committee with three network members and Martin Electronic Systems Canada, Montreal three outside members. One constraint imposed Jewish General Hospital, Urgences Santé. was that the projects should involve The ncm2 has pursued a variety of networking collaboration between members of different activities, encouraging integration. In 1999-2000,

the ncm2 organised the following workshops and

CRM Annual Report 1999-2000 77 I n d u s t r i a l M a t h e m a t i c s conferences: Conférences sur les techniques Laboratoires Universitaires Bell d’optimisation pour améliorer la gestion dans le The CRM is an active participant in the domaine de la santé, M. Gendreau and B. Jaumard; Laboratoires universitaires Bell, part of a joint Nowcasting Workshop, Charles Lin (CERCA); project between the ncm2 and Bell. The L’économie et la gestion des risques majeurs, laboratories aim at creating innovations in the field of multimedia research and applications CIRANO/rcm2/Columbia University. (mainly interactive applications aimed at the Also, a series of workshops called Autour de midi general public, electronic commerce applications were organized by J-M. Lina (CRM). Each and new generations of evolved networks) as workshop was made up of a mini-course and a well as at promoting the training of a highly seminar. The first was given by B. Vidakovic qualified, international calibre workforce in (Duke) on Wavelets and statistics, as well as these areas. Functional Data Analysis via Wavelets. Then Wim The guiding principles of the Bell University Sweldens (Bell Laboratories, Lucent Laboratories are: a deep integration with the Technologies) talked about The Lifting Scheme university environment; a balance between and Second Generation Wavelets, followed by exploratory research, applied research and Digital Geometry Processing. Hugh A. Chipman applications development; a multidisciplinary (Waterloo) made two presentations on The State approach. of the Art in Data Mining, and Segmentation via These objectives and guiding principles are Tree Models. Finally A. Arnéodo (CNRS, France) made possible thanks to a $12M investment over gave a mini-course on Analyses des ondelettes et 3 years which will be used to finance research analyses multifractales (ADN, imagerie). projects, to create an endowment fund in order Moreover, there were 2 presentations as part of to recruit elite researchers, and to establish an the series Grandes Conférences: infrastructure. The year 1999-2000 saw the LUB move into its • 3 November 1999 new quarters, financed through 539K$ from the Richard Anthes (University Corporation for laboratory’s infrastructure fund, as well as Atmospheric Research) contributions from the Canadian Foundation for Global Weather Services in 2025 Innovation (740K$) and the Québec government • 25 May 2000 (570K$). The laboratories are distributed over Michel Balinski (Laboratoire d’Économétrie two locations, the main one being in downtown de l’École Polytechnique, Paris) Montréal, next to CIRANO. As well as offices, it contains a state-of-the-art simulation laboratory Axiomatique appliquée : équité et autres for electronic commerce and experimental applications economics. The other component is located at the Université de Montréal, and is devoted to multi-media research. Fifteen research projects are now underway. Of these, 5 are affiliated with the CRM. They are Yoshua Bengio’s Datamining, Rachida Dssouli’s Service Creation Environment: A Quality Driven Service Engineering Methodology, Bernard Goulard’s M3Int: Multi-Media Mathematical Imaging on the Net, and Jiri Patera’s Development of the Aperiodic Encryption Method and Evaluation and Demonstration of a New Family of Cryptographic Systems.

78 Annual Report 1999-2000 CRM Awards, Distinctions, and Landmarks Researchers play a key role in a research centre such as ours and we are particularly proud of the group that we have assembled. Their scientific and academic influence is outstanding. Here is a short list of the main prizes and awards that they have received in the last year.

Nantel Bergeron of York University has the co-supervision of Pavel Winternitz of CRM received a Premier's Research Excellence Award and Jean-Pierre Gazeau of Université de Paris (PREA) from the Ontario Government for the VII. years 2000 through 2005. These prizes are awarded to the best young researchers in François Lalonde of Université du Québec à Ontario. Montréal is a Killam Research Fellow of the Canada Council for the Arts for the years 2000- Michel Delfour of Université de Montréal was 2002. These fellowships are among the most the Meeting Director and Scientific Chair of the distinguished reseach awards in Canada. In Canadian Mathematical Society Winter 1999 1999, he has also delivered a plenary one-hour Meeting. A report on this activity is found talk at the first Canada-China Math Congress in elsewhere in this report. Peking.

