This report is my first as Director of the CRM, publications programme, was also very active : and it has given me the opportunity to reflect our two joint series with the American somewhat on the nature of the ship of which I Mathematical Society continued to flourish and have taken over the helm, as well as to the CRM series in Mathematical Physics contemplate its record and its achievements. published by Springer-Verlag saw its first three volumes produced and manuscripts were The main result of this contemplation is that submitted for the initial volumes of the CRM it is a remarkably fit and efficient ship. This is subseries of the Springer Lecture Notes in due in large measure to the remarkable efforts Statistics. Finally we had the honour of expended by my predecessors, in particular my publishing the complete works of the eminent immediate predecessor, Luc Vinet. Thanks to his number theorist Sarvadaman Chowla. Our efforts, and to those of the vigourous and computer system got a major and much needed efficient team surrounding him, the CRM now boost, thanks to a grant from the Canadian has stable funding for its activities; these Foundation for Innovation. activities, such as theme programs, general programs, publications, have expanded It is on the industrial front that major considerably, and several large new initiatives in developments occured. The big news was the industrial mathematics such as the ncm2, Bell- funding of MITACS (Mathematics of LUB, and MITACS are now in place. The CRM is Information Technology and Complex Systems) an extraordinary vehicle for the promotion of by the Canadian Networks of Centres of mathematics in all its protean guises, and indeed Excellence program. The proposal comprises it has been performing these many functions about 21 projects, of which 5 are centred in with great effectiveness. Montreal. They are divided into five sectors: biomedical, trading and finance, information Last year was no exception. Let me begin by technology, commercial and manufacturing. The mentioning the core of our scientific programme, MITACS initiative will bring about a major the theme year, which last year focused on realignment of the discipline's dynamics in the number theory and arithmetic geometry. The country, and in particular its relationship with scientific programme committee, under the other fields. inspired leadership of Ram Murty, gave us a year which I think is a model for those to come, Meanwhile, in Montreal, the Network for combining scientific activities and training in a Computation and Mathematical Modelling remarkable way. The year began with a bang in (ncm2) finalised its agreement with Bell Canada Banff, with a Summer School on the Arithmetic to create the Laboratoire Universitaire Bell and Geometry of Algebraic cycles, which was a (LUB). The agreement provides money for resounding success attended by 110 participants. research projects as well as an endowment fund, The year then continued in earnest in Montreal, and is worth a total of $12M. The LUB launched with a relatively modest number of workshops its first series of research projects, of which five being compelemented by a stunningly effective are located at the CRM, covering areas such as series of short courses on focused topics given cryptography, imaging, data mining and quality by experts in the field. The attendance was of service in networks. The infrastructure for the considerable, in particular because the LUB will be financed by an envelope of funds organisers had assembled for the duration of the from Bell, several computer companies, the year a collection of a dozen postdoctoral fellows Quebec government and the Canadian and twenty graduate students in the area, Foundation for Innovation: this will allow the complementing the substantial Montreal construction of two laboratories. contingent with visiting students from all over the country. This does not include participants All in all, then, a busy year. The current year, who attended only some of the activities; in all, as well as the ones to follow, will also be busy over 300 attended the activities of the year. In and replete with major challenges. The first one, assembling this contingent, the CRM was greatly of course, is to run all these networks and assisted by the Centre Interuniversitaire de laboratories: the grant is only the beginning, and Calcul Algébrique (CICMA). they must then be made to thrive, and to develop. A second is to expand and improve the The general programme was quite full, with CRM's links with its various partners, in twelve conferences being funded. The particular the neighbouring universities. There

2 Annual Report 1998-1999 CRM A W O R D F R O M T H E D I R E C T O R are many mutual gains through these This is intimately tied to what I think is the associations, I believe, in particular in most important challenge for the CRM. The incorporating a greater pool of researchers into coming years will see great changes in the the CRM's scientific base. This pool of personnel at our universities, as many of the researchers who view the CRM as one of their faculty hired thirty years ago during the years of scientific homes has always been one of our great expansion in the university system come strengths, and I think that the development and up for retirement. This presents us with the structuring of this base is a priority for the opportunity of shaping our mathematical coming years. community for the years to come. The CRM hopes to participate fully in this process, so as to make it strong and vibrant. The interaction with this community is the central focus of our mission, as we serve it, enrich it and are enriched by it. People, in the end, are our greatest resource.

Jacques Hurtubise, Director

CRM Annual Report 1998-1999 3 PRESENTING THE CRM

The Centre de recherches mathématiques (CRM) was created in 1969 by the Université de This national mandate is complemented by, Montréal through a special grant from the NRC. and indeed supported by, a long-standing It became an NSERC national research centre in vocation of promoting research in the Montréal 1984. It is currently funded by NSERC (Natural area. Indeed the CRM Sciences and Engineering Research Council), by • supports, through partnership agreements, a the Government of Québec through the FCAR local group of researchers chosen mainly (Fonds pour l’aide et le soutien à la recherche) from departments of mathematics and and the Université de Montréal, and by private statistics, but also from departments of donations. The mission of the CRM is to do computer science, physics, economics, research in mathematics and closely related engineering, etc.; disciplines and to provide leadership in the • sponsors joint activities with the ISM development of the mathematical sciences in (Institut des Sciences Mathématiques) Canada. including the weekly CRM/ISM colloquium, graduate courses offered by distinguished The CRM accomplishes its mission in several visitors and a program of postdoctoral ways. As part of its national mandate, fellowships. • it organizes a series of scientific events each • works actively at developing contacts with year, around a given theme (distinguished industry. Its joint activities with liaison and lecture series, workshops, conferences, research centres (CERCA, CIRANO and summer schools, visitor programs, etc.); CRIM) and research centres doing applied • it has a general program which helps to fund research (CRT, GERAD and INRS Télécom) conferences and special events across the led to the creation of the Network for country; Computing and Mathematical Modelling • each year it invites, through the Chaire (ncm2). This network is funded by NSERC Aisenstadt, one or two prestigious and about 20 partners such as financial mathematicians, to give advanced courses as institutions, hightech companies and part of its thematic program; ministries. More recently, a contract has • it awards three prizes yearly: the CRM- been signed with Bell Canada to form BUL Fields Prize recognizing major contribu- (Bell University Laboratory) which will tions to mathematics, the Aisenstadt Prize focus on the development of multimedia given for outstanding work done by a young products. Canadian mathematician, and the CAP- CRM Prize for exceptional achievement in The CRM fulfils its national mission by theoretical and mathematical physics; involving the largest possible number of • it publishes some 150 technical reports and Canadian mathematicians in its scientific 6-8 books per year. Some of its collections programs, both as participants and as are published jointly with the AMS and with organizers. It also supports many events taking Springer Verlag; place outside Montréal and the Prov-ince of • it has an extensive postdoctoral fellowship Québec. It is recognized worldwide as one of the programme, with 20 postdoctoral fellows in major institutes in the mathematical sciences. place last year, funded either solely by the CRM or in partnership with other The director of the CRM is supported by two organisations; managerial structures: the Bureau and the • it informs the community of its activities Advisory Committee. The Advisory Committee through its web site at is a prestigious group of internationally www.CRM.UMontreal.CA renowned mathematicians, both Canadian and non-Canadian, who approve scientific programs • it participates, with the other two Canadian and thematic years, choose recipients of the centres, in groundbreaking national CRM-Fields and Aisenstadt prizes, and suggest initiatives such as the MITACS new scientific ventures to explore. The president (Mathematics of Information Technology of the Canadian Mathematical Society is a and Complex Systems) proposal. Another member ex officio. example is found in the National Program Committee which provides funding for offsite research activities.