Stéphane Durand of Collège Édouard- Christian Léger of Université de Montréal has Montpetit was awarded the first prize of the been awarded the 2000 Excellence in Teaching World Mathematical Year 2000 Poster Award for the Science Sector of the Faculty of Competition of the European Mathematical Arts and Sciences of Université de Montréal. Society. These posters can be seen at http://www.crm.umontreal.ca/math2000/table Colin Rogers of New South Wales University in au.html Australia has been elected Fellow of the Australian Science Academy in 1999. Martin Gander of McGill University gave two prestigious invited talks: Optimized Schwarz Christiane Rousseau of Université de Methods during the 12th International Conference on Montréal received the Abel-Gauthier Prize of the Domain Decomposition Methods at Chiba Association mathématique du Québec (AMQ) as the University in Japan and Why are Schwarz Domain 1999 Personality of the year. The citation Decomposition Methods Slow?, during the mentions that "AMQ wishes to recognize your Householder Symposium XIV at Whistler in British exceptional contribution to the mathematical Columbia. Moreover, Martin has obtained one of community of Québec by your research, your the prestigious positions of the Strategic teaching, as well as your significant implication Programme of Professor-Researcher of the Fonds in extra-academic activities such as the FCAR in Québec. organization of the AMQ math camps and your active participation in many projects for the Thomas Hagedorn of Harvard University has World mathematical year in Québec." Christiane been awarded a Sloan Postdoctoral Fellowship also received the Prize for the best co- in computational molecular biology for the years supervision of a thesis of the Québec Ministry of 1999-2001. His work at CRM is under the International Relations and the Consulate of supervision of David Sankoff. France in Québec. This prize, awarded jointly to Robert Roussarie in May 2000, recognizes their Stéphane Lafortune of Université de Montréal work in the co-supervision of Louis-Sébastien won the Prize for the best thesis with co- Guimond’s thesis. supervision of the Québec Ministry of International Relations and the Consulate of Dana Schlomiuk of Université de Montréal is a France in Québec. This prize is awarded to the member of the Council of NSERC (1998-2001). In best thesis done under the co-supervision of a 1999, she has presided over the Selection Director from Québec and one from France. The Committee for the Gold Medal in Science and thesis entitled Symétries et intégrabilités des Engineering. She is also Chair of the Canadian équations aux différences finies was written under

CRM Annual Report 1999-2000 79 A w a r d s , D i s t i n c t i o n s , a n d L a n d m a r k s

Mathematical Society's Selection Committee for of the one hundred recipients come from the best doctoral thesis (1998-2000). Canadian universities.

John Toth of McGill University has been Keith Worsley of McGill University is a Killam awarded a Sloan Research Fellowship. Only two Research Fellow of the Canada Council for the Arts for the years 2000-2002.

80 Annual Report 1999-2000 CRM Publications The CRM publishes monographs, lecture notes, proceedings, software, videos and research reports. It has several collections. The in-house collection Les Publications CRM offers many titles in both English and French. The CRM also has publishing agreements with the American Mathematical Society (AMS), Springer-Verlag and International Press. 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-Verlag publishes the CRM Series in Mathematical Physics and the CRM Subseries of the Springer Lecture Notes in Statistics. During the year 1999-2000, the first three volumes of the series in Physics appeared and the first two volumes of the Lecture Notes in Statistics were delivered to the publisher. The following list of “Recent Titles” contains books that have appeared during the year 1999-2000 or that will be published soon. Recent Titles

AMS: CRM Monograph Series • Alan Coley, Decio Levi, Robert Milson, Colin • Spencer J. Bloch, Higher Regulators, Algebraic Rogers & Pavel Winternitz (eds.), Bäcklund K-Theory, and Zeta Functions of Elliptic Curves, and Darboux Transformations: The Geometry of vol. 11, (to appear). Soliton Theory, (to appear). • Masayoshi Miyanishi, Open Algebraic • John McKay & Abdellah Sebbar (eds.), The Surfaces, vol. 12, (to appear). Moonshine Workshop, (to appear). • Michael Baake & Robert V. Moody (eds.), Directions in Mathematical Quasicrystals, vol. Springer-Verlag: CRM Series in 13, (to appear). Mathematical Physics • Joel Feldman, Horst Knörrer & Eugene • Jan Felipe van Diejen & Luc Vinet (eds.), Trubowitz, Fermionic Functional Integrals and Calogero-Moser-Sutherland Models, 1999. the Renormalization Group (to appear). • Yvan Saint-Aubin & Luc Vinet (eds.), • Eyal Z. Goren, Lectures on Hilbert Modular Algebraic Methods in Physics - A Symposium Varieties and Modular Forms (to appear). for the 60th Birthday of Jíri Patera and Pavel • Jose I. Burgos, The Regulators of Beilinson and Winternitz, 2000. Borel (to appear). • Yvan Saint-Aubin & Luc Vinet (eds.), Theoretical Physics at the End of the XXth AMS: CRM Proceedings & Lecture Notes Century. Lecture Notes of the CRM Summer • Pierre Hansen & Odile Marcotte (eds.), School, June 27-July 10, 1999, Banff, Alberta, Graph Colouring and Applications, vol. 23, Canada, (to appear). 1999. • Roman Jackiw, (A Particle Field Theorist’s) • B. Brent Gordon, James D. Lewis, Stefan Lecture on (Supersymmetric, Non-Abelian) Müller-Stach, Shuji Saito & Noriko Yui Fluid Mechanics (and d-Branes), (to appear). (eds.), The Arithmetic and Geometry of Algebraic Cycles, vol. 24, 2000. CRM Subseries of the Springer-Verlag • Decio Levi & Orlando Ragnisco (eds.), SIDE Series: Lecture Notes in Statistics III - Symmetry and Integrability of Difference • S.Ejaz Ahmed & Nancy Reid (eds.), Empirical Equations, vol. 25, 2000. Bayes and Likelihood Inference, (to appear). • John Harnad, Gert Sabidussi & Pavel • Marc Moore (ed.), Spatial Statistics, (to Winternitz (eds.), Integrable Systems: From appear). Classical to Quantum, vol. 26 (to appear). • Israel M. Sigal & Catherine Sulem, Nonlinear Les Publications CRM Dynamics and Renormalization Group, vol. 27, • James G. Huard & Kenneth S. Williams (to appear). (eds.), The Collected Papers of Sarvadaman • J.C. Taylor (ed.), Topics in Probability and Lie Chowla, I, II, III, 2000. Groups : Boundary Theory, vol. 28, (to appear).