4 Annual Report 1998-1999 CRM PERSONNEL

The Director’s Office

Luc Vinet Director Martin Goldstein Deputy Director Yvan Saint-Aubin Deputy Director Jacques Hurtubise Deputy Director Diane Poulin Secretary

Administration

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

Scientific Activities

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

Publications

André Montpetit TeX Expert Louise Letendre Technician

C omputer Services

Daniel Ouimet UNIX Systems Manager David Rand Web Master and Macintosh expert

MITAC S/MaTISC (Mathematics of Information Technology and Complex Systems)

Yoshua Bengio Deputy Director Marie Pineau Business Development Officer

CRM Annual Report 1998-1999 5 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 program 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 6 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 Concordia Univ. Grundland Michel Univ. du Québec à Trois- Angers, Jean-François Dép. de math. et de stat., Rivières Univ. de Montréal Harnad, John Concordia Univ. Arminjon, Paul Dép. de math. et de stat., Hurtubise, Jacques McGill Univ. Univ. de Montréal Hussin, Véronique Dép. de math. et de stat., Beaulieu, Liliane Collège Rosemont Univ. de Montréal Bélair, Jacques Dép. de math. et de stat., Joffe, Anatole Dép. de math. et de stat., Univ. de Montréal Univ. de Montréal Bélair, Luc Dép. de mathématiques Kamran, Niky McGill Univ. Univ.du Québec à Montréal Kisilevsky, Hershy Dép. de math. et de stat., Bengio, Yoshua Dép. d’info. et de recherche Concordia Univ. opérationnelle, Univ. de Lalonde, François Univ. du Québec à Montréal Montréal Langlands, Robert Institute for Advanced Bergeron Nantel York University Study, Princeton Boyer, Steven Dép. de mathématiques Léger, Christian Dép. de math. et de stat., Univ.du Québec à Montréal Univ. de Montréal Broer, Abraham Dép. de math. et de stat., Lessard, Sabin Dép. de math. et de stat., Univ. de Montréal Univ. de Montréal Clarke Francis Univ. de Lyon LeTourneux, Jean Dép. de physique, Univ. de Darmon, Henri McGill University Montréal Delfour, Michel Dép. de math. et de stat., Lina, Jean-Marc CRM Univ. de Montréal Univ. de Montréal Dssouli, Rachida Dép. d’info. et de recherche McKay, John Concordia University opérationnelle, Univ. de Mathieu, Pierre Dép. de physique Montréal Univ. Laval Durand, Stéphane Collège Édouard-Montpetit Nekka, Fahima Faculté de Pharmacie Fournier, Richard Collège Dawson Univ. de Montréal Fleischer, Isidore Univ. of Windsor Patera, Jiri Dép. de math. et de stat., Gagnon, Langis Lockheed Martin Canada Univ. de Montréal Gauthier, Paul Dép. de math. et de stat., Perron, François Dép. de math. et de stat., Univ. de Montréal Univ. de Montréal Goldstein, Martin Dép. de math. et de stat., Rahman, Qazi Dép. de math. et de stat., Univ. de Montréal Univ. de Montréal Goulard, Bernard Groupe PhysNum; Dép. de Rogers, Colins Univ. of New South Wales physique, Univ. de Montréal Australia Granas, Andrzej Dép. de math. et de stat., Rosenberg, Ivo Dép. de math. et de stat., Univ. de Montréal Univ. de Montréal Greiter, Cornelius Dép. de math. et de stat. Rousseau, Christiane Dép. de math. et de stat., Univ. Laval Univ. de Montréal

6 Annual Report 1998-1999 CRM S C I E N T I F I C P E R S O N N E L

Roy, Roch Dép. de math. et de stat., Valin, Pierre Lockheed Martin Canada Univ. de Montréal van Vliet, Carolyne Univ. of Florida Sabidussi, Gert Dép. de math. et de stat., Vinet, Luc Dép. de physique, Univ. de Montréal Univ. de Montréal Saint-Aubin, Yvan Dép. de math. et de stat., Winternitz, Pavel Dép. de math. et de stat., Univ. de Montréal Univ. de Montréal Sankoff, David Dép. de math. et de stat., Yatracos, Yannis Dép. de math. et de stat., Univ. de Montréal Univ. de Montréal Schlomiuk, Dana Dép. de math. et de stat., Yui, Noriko Dép. de math. et de stat., Univ. de Montréal Queen’s Univ. Shahbazian, Elisa Lockheed Martin Canada Zolésio, Jean-Paul Institut non linéaire de Sharp, Robert McGill Univ. Nice Soumis, François GERAD Stern, Ron Concordia Univ.

CRM Annual Report 1998-1999 7 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 program like the NSERC postdoctoral program, the NATO international program 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 program which, in association with its ncm2 partners, now offers postdoctoral fellowships, as the MITACS program began to do last year. We have also included below the joint CICMA/CRM fellows who participated in the thematic year’s activities.

Aassila, Mohammed Univ. Louis Pasteur et Oppenheim, Henri C.E.R.M.I.C.S. (ENPC ) C.N.R.S. Abdeljelil, Farhat Université de Tunis, Perron, Sylvain École Polytechnique de (MITACS) Montréal, (MITACS) Anderson, Parreira, Ecole Polytechnique de Rajaei, Ali Princeton Univ. Montréal, (MITACS) Bracken, Paul Univ. of Waterloo Rousseau, Guillaume Univ. of Toronto, (MITACS) Bryant, Dave Univ. of Canterbury Saint-Cyr, Amik Univ. de Montréal

Caprioglio, Myriam Systèmes Électroniques Saint-Jean, Philippe Univ. de Montréal Lockheed Martin Canada Chen, Imin McGill Univ. Schaefer, Carsten McGill Univ., (MITACS) De Guise, Hubert Univ. de Toronto Schweizer, Andreas Concordia Univ.

Derakhchan, Katayoun Institut de cardiologie de Sebbar, Abdellah State University of New Montréal (MITACS) York at Stony Brook Deteix, Jean Univ. de Montréal Shinagawa, Kaori Institut de cardiologie de Montréal (MITACS) Hadjar, Ahmed École Polytechnique de Spiteri, Raymond Univ. of British Columbia Montréal, (MITACS) Huan, Min Yi McGill Univ., (MITACS) Stojkovic, Goran École Polytechnique de Montréal, (MITACS) Jurco, Branislav Palacky Univ. Tateno, Katsumi McGill Univ., (MITACS) Kagabo, lssa Polytechnique, (MITACS) Tekogan, Hemazro École Polytechnique de Montréal, (MITACS) Lesage, Frédéric Systèmes Électroniques Villeneuve, Daniel École Polytechnique de Lockheed Martin Canada Montréal, (MITACS) Madrane, Aziz Univ. de Montréal Zabrocki, Mike Univ. du Québec à Montréal Muzy, Jean-François Centre de Recherches Paul Zaugg, Philippe CNRS, LAPP Pascal (CNRS) Nagai,Yoshihiko McGill Univ., (MITACS) Ziarati, Koorush HEC, (MITACS) Nagih, Anass HEC

8 Annual Report 1998-1999 CRM 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 1998-99, 340 participants registered for workshops run solely by the CRM. In addition, the CRM helped fund 12 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.

Adhikari, Sukumar Das Mehta Research Kunisawa, Takashi Sciences Univ. of Tokyo Institute Lemire, Frank Univ. of Windsor Atakishiyev, Natig IIMAS-UNAM Levi, Decio Universita di Roma (Mexico) Lewis, James D. Univ. of Alberta Bacry, Emmanuel École Polytechnique, Lieman, David Univ. of Missouri Paris MacPherson, Robert D. Institute for Advanced Banks, Bill Univ. of Missouri Study Benali, Habib CHU, Pitié-Salpêtrière Mahaffy, Joseph San Diego State Univ. Bertolini, Massimo Univ. di Pavia Mardesic, Pavao Univ. de Bourgogne Chandrasekher, Madhav Univ. of Illinois at Martina, Luigi Univ. de Lecce Urbana-Champaign Masakova, Zuzana Faculty of Nuclear Sc. Chen, Huaihui Nanjing Normal Univ. and Physics Eng. Cho, Yong-Min APCTP (Czech Republic) Choi, Seung-Il Univ. of Michigan Mestre, Jean-François Univ. Paris VII Christopher, Colin Bogazici Univ. Moody, Robert V. Univ. of Alberta Coleman, Mark David UMIST Mourtada, Albelraouf Univ. de Bourgogne Conte, Robert CEA - Saclay Murnaghan, Fiona Univ. of Toronto Dorodnitsyn, Vlad, D. Russian Academy of Murty, Kumar Univ. of Toronto Sciences (Moscow) Murty, Ram Queen's Univ. Dumortier, Freddy Limburgs Universitair Musette, Micheline Vrije Universiteit Centrum, Belgique Brussel Elliott, George A. Univ. of Toronto & Ng, Nathan Univ. of British Univ. of Copenhagen Columbia Ferapontov, Evgeny Technische Universität Nikolaev, Igor Institute of Berlin Mathematics, Moldavie Fernandez, David J. CINVESTAV IPN Odzijewicz, Anatol Univ. of Warsaw Françoise, Jean-Pierre Univ. Paris VI Ohyama, Yousuke Osaka Univ. Fu, Lei Nankai Univ. Oort, Frans Universiteit Utrecht Gardeyn, Francis Universiteit Gent Ota, Kaori Tsuda College Gazeau, Jean-Pierre Univ. Paris VII Patera, Jan Czech Technical Univ. Giroud, Patrick Univ. Joseph Fourier Pelantova, Edita Faculty of Nuclear Sc. Gomez, Nicolas INRIA and Physics Eng. Gomez-Mont, Xavier Guanajuato, Mexico (Czech Republic) Gordon, Brent Univ. of Oklahoma Phan, Quoc Khanh Vietnam National Goresky, Mark Institute for Advanced University - HCM City Study Picinbono, Bernard École Supérieure Granville, Andrew Univ. of Goergia d'Électricité et Gross, Benedict Harvard Univ. Université de Paris-Sud Havlicek, Miloslav Faculty of Nuclear Sc. Pogosyan, Georges Joint Institute for and Physics Eng. Nuclear Research (Czech Republic) (Dubna) Henry, Jacques INRIA-Rocquencourt Posta, Severin Czech Technical Univ. Iovita, Adrian Univ. of Washington Raghunathan, Ravi Caltech Ito, Hiroyuki Tôhoku Univ. & Raghuram, Anantharam Tata Institute Harvard Univ. Kaloshin, Vadim Princeton Univ. Rajan, Conjeeveram S. Tata Institute of Kani, Ernst Queen's Univ. Fundamental Research Korotkin, Dmitri Max Planck Institut Ribenboim, Paulo Queen's Univ. Kudla, Stephen Univ. of Maryland Ribet, Kenneth A. Harvard Univ.