CRM Annual Report 1999-2000 81 P u b l i c a t i o n s

Previous Titles

AMS: CRM Monograph Series • Peter G. Greiner, Victor Ivrii, Luis A. Seco & • James D. Lewis, A Survey of the Hodge Catherine Sulem (eds.), Partial Differential Conjecture, 2e Édition (with an appendix by Equations and their Applications (Toronto, B. Brent Gordon), vol. 10, 1999. 1995), vol. 12, 1997. • Yves Meyer, Wavelets, Vibrations and Scaling, • Luc Vinet (ed.), Advances in Mathematical vol. 9, 1997. Sciences: CRM’s 25 Years (Montréal, 1994), • Ioannis Karatzas, Lectures on Mathematics of vol. 11, 1997. Finance, vol. 8, 1996. • Donald E. Knuth, Stable Marriage and its • John Milton, Dynamics of Small Neural Relation to Other Combinatorial Problems. An Populations, vol. 7, 1996. Introduction to the Mathematical Analysis of • Eugene B. Dynkin, An Introduction to Algorithms, vol. 10, 1996. Branching Measure-Valued Processes, vol. 6, • Decio Levi, Luc Vinet, & Pavel Winternitz 1994. (eds.), Symmetries and Integrability of • Andrew M. Bruckner, Differentiation of Real Difference Equations (Estérel, 1994), vol. 9, Functions, vol. 5, 1994. 1995. • David Ruelle, Dynamical Zeta Functions for • Joel S. Feldman, Richard Froese, & Lon M. Piecewise Monotone Maps of the Interval, vol. 4, Rosen (eds.), Mathematical Quantum Theory 1994. II : Schrödinger Operator (Vancouver, 1993), • V. Kumar Murty, Introduction to Abelian vol. 8, 1995. Varieties, vol. 3, 1993. • Joel S. Feldman, Richard Froese, & Lon M. • Maximilian Ya. Antimirov, Andrei A. Rosen (eds.), Mathematical Quantum Theory I: Kolyshkin, & Rémi Vaillancourt, Applied Many-Body Theory and Group Theory Integral Transforms, vol. 2, 1993. (Vancouver, 1993), vol. 7, 1994. • Dan V. Voiculescu, Kenneth J. Dykema, & • Guido Mislin (ed.), The Hilton Symposium Alexandru Nica, Free Random Variables, vol. 1993 : Topics in Topology and Group Theory 1, 1992. (Montréal, 1993), vol. 6, 1994. • Donald A. Dawson (ed.), Measure-valued AMS: CRM Proceedings & Lecture Notes Processes, Stochastic Partial Differential • Jan Felipe van Diejen & Luc Vinet (eds.), Equations and Interacting Systems (Montréal, Algebraic Methods and q-Special Functions, vol. 1992), vol. 5, 1994. 22, 1999. • Hershy Kisilevsky & M. Ram Murty (eds.), • Michel Fortin (ed.), Plates and Shells, vol. 21, Elliptic Curves and Related Topics (Sainte- 1999. Adèle, 1992), vol. 4, 1994. • Katie Coughlin (ed.), Semi-Analytic Methods • Andrei L. Smirnov & Rémi Vaillancourt for the Navier-Stokes Equations, vol. 20, 1999. (eds.), Asymptotic Methods in Mechanics, vol. • Rajiv Gupta & Kenneth S. Williams (eds.), 3, 1993. Number Theory, vol. 19, 1999. • Philip D. Loewen, Optimal Control via • Serge Dubuc & Gilles Deslauriers (eds.), Nonsmooth Analysis, vol. 2, 1993. Spline Functions and the Theory of Wavelets, • M. Ram Murty (ed.), Theta Functions. From vol. 18, 1999 the Classical to the Modern, vol. 1, 1993. • Olga Karlampovich (ed.), Summer School in Group Theory (Banff, 1996), vol. 17, 1998. Springer-Verlag: CRM Series in • Alain Vincent (ed.), Numerical Methods in Mathematical Physics Fluid Mechanics (Montréal, 1995), vol. 16, • Robert Conte (ed.), The Painlevé Property: One 1998. Century Later, 1999 • François Lalonde (ed.), Geometry, Topology • Richard MacKenzie, Manu B. Paranjape & and Dynamics, (Montréal, 1995), vol. 15, 1998. Wojciech J. M. Zakrzewski (eds.), Soliton: • John Harnad & Alex Kasman (eds.), The Properties, Dynamics, Interactions, Appli- Bispectral Problem (Montréal, 1997), vol. 14, cations, 1999 1998. • Luc Vinet & Gordon Semenoff (eds.), • Michel Delfour (ed.), Boundaries, Interfaces Particles and Fields (Banff, 1994), CRM Series and Transitions (Banff, 1995), vol. 13, 1998.

82 Annual Report 1999-2000 CRM P u b l i c a t i o n s

in Mathematical Physics, Springer, New • David W. Rand & Tatiana Patera, Le York, 1998. Concordeur: un logiciel de concordances pour le Macintosh, Montréal, 1991 (software and user Les Publications CRM guide). • Michael Barr & Charles Wells, Category • Véronique Hussin (ed.), Lie Theory, Theory for Computing Science, 1999 Differential Equations and Representation • Maximilian Ya. Antimirov, Andrei A. Theory (Montréal, 1989), Montréal, 1990. Kolyshkin & Rémi Vaillancourt, • John Harnad & Jerrold E. Marsden (eds.), Mathematical Models for Eddy Current Testing, Hamiltonian Systems, Transformation Groups 1998. and Spectral Transform Methods (Montréal, • Xavier Fernique, Fonctions aléatoires 1989), Montréal, 1990. gaussiennes, vecteurs aléatoires gaussiens, • M. Ram Murty (ed.) Automorphic Forms and Montréal, 1997. Analytic Number Theory (Montréal, 1989), • Faqir Khanna & Luc Vinet (eds.), Field Montréal, 1990. Theory, Integrable Systems and Symmetries, • Wendy G. McKay, Jirí Patera & David W. Montréal, 1997. Rand, Tables of Representations of Simple Lie • Paul Koosis, Leçons sur le théorème de Beurling Algebras. I. Ex-ceptional Simple Lie Algebras, at Malliavin, 1996. Montréal, 1990. • David W. Rand, Concorder Version Three: • Anthony W. Knapp, Representations of Real Concordance Software for the Macintosh, Reduc-tive Groups, Montréal, 1990. Montréal, 1996 (software and user guide). • Wendy G. McKay, Jirí Patera & David W. • Decio Levi, Curtis R. Menyuk, & Pavel Rand, SimpLie User’s Manual–Macintosh Winternitz, Self-Similarity in Stimulated Software for Representations of Simple Lie Raman Scattering (Montréal, 1993), Montréal, Algebras, Montréal, 1990 (software and user 1994. guide). • Jacques Gauvin, Theory of Nonconvex • Francis H. Clarke, Optimization and Programming, Montréal, 1994. Nonsmooth Analysis, Montréal, 1989. • Rémi Vaillancourt, Compléments de • Hedy Attouch, Jean-Pierre Aubin, Francis mathématiques pour ingénieurs, Montréal, Clarke & Ivar Ekeland (eds.), Analyse non 1993. linéaire (Perpignan, 1987), Montréal & • Robert P. Langlands & Dinakar Gauthiers-Villars, Paris, 1989. Ramakrishnan (eds.), The Zeta Functions of • Samuel Zaidman, Une introduction à la théorie Picard Modular Surfaces (Montréal, 1988), des équations aux dérivées partielles, Montréal, Montréal, 1992. 1989. • Florin N. Diacu, Singularities of the N-Body • Lucien Le Cam, Notes on Asymptotic Methods Problem, Montréal, 1992. in Statistical Decision Theory, Montréal, 1974. • Jacques Gauvin, Théorie de la programmation mathématique non convexe, Montréal, 1992. AMS/International Press • Pierre Ferland, Claude Tricot, & Axel van de • Duong H. Phong, Luc Vinet & Shing-Tung Walle, Analyse fractale: Application W indows Yau (eds.), Mirror Manifolds and Geometry, ™ 3.x d’initiation aux ensembles fractals, AMS/IP Studies in Advanced Mathematics, Montréal, 1992 (software and user guide). Amer. Math. Soc., Providence, RI, Internat. • Stéphane Baldo, Introduction à la topologie des Press, Cambridge, MA, & CRM, Montréal, ensembles fractals, 1991. 1998(vol.10). • Robert Bédard, Groupes linéaires algébriques, Montréal, 1991. Collection de la Chair Aisenstadt • Rudolf Beran & Gilles R. Ducharme, • Yuri I. Manin, Quantum Groups and Asymptotic Theory for Bootstrap Methods in Noncommutative Geometry, Les Publications Statistics, Montréal, 1991. CRM, 1988. • James D. Lewis, A Survey of the Hodge • Laurent Schwartz, Semimartingales and Their Conjecture, Montréal, 1991. Stochastic Calculus on Manifolds, Presses de • David W. Rand & Tatiana Patera, Concorder: l’Université de Montréal, 1984. Concordance Software for the Macintosh, Montréal, 1991 (software and user guide).