CRM Annual Report 1998-1999 9 S C I E N T I F I C P E R S O N N E L Roche, Philippe MIT et École Terras, Audrey A. Univ. of California, San Polytechnique Diego (Palaiseau, France) Thalmann Nadia Univ. de Genève Roussarie, Robert Univ. de Bourgogne Thomova, Zora SUNY-Institute of Rowe, David Univ. of Toronto Technology Saidak, Filip Queen's Univ. Tuszynski, Jacek A. Univ. of Alberta Saito, Masahiko Kobe Univ. Verger-Gaugry, Jean- Université J. Fourier Schwartz, Laurent Membre de l'Académie Louis des sciences, Paris Vicher, Anne Université Paris V Sheftel, Misha B. North-Western Vivolo, Olivier Laboratoire Emile Correspondence Picard, UPS Polytechnical Institute Zakrzewski, Wojciech Univ. of Durham (St.Petersburg, Russia) J.M. Skinner, Chris Harvard Univ. Zhang, Yuanli Purdue Univ. Sorba, Paul LAPP Zhedanov, Alexei Donetsk University Souriau, Jean-Marie Univ. de Provence Steer, Brian Oxford College

10 Annual Report 1998-1999 CRM 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.

Bergeron, François UQAM Bengio Yoshua Univ. de Montréal

Brassard, Gilles Univ. de Montréal Goldstein Martin Univ. de Montréal

Caillé, Alain Vice-recteur à la Hambleton Ian McMaster Univ. recherche, Univ. de Montréal Cléroux, Robert Univ. de Montréal Hurtubise Jacques McGill Univ.

Goldstein, Martin Dir. adj., CRM, Kane Richard Univ. of Western Ontario Univ. de Montréal Habashi, Wagdi G. Univ. Concordia Lalonde François UQAM

Hubert, Joseph Vice-doyen à la rech., Lawless Jerry Univ. de Waterloo FAS, Univ. de Montréal Hurtubise, Jacques McGill Univ. Melrose Richard MIT

Hussin, Véronique Univ. de Montréal Miller Willard IMA

Jeffrey, Lisa Univ. of Toronto Murty Ram Queen’s Univ.

Lessard, Sabin Univ. de Montréal Odlyzko Andrew AT&T Labs

Ransford, Thomas J. Univ. Laval Pianzola Arturo Univ. of Alberta

Rousseau, Christiane Univ. de Montréal Putnam Ian Univ. of Victoria

Roux, Benoît Univ. de Montréal Saint-Aubin, Yvan Univ. de Montréal

Saint-Aubin, Yvan Dir. adj., CRM, Treves Francois Rutgers Univ. Univ. de Montréal Vaillancourt, Jean Univ. de Sherbrooke Ward Michael Univ. of British Columbia

Vinet, Luc Directeur, CRM, Univ. de Montréal

CRM Annual Report 1998-1999 11 M A N A G E M E N T

Computer Facilities

The CRM offers to its members and visitors a Since the end of 1998, it is now possible for Unix environment based on a Sun Enterprise-450 our users and guests to access our local network equipped with four 400-MHz Ultra-Sparc with phone link through our new PPP server processors and 2 Gb of memory as a main and its 4 modems. server, and a secondary server Sun Sparc-1000 with eight 40-MHz processors and 384 Mb of The CRM also has a Silicon Graphics memory for lightweight tasks. This computing Challenge L with six R4400 processors at power is distributed through the offices and 100MHz and 128 Mb of memory, purchased common rooms via more than 30 Sun through the NSERC grant of one of its research workstations (from Sparc-4 to Ultra-10) and teams. Access to this server is limited to the several X-terminals. The software libraries members of that team or, upon request, to other include compilers (SparcWorks environment for members with numerical processing needs. The C, C++ and Fortran, GNU compilers, Java, etc.), support staff works on Sun stations, X-terminals symbolic manipulation programs (Mathematica, or on Macintoshes tied to the Sun server for all Maple, Macaulay), several text editors, web services, such as mail and backups. browsers, a web server, mail tools, and most utilities common to the mathematical world In 1998, the CRM installed its servers in a (SPLUS, etc.). Upgrades to TeX and its dialects new room specifically designed for computers, are uploaded whenever they are released. with indepedent controlled environment and UPS (Uninterruptible Power Supply). In 1999, the CRM installed its own private local area network (LAN) : four BayNetworks *The main server (Enterprise-450), 22 Sun Baystack-450 switches, twisted-pair and optic workstations Ultra-5 and Ultra-10 and the complete fiber links supporting 10/100 Mb/s and Gigabit Local Area Network installed in 1999 were all paid by Ethernet. This private local network is linked to a grant from the Canadian Foundation for Innovation the network of the Université de Montréal that together with the Government of the Province of maintains the connections with RISQ (Réseau Quebec and a donation (20% of total value) from Sun interordinateurs scientifique québécois) and Microsystems (for computers) and Anixter (for the CA*net (the Canadian internet transit service). network).

12 Annual Report 1998-1999 CRM SCIENTIFIC ACTIVITIES

The core of each year’s scientific program at the CRM is its thematic program. 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). 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 1998-1999Ê: Number Theory and Arithmetic Geometry

Overview thought that the following format would better Number theory is at the core of mathematics. serve the needs of the community: six seminar It has been a rich source of research problems courses (given for the benefit of graduate that have given rise to fundamental concepts in students and postdoctoral fellows), ten mini- many parts of mathematics. The CRM has courses (presenting more specialized research played an active role in promoting research in topics), five research workshops and three this area: the thematic year 91-92 was related to conferences, including a summer school in Banff. number theory and was organized by Ram The seminar courses and mini-courses were Murty and earlier, during the spring of 1988, offered with the idea of preparing for and/or Robert Langlands and Dinakar Ramakrishnan supplementing the research workshops. held a workshop at the CRM on the zeta Students participating in the seminar courses functions of Picard modular surfaces. Both the received university credit toward their thematic year and the workshop were extremely programs. successful, not only in terms of the number of It is safe to say that perhaps the most participants and of their quality, but also of their successful aspect of the special year were the legacy: four important publications came out of courses and mini-courses which drew a large them (Elliptic Curves and Related Topics, CRM audience of faculty, postdoctoral fellows, Proceedings and Lecture Notes, Vol. 4; Theta graduate students, and even undergraduates Functions, CRM Proceedings and Lecture Notes, students. These courses creating an atmosphere Vol.1; Introduction to Abelian Varieties, Kumar of almost continuous and lively activity in Murty, CRM Monograph series, Vol. 3; The Zeta number theory in Montreal. Functions of Picard Modular Surfaces, eds. R. P. Langlands, D. Ramakrishnan, Les Publications 8th CRM Summer School at Banff: CRM) and several recent results can be traced The Arithmetic and Geometry of back to them. Algebraic Cycles In 1994, Andrew Wiles resolved the 350 year 7-23 June, Banff (Alberta) old problem of Fermat's Last Theorem. This Org.Ê: James D. Lewis (Univ. of Alberta), Noriko Yui work has introduced a new universe of methods (Queen’s), Brent Gordon (Univ. of Oklahoma), Stefan into the subject that needs to be understood, Muller-Stach (Universitat Essen), Shuji Saito (Tokyo simplified and explained so that further Institute of Technology). problems may be solved. It was the aim of the CRM thematic year 98- The purpose of the Summer School was to 99 to address this need. The format of the year bring together two mathematical schools under emphasized both research and teaching. the same umbrella, namely those that study Number theory is an extremely wide area and algebraic cycles from an arithmetic point of most universities cannot offer the many view, and those that approach the subject specialized courses necessary to provide young geometrically. This interaction was strikingly students with a sound basis. It was consequently successful - both schools benefiting from the presence of the other. For a student learning the subject of algebraic cycles, the conference offered