CRM Annual Report 1999-2000 83 P u b l i c a t i o n s

• Yuval Ne’eman, Symétries, jauges et variétés de • Mark Kac, Quelques problèmes mathématiques groupe, Presses de l’Université de Montréal, en physique statistique, Presses de l’Université 1979. de Montréal, 1974. • R. Tyrrell Rockafellar, La théorie des sous- • Sybreen de Groot, La transformation de Weyl gradients et ses applications à l’optimisation, et la fonction de Wigner: une forme alternative de fonctions convexes et non convexes, Presses de la mécanique quantique, Presses de l’Université de Montréal, 1979. l’Université de Montréal, 1974. • Jacques-Louis Lions, Sur quelques questions d’analyse, de mécanique et de contrôle optimal, Miscellaneous Presses de l’Université de Montréal, 1976. • Pierre Ferland, Claude Tricot, & Axel van de • Donald E. Knuth, Mariage stables et leurs Walle, Fractal analysis user’s guide. relations avec d’autres problèmes combinatoires, Introduction to fractal sets using Windows ™ Presses de l’Université de Montréal, 1976. 3.x., Amer. Math. Soc., Providence, RI & • Robert Hermann, Physical Aspects of Lie Centre de recherches mathématiques, Group Theory, Presses de l’Université de Montréal, 1994. Montréal, 1974.

84 Annual Report 1999-2000 CRM P u b l i c a t i o n s

Research Reports

[CRM-2566] Stéphane Lafortune, Pavel to the Square of the Sum: Exact and Asymptotic Winternitz & Luis Martina, Point Symmetries of Results, October 1999. Generalized Toda Field Theories, January 2000. [CRM-2631] Paul Bracken & A. Michel [CRM-2615] Luc Vinet, Oksana Yermolayeva & Grundland, On the Bäcklund Transformation and Alexei Zhedanov, A New Family of Krall the Theorem of Permutability for the Generalized Polynomials, June 1999. Weierstrass System, October 1999. [CRM-2616] Luc Vinet & Alexei Zhedanov, [CRM-2632] Louis-Sébastien Guimond & Jirí Spectral Transformations of the Laurent Biorthogonal Patera, Proving the Deterministic Period Breaking of Polynomials, June 1999. Linear Congruential Generators Using Two Tile Quasicrystals, October [CRM-2617] Luc Vinet & Alexei Zhedanov, 1999. Spectral Transformations of the Laurent Biorthogonal [CRM-2633] Paul Koosis, Hartree's Theorem on Polynomials. II. Pastro polynomials, June 1999. Existence of the Quantum Defect, October 1999. [CRM-2618] Vyacheslav Spirodonov & Alexei [CRM-2634] Vladimir Dorodnitsyn, Roman Zhedanov, Classical Biorthogonal Rational Kozlov & Pavel Winternitz, Lie Group Functions on Elliptic Grids, June 1999. Classification of Second-Order Ordinary Difference [CRM-2620] Paul Bracken, Renormalization of Equations, October 1999. Scalar φ4 Theory to Second Order in the Coupling [CRM-2635] Stéphane Lafortune, Basile Constant, July 1999. Grammaticos, Alfred Ramani & Pavel [CRM-2621] Paul Bracken, Analysis of a Winternitz, Discrete Systems Related to Equations of Renormalization Group Equation by the Prolongation the Painlevé-Gambier Classification, November Method, July 1999. 1999. [CRM-2622] Eric McSweenn & Pavel Winternitz, [CRM-2636] Lubomir T. Dechevsky, Atomic Integrable and Superintegrable Hamiltonian Systems Decomposition of Function Spaces and Fractional in Magnetic Fields, August 1999. Integral and Differential Operators, November [CRM-2623] Miloslav Havlícek, Jirí Patera & 1999. Edita Pelantovà, On Lie Gradings. III. Gradings of [CRM-2637] Lubomir T. Dechevsky, Near- the Real Forms of Classical Lie Algebras, August Degenerate Finite Element and Lacunary 1999. Multiresolution Methods of Approximation, [CRM-2624] Louis-Sébastien Guimond, Jirí November 1999. Patera, Zuzana Masáková & Edita Pelantová, [CRM-2638] Zuzana Masáková, Jirí Patera & Deterministically Broken Periodicity of Linear Edita Pelantová, Lattice-like Properties of Congruential Generators Using Quasi-Crystals, Quasicrystal Models with Quadratic Irrationalities, August 1999. November 1999. [CRM-2625] Paul Bracken & A. Michel [CRM-2639] Zuzana Masáková, Jirí Patera & Grundland, Multi-Soliton Solutions of the Edita Pelantová, S-convexity, Model Sets and Their Generalized Weierstrass System, September 1999. Relation, November 1999. [CRM-2626] Hubert de Guise & Marc de [CRM-2640] Zuzana Masáková, Jirí Patera & Montigny, Grading Preserving Contractions of Edita Pelantová, Substitution Rules for Cut-and- Semi-Simple Lie Algebras and Central Extensions, Project Sequences, November 1999. September 1999. [CRM-2641] Jean-François Angers, Credence and [CRM-2627] Richard Fournier & Stephan Robustness Behavior, November 1999. Ruscheweyh, A Generalization of the Schwarz- [CRM-2642] Jean-François Angers, Bayesian Carathéodory Reflection Principle and Spaces of Inference for the Location Parameter of a Student-t Pseudo-Metrics, September 1999. Density, November 1999. [CRM-2628] Éric Marchand & François Perron, [CRM-2643] Marc Fredette & Jean-François Improving on the MLE of a Bounded Normal Mean, Angers, A New Approximation of the Posterior September 1999. Distribution of the log-odds Ratio, November 1999. [CRM-2629] Bourama Toni, Bifurcations of Limit [CRM-2644] Paul Bracken, A Differential Cycles from Hamiltonian Isochrones: A Darboux Geometric Approach to Helmholtz Equations: An Linearization Approach, September 1999. Application to a Space With a Nontrivial Riemannian [CRM-2630] Aimé Fuchs, Anatole Joffe & Jozef L. Metric, December 1999. Teugels, Expectation of the Ratio of a Sum of Squares