CRM Annual Report 1998-1999 13 S C I E N T I F I C A C T I V I T I E S the unique opportunity to view the depth of this • The CRM Summer School Proceedings on subject in its entirety. the Arithmetic and Geometry of Algebraic A full and in-depth account of the arithmetic Cycles. and geometry of algebraic cycles was offered, • The NATO ASI Proceedings on the ranging from introductory courses on the subject Arithmetic and Geometry of Algebraic by the leading experts to discussions of the latest Cycles. developments in the fields. Several points of view were considered, including arithmetic Main Lectures methods, transcendental methods, topological • methods, and motives and K-theoretic methods. Spencer Bloch (University of Chicago) Algebraic cycles and differential forms There were a series of lectures given by V. (2). • Voevodsky, and one by H. Gillet aimed at Jean-Louis Colliot-Thélène (Université de Local-global principle for zero-cycles discussing the topology of algebraic varieties Paris-Sud), on conic bundles from the point of view of motives. D. Zagier's . • A remark lectures and also that of N. Yui were aimed at Hélène Esnault (Universität Essen), on Bolibruch's theorem. discussing the relation between algebraic cycles • and L-series, as well as a discussion of Pawel Gajer (Johns Hopkins University), Geometry of Deligne cohomology. polylogarithms and more generally regulator • maps. S. Bloch and H. Esnault discussed their Henri Gillet (University of Illinois at Motives for arithmetic varieties. recent work of the application of Chern-Simons Chicago), • invariants to algebraic cycles via the study of B. Brent Gordon (University of Oklahoma), Indecomposabe Bloch--Quillen cycles. algebraic vector bundles with algebraic • Algebraic cycles and connection. Mark Green (UCLA), Hodge theory (3). A recurring theme in this conference was the • notion of a higher regulator map, often referred Uwe Jannsen (Universität zu Köln), Equivalence relations on algebraic cycles (2). to as the arithmetic Abel-Jacobi map by others • The interested in the arithmetic aspects of the subject. Manfred Kolster (McMaster University), Lichtenbaum conjectures revisited. This is very important for studying cycles on • Zero- arithmetic varieties, and number of results along Andreas Langer (Universität Münster), cycles on Hilbert-Blumenthal surfaces. these lines was discussed in the lectures of W. • Raskind, C. Schoen, D. Ramakrishnan, J. James D. Lewis (University of Alberta), Remarks on indecomposable motives. Nekovar and J.-L. Colliot-Thélène. • Two of the more striking lecture series were Stefan Müller-Stach (Universität Essen), Algebraic cycle complexes. those given by M. Green and S. Saito. Both • lecturers discussed higher regulators, one Jacob P. Murre (University of Leiden), On cycles on abelian varieties. approach being geometric and the other • arithmetic. It was later discovered was that both V. Kumar Murty (University of Toronto), Hodge cycles on abelian varieties. approaches (arithmetic/geometric) to regulators • were essentially the same when computed V. Kumar Murty (University of Toronto), Hodge cycles on abelian varieties. infinitesimally. Much of this was centered • around the elusive Bloch-Beilinson filtration, for Jan Nekovar (University of Cambridge), p- adic Abel-Jacobi maps and p--adic heights. which U. Jannsen was able to provide us with a • more precise conjectural description. Dinakar Ramakrishnan (California Institute of Technology), Zero cycles on surfaces (3). Some explicit example calculations of the • images of real regulator maps were provided by Wayne Raskind (University of Southern J. Lewis and B. Gordon. California), Higher Abel-Jacobi mappings and filtrations on Chow groups. Four lectures were delivered by invited • speakers everyday, followed by sessions of Masahiko Saito (Kobe University), contributed talks. Many informal discussions Prepotentials of Yukawa couplings of certain Calabi-Yau 3-folds and lattice Theta functions. and working sessions involving small groups • were organized by individual participants. Shuji Saito (Tokyo Institute of Technology), The NATO ASI/CRM SUMMER SCHOOL Filtrations on Chow groups and higher Abel- Jacobi maps (3). provided a unique opportunity for two camps of • mathematicians participating together at the Takeshi Saito (University of Tokyo), Modular forms p-adic Hodge theory. same conference, and gaining so much by this • interaction. There will be two publication series Chad Schoen (Duke University), Cycle class produced, published by Kluwer academic maps for nullhomologous cycles on a variety over publishers : a finite field.

14 Annual Report 1998-1999 CRM S C I E N T I F I C A C T I V I T I E S

• Anthony Scholl (University of Durham), CICMA), Gisbert Wustholz (ETH), Ernst Kani Algebraic cycles and modular forms. (Queen's), Shuzo Takahashi (Harvard), et • Christopher Soulé (IHES), Perfect forms and Eyal Goren (Concordia, McGill et CICMA). the Vandiver conjecture. • Vasudevan Srinivas (Tata Institute), Zero Il y avait environ 50 participants inscrits à cycles on singular varieties. l'atelier dont de nombreux étudiants venant de • Bert van Geemen (Universita'di Pavia), Montréal et de plusieurs universités canadiennes Cycles on abelian fourfolds. et américaines. • Vladimir Voevodsky (Northwestern University), Motivic cohomology (2). • Workshop on analytic number theory Noriko Yui (Queen's University), The L- 23-28, October 1998 series, periods, and special values of L-series of Org. : R. Murty (Queen’s) certain Calabi--Yau varieties. • Don Zagier (Max-Planck-Institut), Polylo- The workshop brought together leading garithms, elliptic polylogarithms, periods and experts in analytic number theory with the L—values (3). purpose of exposing the latest methods and • Yuri Zarhin (Pennsylvania State University), results in the field. Semistable reduction of abelian varieties and The most notable of the lectures was that of inertia groups. Iwaniec where he announced an improvement of estimates of Dirichlet L-functions on the critical line Re(s)=1/2. His work involves new Workshop on algebraic modular forms methods applicable in a more general context and modular forms mod p and are significant because they improve work 2-8 October, 1998 of Burgess of the 1950's. There were also Org. : H. Darmon (McGill) excellent lectures by Gonek, Friedlander, K. La dernière décennie a connu l'émergence Murty, R. Murty, A. Zaharescu, Y. Petridis, A. d'une "philosophie de Langlands modulo p" qui Akbary, S. Adhikari, F. Sica, K. Dilcher, C. lie les représentations galoisiennes aux formes Stewart, C. S. Rajan, R. Raghunathan, M. Nair, modulaires mod p. L'atelier sur les formes and J. Hoffstein. modulaires algébriques et les formes modulaires The meeting also brought together students mod p qui s'est déroulé au CRM du 2 au 8 and scholars from across Canada and around the octobre 1998 s'est penché sur deux world and enabled them to discuss topics of développements récents qui s'inscrivent dans ce current research. It also gave opportunity for cercle d'idées: la théorie des "formes modulaires many postdocs to expose their work which they algébriques" de Gross, et les progrès sur les normally are unable to do in general meetings. conjectures de Serre qui découlent des travaux récents de Ribet, Taylor et Wiles. Trois séries de CMS Winter MeetingÊ: conférences ont été organisées autour de ce Special Session in Number Theory thème. 13-15 December 1998, Queen’s, Kingston, Ontario 1. B. Gross (Harvard) a donné trois heures Org. : R. Murty and N. Yui (Queen's) d'exposé sur les Formes modulaires A. Akbary (Concordia University), On the distribution algébriques, et trois de ses anciens étudiants of the values of symmetric square L-functions in the half (Lansky, Pollack, et Padowitz) ont donné des plane Re(s) > 3/2. exposés d'une heure chacun sur des sujets Henri Darmon (McGill University), Modularity of connexes. hypergeometric abelian varieties. Eyal Goren (CICMA Concordia and McGill 2. K. Ribet (UC Berkeley) a donné cinq heures University), Stratifications of moduli spaces and modular de conférences sur le sujet des congruences forms. entre formes modulaires, où il a expliqué la C. Greither (Université Laval), On Bruner's conjecture. démonstration de son célèbre résultat sur la James Huard (Canisius College, Buffalo), An arithmetic conjecture de Serre qui établit un lien entre le reciprocity relation of Liouville type and applications. théorème de Fermat et la conjecture de Hershey Kisilevsky (Concordia University), Henri Shimura-Taniyama. Darmon's Coxeter-James prize. 3. S. Kudla (Maryland) a donné trois heures Manfred Kolster (McMaster University), Higher d'exposé sur la formule de Siegel-Weil. De relative class number formulas. Arne Ledet (Queen's University), Some small 2-groups plus, l'atelier a joui de la participation active as Galois groups. d'un grand nombre de conférenciers invités: C. Levesque (Université Laval), Explicit solutions of a Kevin Buzzard (Cambridge), Wee Teck Gan family of Thue diophantine equations. (Princeton), Ali Rajaei (McGill, Concordia et Kumar Murty (University of Toronto), Zeros of CICMA), Kamal Khuri-Makdisi (McGill et Dedekind zeta functions in towers of fields.

CRM Annual Report 1998-1999 15 S C I E N T I F I C A C T I V I T I E S

W. Georg Nowak (Universität für Bodenkultur, • David Manderscheid (University of Iowa),

Austria), Large convex domains sometimes contain more Quadratic base change for p-adic SL2 as a theta lattice points than we would expect. correspondence. Yannis Petridis (McGill University), Zeros of the • Brooks Roberts (University of Idaho), Zeta Riemann zeta function and central values of L-series of integrals for the symplectic group. holomorphic cusp forms. Distinguished representations D. Roy (University of Ottawa), Criteria of algebraic • Aloysius Helminck (University of North independence and approximation by hypersurfaces. Carolina), On representations associated with p-adic Gary Walsh (University of Ottawa), Old and new reductive symmetric varieties. results on quartic diophantine equations. • Fiona Murnaghan (University of Toronto), Hugh Williams (University of Manitoba), Computer Distinguished tamely ramified supercuspidal verification of the Ankeny-Artin-Chowla conjecture for all representations of GL . p < 5.10l0. n Kenneth Williams (Carleton University), Values of the Dedekind eta function at quadratic irrationalities. Workshop on arithmetical algebraic geometry De plus trois conférences ont été données par 14-18 May, 1999. Chantal David, Jacek W. Frabrykowski and G. Org. : M. Goresky (IAS) and K. Murty (Univ. of Frei. Toronto) The Workshop on Arithmetical and Algebraic Workshop on representations of Geometry was held from May 14 to May 18, as reductive p-adic groups part of the theme year in Number Theory and 9-13 May 1999 Arithmetic Geometry. It was organized by Org. : F. Murnaghan (Univ. of Toronto) Kumar Murty and Mark Goresky. Participants There were 16 hour long lectures. Most of the came from across Canada and the United States, topics of interest in current research in the and most lectures had an audience of 30 to 35 representation theory of p-adic groups were present. discussed in at least one of the talks. Summaries Since the subject matter covered a wide range of the lectures are given below, grouped of topics, and since a number of graduate according to topic under one of five areas. students were attending the workshop, speakers made a special effort to address their lectures to The Bruhat-Tits building in harmonic analysis a wide audience and to attempt to deliver and representation theory survey talks. • Allen Moy (University of Michigan), A new proof Concurrent with these sessions, Professor F. of the Howe conjecture on group distributions via the Oort (Utrecht) delivered the Aisenstadt Chair Bruhat-Tits building. Lecture and a follow-up minicourse on his proof • Stephen DeBacker (University of Chicago), The of a conjecture of Grothendieck, while Professor utility of G-domains. Goresky gave a 5-lecture series on the geometry • Jeff Adler (University of Akron) Buildings, of modular varieties. filtrations and wild ramification. • Several participants of the workshop Jiu-Kang Yu (Princeton University), Construction (including the organizers, R. MacPherson of the of tame supercuspidal representations • Clifton Cunningham (University of Institute for Advanced Study in Princeton, and Massachusetts), Kazhdan-Lusztig sets via orbital A. Terras from UCSD) took advantage of the integrals and the Bruhat-Tits building. hospitality of the CRM and extended their visit Parabolic induction for the full month of May, thereby overlapping • Alan Roche (Purdue University), Parabolic with the preceding workshop (on reductive p- induction and the Bernstein center. adic groups) and the following workshop (on • David Goldberg (Purdue University), On the Moonshine). Many individual discussions and tempered spectrum of quasi-split unitary groups. informal meetings took place during this period. • Chris Jantzen (Ohio State University), Discrete series for classical groups. • Yuanli Zhang (CRM), L-packets and irreducibilities. Moonshine workshop Depth zero representations 29 May to 4 June 1999 • Lawrence Morris (Clark University), Hecke Org. : J. Mckay (Concordia) algebras and parabolic induction. A very successful workshop was held at • Mark Reeder (Boston College), Euler Poincaré CRM. There were 25 speakers and many local pairings and elliptic representations. visitors. Particularly in evidence were the The theta correspondence Japanese mathematicians. • Gordan Savin (University of Utah), Symplectic- The talks ranged over many topics which orthogonal theta lifts of generic discrete series. appear closely related to moonshine; there were talks on Hirzebruch's "Prize Question"- Does