CRM Annual Report 1999-2000 85 P u b l i c a t i o n s

[CRM-2645] Zora Thomova & Pavel Winternitz, [CRM-2674] L. Martina, Stéphane Lafortune & Separation of Variables and Darboux Pavel Winternitz, Point Symmetries of Generalized Transformations, January 2000. Toda Field Theories. II. Applications of the [CRM-2646] Jean-François Angers & Atanu Symmetries, March 2000. Biswas, Estimation of Monotone Function for Data [CRM-2675] Paul Arminjon & Amik St-Cyr, New on Records, January 2000. 2 and 3-dimensional non-oscillatory central finite [CRM-2647] Andrei A. Kolyshkin & Rémi volume methods on staggered Cartesian grids March Vaillancourt, Series Solution of an Eddy Current 2000. Problem for a Sphere With Varying Conductivity and [CRM-2676] Ervig Lapalme & Yvan Saint-Aubin, Permeability Profiles, December 1999. Crossing Probabilities on Same-Spin Clusters in the [CRM-2648] Huaiping Zhu & Christiane Two-Dimensional Ising Model, May 2000. Rousseau, Finite cyclicity of Graphics With a [CRM-2677] Paul Bracken, The Cartan Form and Nilpotent Singularity of Saddle or Elliptic Type, its Relation to the Inverse Problem of the Calculus of December 1999. Variations and the Helmotz Equations, May 2000. [CRM-2649] Dinh Tuan Pham, Roch Roy & Lyne [CRM-2716] Yoshua Bengio & C. Dugas, Learning Cédras, Tests for Non-Correlation of Two Simple Non-Stationarities With Hyper-Parameters Cointegrated ARMA Time Series, January 2000. [CRM-2717] Yoshua Bengio, Continuous [CRM-2650] Ryuichi Ashino, Christopher Heil, Optimization of Hyper-Parameters 1999 Michihiro Nagase & Rémi Vaillancourt, [CRM-2718] C. Nadeau & Yoshua Bengio, Microlocal Filtering With Multiwavelets, January Inference and the Generalization Error, 1999 2000. [CRM-2719] Yoshua Bengio & R. Ducharme, A [CRM-2651] Ryuichi Ashino, Michihiro Nagase Neural Probabilistic Language Model, 2000 & Rémi Vaillancourt, A Survey of the MATLAB [CRM-2720] Steven Boyer & X. Zhang, A Proof of ODE Suite, February 2000. the Finite Filling Conjecture, 1999 [CRM-2652] Jean-François Angers, Bayesian [CRM-2721] Steven Boyer, On the Local Structure of Inference for the Location Parameter of a Student-t SL2(C)-character varieties at reducible characters, Density, February 2000. 1999 [CRM-2653] Marc-André Lewis & Yvan Saint- [CRM-2722] Steven Boyer, M. Culler, P. Shalem Aubin, Boundary States for a Free Boson Defined on & X. Zhang, Small Dehn Fillings, 2000 Finite Geometries, February 2000. [CRM-2723] Steven Boyer, C. Gordon & X. [CRM-2654] Jean-Marc Lina, Diego Clonda & Zhang, Dehn Fillings of Large Hyperbolic 3- Bernard Goulard, Statistical Modeling With Manifolds, 2000 Complex Dyadic Wavelets, February 2000. [CRM-2724] Steven Boyer, D. Rolfsen & B. Wiest, [CRM-2655] Philippe St-Jean & Jean-Marc Lina, On the Orderability of 3-Manifold Groups Exceedence Statistics of Irregular Random Field [CRM-2725] Isidore Fleischer & John E. Porter, Using Wavelets and Euler Characteristics, February Convergence of Metric Space-Valued BV Functions, 2000. May 2000 [CRM-2656] A. Michel Grundland, M. B. Sheftel [CRM-2726] Langis Gagnon & M. Lalonde, Vision & Pavel Winternitz, Invariant Solutions of artificielle et traitement d'images, November 1999 Equations of the Hydrodynamic Type, March 2000. [CRM-2727] A. Michel Grundland & Decio Levi, [CRM-2670] Marco Bertola, Jacques Bros, Vittorio On a New Integrable Equation of Toda Type, 2000 Gorini, Ugo Moschella & Richard Schaeffer, [CRM-2728] Paul Bracken & A. Michel Decomposing Quantum Fields on Branes, March Grundland, Links Between the Weierstrass 2000. Representation, the Complex Sine-Gordon Equation [CRM-2671] Thomas R. Hagedorn, A and Multivortex Solutions, 2000 Combinatorial Approach for Determining [CRM-2729] Paul Bracken & A. Michel Phylogenetic Invariants for the General Model, Grundland, Conditional Symmetries for the March 2000. Generalized Weierstrass System, 2000 [CRM-2672] Paul Bracken, An Arithmetic- [CRM-2730] Jacques Hurtubise & Lisa Jeffreys, Geometric Mean Inequality, March 2000. Representations With Weighted Frames and Framed [CRM-2673] Paul Bracken & A. Michel Parabolic Bundles, June 1999 Grundland, Symmetry Properties and Explicit [CRM-2731] Jacques Hurtubise & E,. Markman, Solution of the Generalized Weierstrass System, Calogero-Moser Systems and Hitchin Systems, 2000 March 2000.

86 Annual Report 1999-2000 CRM P u b l i c a t i o n s

[CRM-2732] Paul Koosis, Use of Logarithmic Sums to [CRM-2736] C. Ibrahim & F. Nekka, Amélioration Estimate Polynomials, 1999 du traitement des images, applications aux réseaux [CRM-2733] Paul Koosis, On Perturbed Coulomb vasculaires de la rétine, October 1999 Solutions of the Schrödinger Equation, February [CRM-2737] F. Nekka & J. Li, Intersection of 2000 Cantor Sets With Their Translates. I. Fundamental [CRM-2734] François Lalonde & D. McDuff, Properties, 2000 Symplectic Structures on Fibered Manifolds, 2000 [CRM-2738] Z. Masáková, Jíri Patera, & E. [CRM-2735] François Lalonde & D. McDuff, Pelantová, Exceptional Algebraic Properties of the Cohomological Properties of Ruled Symplectic Three Quadratic Irrationalities, 2000 Manifolds, March 2000 [CRM-2739] C. Rogers & W. K. Schief, On the Heisenberg Spin Equation in Hydrodynamic, 2000.

CRM Annual Report 1999-2000 87 Financial Report

The CRM benefits from numerous sources of ncm2: the Centre de recherche en calcul appliqué funding to sustain its various sectors of activity. (CERCA); the Centre interuniversitaire de This report distinguishes the amounts awarded recherche en analyse des organisations to the CRM from those awarded to the Centre’s (CIRANO); the Centre de recherche sur les researchers. transports (CRT); and the Groupe d’études et de recherche en analyse des décisions (GERAD). The Centre’s Funding As one of the three mathematics institutes in The various sources of funding are presented in Canada that established the Mathematics of Table 1. In 1999-2000, the CRM received $874,650 Information Technology and Complex Systems for the first year of a four-year NSERC institutes Network of Centres of Excellence (MITACS), the grant. This grant enables the Centre to fulfil its CRM supervises the activities of five of the national mandate centred on the organization of Network’s research projects. It also promotes scientific activities each year (postdoctoral networking activities. The CRM received $75,000 fellowships, student scholarships, visiting in 1999-2000 for these tasks from the overall researchers, thematic scientific activities as well NCE funding provided to MITACS. In addition, as a general program of scientific activities, the five research projects just mentioned research support personnel). (See the section received $686,667 in NCE funding in 1999-2000 titled “Financial statements” for more details.) (see the footnote below Table 3). The CRM is not The Comité d’étude et d’administration de la responsible for the financial management of this recherche (CÉDAR) of the Université de last amount. Montréal provided an operating grant of Other contributions to the CRM’s funding, $722,000 in 1999-2000. This budget is principally allocated for the remuneration of the scientific totaling $407,429, come from the Institut des personnel of the Centre. The budget also covers sciences mathématiques (ISM) for joint CRM- the release time of the mathematicians who ISM postdoctoral fellowships and for the joint direct the CRM and a part of the salary of CRM-ISM colloquium series; from researchers of administrative staff and operating expenses. the Montréal universities for joint postdoctoral fellowships and student scholarships; from the The Fonds FCAR supports the CRM with two André Aisenstadt endowment; from the grants. The Centre’s three-year operating grant Canadian Institute for Advanced Research was renewed in 1999. This grant of $210,000 per (CIAR); from various contributions and year covers a part of the salary expenditures for sponsorships for the “Mathématiques et société” the research support personnel, the publications insert published in the magazine Québec Science personnel, the administrative personnel and in May 2000 (in addition, $10,000 were provided operating costs. An annual amount of $14,000 by the Québec Ministry of Culture and from this grant is set aside for the research Communications in 1998-1999). Furthermore, the activities of two college (CEGEP) researchers on CRM received funding from several release time to the CRM. In 1999-2000, the FCAR contributors, donators and sponsors supporting also awarded the CRM a three-year grant of a promotional campaign held in January- $50,000 for computer equipment. February 2000 in the Montréal public transit The CRM manages the common scientific system for the World Mathematical Year 2000. activities and the general administration of the Finally, contributions were also provided by the Network for Computing and Mathematical PIMS and the Canadian Institute of Theoretical Modeling (ncm2). A budget of $83,000 was Astrophysics for workshops held during the allocated for these tasks in 1999-2000. In Mathematical Physics thematic year. addition, the CRM received $81,444 from the Network for the four research projects of the The CRM generated revenues of $64,481 from its Centre’s members. These amounts come from publishing programs (sales and royalties from the Network’s annual NSERC grant of $648,894. the American Mathematical Society, Springer The balance of this amount goes to the research Verlag and the CRM’s in-house collection) and projects of the four other founding centres of $24,459 from registrations to the summer school and thematic year activities. Other funds came