16 Annual Report 1998-1999 CRM S C I E N T I F I C A C T I V I T I E S there exist a compact closed 24-dimensional Simons gave an account of his work with "Monster manifold" with the Monster action and Conway on presentations for bimonster and certain characteristic number restrictions? This related groups. talk by Baker was nicely complemented by one Tuite discussed his recent results on genus by his student Brightwell, who has constructed a two conformal field theory. manifold for the Suzuki sporadic group. Verrill gave an account of her work on Picards- John Conway talked on the early history of Fuchs equations and Beauville surfaces and the moonshine and the extent to which it has been modular forms which arise. explained. Yui discussed several examples of mirror Dolgachev gave a talk on connections with maps of lattice polarized K3 surfaces and the surfaces (Kummer, Hessian, and cubic), their functions attached to them. algebraic geometry, and mysterious connections Wednesday was free for trips to Quebec City with the Leech lattice. and elsewhere. A photo of the participants was The mysteries of the Mirror map and its taken with a digital camera and was up on the relation to moonshine functions were web for viewing in a few hours! expounded by Doran. There was plenty of interaction among the Glauberman adumbrated what seems known participants and the workshop was considered a of the relations between the affine E8 Dynkin great success. combinatorics and the Monster and some Proceedings will appear under the CRM subgroups. series logo, published by the AMS. Griess described his new theoretical foundations of the Leech lattice and its 6th Conference of the CNTA combinatorics. 20-24 June 1999, Winnipeg, Manitoba Harada sketched his proposal for a re- Org . : J. Borwein (SFU), D. Boyd (UBC), C. David examination of the Sylow 2-subgroups of simple (Concordia), R.Murty (Queen’s), C. Stewart (Univ. of groups. Waterloo), H. Williams (Univ. of Manitoba). Kaneko described number theoretic results on modular forms and j-invariants. The Canadian Number Theory Association Shigeyuki Kondo sketched his recent work (CNTA) was founded in 1987 at the International on Mukai's classification of automorphisms of Number Theory Conference at Laval University. K3 surfaces and their connections with Niemeier The purpose of the CNTA is to enhance and lattices. promote learning and research in Number C.H. Lam constructed moonshine vertex Theory, particularly in Canada where we operator algebras from a tensor product based already have a great deal of strength in this area. on a coset decomposition of the Leech lattice. To advance these goals the CNTA has now Li talked on regular representations of vertex organized six major international conferences, operator algebras. which have succeeded in exposing many Dong & Mason surveyed results in conformal Canadian students, faculty and researchers to field theory and modular invariance. Hoehn gave a survey of his work on super the latest ideas in number theory worldwide, VOAs and connections with the baby monster and provided further opportunities for Canada’s group. best and brighest to exhibit their talents and McKay and Sebbar described connections ideas to a global audience. The focus of CNTA between Hecke operators and the Schwarz was mainly on the following areas : derivative and how they can be used to combinatorial/computational number theory, characterize the j-function and replicable analytic number theory, diophantine problems functions. and arithmetic geometry. All of these areas have Miyamoto talked on both modular invariance seen rapid development in recent years, both in of the trace on multivariate vertex operator Canada and internationally. algebras (VOAs) and on the automorphism For CNTA 99 there were 8 plenary one-hour group of holomorphic framed VOAs. talks and 17 invited 40 minute talks. The plenary Norton discussed irrational moonshine. speakers were : H. Darmon (McGill), J. Ohyama described how to convert defining Friedlander (Toronto), E. Goren (McGill) A. Schwarz differential equations for Haupt Granville (Georgia), P. Sarnak (Princeton), W. modules into non-associative commutative Schmidt (Colorado), C. Skinner (Princeton), and algebras derived from dynamical systems. T. Wooley (Michigan). These were chosen on the Kyoji Saito discussed his work on eta basis of the importance of their recent and past products and the signs of the q-coefficients. work and their undoubted stature as internationally recognized number theorists.