88 Annual Report 1999-2000 CRM F i n a n c i a l R e p o r t from compensation for services rendered and Table 3 operating costs incurred for the Bell University Research partnerships: contracts and grants from industry, foundations, etc., CRM researchers, 1999-2000 Laboratories (the CRM housed this division of Partner Number $Amount $Account ncm2 during several months after its establishment, and the Centre also provided IT at CRM expertise to the Bell University Laboratories Bell University Laboratories 2 110,000 110,000 ncm (ANIQ, Lockheed Martin, when they moved into new quarters). MITACS 2 also compensated services delivered by the CRM industry partners of GIREF) 6 62,850 62,850 before NCE funding was confirmed. Finally, the MITACS* (Microcell, sale of coffee cups and posters generated a small Bell University Laboratories) 2 70,000 0 income. Lockheed Martin 1 11,000 11,000 Others (Merck Frosst, Table 1 US Air Force) 2 110,000 0 Main sources of funding of the CRM, 1999-2000 Total 13 363,850 183,850 $ Amount *The total amount of the MITACS NCE funding NSERC (Institutes and Initiatives Program) 874,650 awarded to the five projects supervised by the CRM is CÉDAR-Université de Montréal 722,000 $686,667 (of which $108,750 was awarded to FCAR (Research Centres Program) 260,000 researchers of the CRM). The industrial partners of

NSERC (Research Network Program for ncm2) 164,444 these five MITACS projects contributed $325,300 (of National Centres of Excellence (MITACS) 75,000 which $70,000 was obtained by researchers of the Contributions from Universities & Partners 407,429 CRM). Sales, Registrations & Other Revenues 199,077 Furthermore, the CRM, for the benefit of ncm2, Total 2,702,600 prepared and obtained a grant of $740,000 from the Canadian Foundation for Innovation (CFI). Funding for Research This grant served to establish the research In addition to the CRM’s grants, its researchers installations of the Bell University Laboratories. obtained $1,717,435 in research funding during The Government of Québec ($570,000), Bell the 1999-2000 fiscal year. The two following Canada ($500,000) and other enterprises tables provide details on funding awarded by ($40,000) also contributed to the establishment of granting agencies and by categories of research the laboratories. As for other CFI grants, the partnerships. The last column in each table Université de Montréal Office of Research indicates the amount of funding that is managed managed these funds. directly by the CRM in its accounts at the Université de Montréal. Financial Statements Table 2 The following financial statements present, on a Research grants, individual and team, CRM researchers, cash accounting basis, the revenues and 1999-2000 expenditures of the CRM for the fiscal year that Granting agency Number $ Amount $ Account at CRM ended on May 31, 2000. The financial statements do not include the research funding of NSERC 32 812,910 230,895 individual researchers. NSERC-Equipment 3 84,918 0 FCAR 7 243,230 117,000 Expenditures are divided in three broad FCAR-Equipment 1 33,777 0 categories: Scientific Activities, Publications and NCE-MITACS* 3 108,750 10,000 Administration. The main line items under NCE-IRIS 1 60,000 0 Scientific Activities are: • AOSQ 1 10,000 0 scientific personnel (that is, remuneration of Total 48 1,353,585357 895 professors at the Université de Montréal who undertake research on a full-time basis at the CRM; expenses associated with the release of professors and researchers from other institutions for prolonged periods so that they may work as invited researchers or as members of the CRM (this includes the André Aisenstadt Chair and the visiting

CRM Annual Report 1999-2000 89 F i n a n c i a l R e p o r t

researchers taking part in the scientific • the research support personnel delivering activities of the Centre); and postdoctoral computer services and electronic-publishing fellowships and student scholarships); services for the preparation of research • scientific programmes (that is, the annual reports. thematic programme; the 1999 Banff The rubric Publications includes all production summer school and advance payment for costs associated with the CRM’s publishing the 2000 summer school; the general programmes (remuneration of personnel scientific programme made up of preparing publications as well as direct costs contributions to off-site scientific activities such as printing). Finally, the rubric and events, mini-programmes on particular Administration includes remuneration of the topics, colloquia organized jointly with the executive and the administrative personnel, the ISM, and to cover expenses associated with computer systems analyst, and expenses related the four prizes of excellence in the to executive and advisory business meetings, mathematical sciences (the André Aisenstadt current operating costs (including computer Prize, the CAP-CRM Prize in Theoretical equipment and maintenance). and Mathematical Physics, the CRM-Fields Institute Prize and the CRM-SSC Prize), and The year end surplus is explained in great part finally, the programmes of activities by two exceptional factors: the FCAR equipment (workshops, seminars, lectures, conferences) grant, which appears in full as revenue but is to

of the two networks, MITACS and ncm2); be spent over three years, and the • the personnel involved directly in the reimbursement for services from the Bell management and organization of the University Laboratories. scientific programs; and

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CRM Annual Report 1999-2000 91