CRM Annual Report 1998-1999 17 S C I E N T I F I C A C T I V I T I E S

They presented knowlegeable survey lectures The purpose of the course was to introduce concerning recent progress in their respective the participants to the theory of modular forms, fields. The 17 invited speakers were selected to in particular the theory of modular forms of represent the themes of the conference and did several variables with respect to the modular so very effectively. To mention just a few of group GL_2(R), where R is the ring of integers of these talks, A. Odlyzko gave a very nice survey a totally real field. Emphasis was put on of his recent work in computing the zeros of the characteristic p methods, with applications to Riemann zeta function, D. Bressoud gave a very congruences between special values of L nice account of the alternating sign matrix functions. conjecture, A. Bremner gave a beautiful The first semester concentrated on the presentation of his work on magic squares and fundamental theory of abelian varieties and elliptic curves, C. Greither provided a lovely algebraic tori, on line bundles and polarizations, account of his work on generalizing the Redei- and on the theory of moduli of abelian varieties Reichardt theorem and M. Harper gave the first over the complex numbers and over a general proof of a very important result: Z[sqrt(14)] is field. Methods for studying abelian varieties Euclidean. There were also 40 contributed talks over a general field were introduced and organized in 8 sessions representing a particular demonstrated by many applications. Included theme of the conference. These talks were very were Serre-Tate coordinates and Honda-Tate strong, and in some cases, outstanding. In theorem. particular. The talk of K. Williams on bounding The second semester focused on congruences the size of the least solutions of diatonal and the relation to geometry of Hilbert modular quadratic equations come to mind, but there varieties in positive characteristic. Partial Hasse were many others. The talks were all very well invariants and their applications to congruences attended. It should also be mentioned that it was and geometry. Serre and Katz work on p-adic at this meeting that the first Ribenboim medal modular forms and its extension to totally real was presented. This is a prize which was fields were discussed. recently established by the CNTA to honour The second semester of the course was fused distinguished research in number theory ; it is with a mini-course on the theory of deformation awarded, in conjunction with a CNTA meeting, of abelian varieties in positive characteristic to a mathematician who is either Canadian or (leading, in particular, to proof of the basic who has maintained close connections to properties of the stratification by Goren and Canadian mathematics. The winner this time Oort). was Andrew Granville, a former Ph. D. student Notes of the two courses and the minicourse of P. Ribenboim from 1984-87. He also presented will appear on the AMS-CRM lecture notes the Ribenboim Lecture. This was an account of series. his joint work with Soundararajan on how large or small character sums can be, both The Chebotarev density theorem and some conjecturally and unconditionally, and how their applications values are distributed in the complex plane. October 1998 Lecturer : Kumar Murty (Univ. of Toronto) Seminar Courses The Chebotarev Density Theorem is a Modular forms and the Birch and Swinnerton- fundamental tool in number theory and Dyer conjecture arithmetic geometry. Effective versions of this September 1998 to March 1999 theorem and some of its applications were Lecturer : Henri Darmon (McGill and CICMA) discussed. The goal of this seminar was to survey the recent progress on the Birch and Swinnerton Dyer conjecture which follows from the work of Kolyvagin and Wiles. In particular we tried to present a complete proof of the following An Introduction to Sieve Methods statement: Let E be an elliptic curve over Q November 1998 whose L at s=1. Then the Mordell-Weil group Lecturer : Ram Murty (Queen's) E(Q) is finite. This short course surveyed sieve methods and some of its applications. After looking at the Elliptic and Hilbert Modular forms sieve of Eratosthenes, the sieve methods of Brun, September 1998 to March 1999 Selberg and Linnik were discussed. Then Lecturer : Eyal Goren (CICMA, Concordia & McGill) applications of these methods to such questions as Artin's primitive root conjecture, squarefree

18 Annual Report 1998-1999 CRM S C I E N T I F I C A C T I V I T I E S values of polynomials, and structure of the Modular Forms and Modular Curves group of points mod p of a global elliptic curve January 1999 were discussed. The course consisted of a total of Lecturer : Imin Chen (CICMA, Concordia & McGill) six lectures. Automorphic forms over function fields January 21, 26, 28 and February 2, 1999 Mini-courses Lecturer : Andreas Schweizer (CICMA, Concordia & McGill) Several two-week mini-courses were offered. Topics in p-adic Galois representations February 1999 Iwasawa Theory of Modular Forms Lecturer : A. Iovita (CICMA, Concordia & McGill) September 1998 Hilbert modular varieties Lecturer : Massimo Bertolini (Universita di Pavia) February 18 and March 2, 1999 Ordinary Representations and Modular Forms Lecturer : Eyal Goren (CICMA, Concordia & McGill) October 1998 The spectrum of multiplicative values Lecturer : Chris Skinner (Institute for Advanced Study) Rankin-Selberg L-functions The distribution and extreme values of L- November 1998 functions Lecturer : C.S. Rajan (Tata Institute) March 1999 Lecturer : Andrew Granville (Georgia) Polynomial constructions, Galois theory and elliptic curves March 1999 Lecturer : Jean-François Mestre (Paris VII, Jussieu) Representations of reductive p-adic groups April 1999 Lecturer : Fiona Murnaghan (Toronto)

CRM Annual Report 1998-1999 19 S C I E N T I F I C A C T I V I T I E S

Chaire Aisenstadt

The Chaire Aisenstadt 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 Chaire Aisenstadt 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 and David Cox. The CRM was honoured to have as Aisenstadt chairholder, during the 1998-99 Theme Year in Number Theory and Arithmetic Geometry, Frans Oort of the Utrecht Universiteit .

Professor Frans Oort (Universiteit Utrecht) pioneer in the study of abelian varieties, their May 4, 18, 20, 25, 27 and 28, 1999 moduli spaces, and ensuing questions on group schemes. Following fundamental work by Y. Professor Frans Oort has spent the better part Manin, Frans Oort studied moduli of abelian of his professional and private life in his native varieties in positive characteristic, and he is Holland. Immediately after obtaining his largely responsible for most of the knowledge masters' degree from the Leiden University in we have on the special features of these varieties, 1958, he began his doctoral studies at the same that play a fundamental role in arithmetic institution under the direction of W. T. van Est algebraic geometry and number theory. and J. P. Murre. He continued these studies in In trying to put Professor Oort's numerous Pisa (1959-60) under A. Andretti and in Paris research papers and books in perspective, we (1960-61) under J.-P. Serre, returning to Leiden would like to mention in particular his works on to receive his Ph. D. (cum laude) in 1961. The stratification of moduli spaces (some with period in Paris proved to be a decisive one for collaborators) by Newton polygons and by his mathematical career. It was at this time that structure of the first deRham cohomology; his he assimilated the then developing language of characterizations and deep study of schemes and modern algebraic geometry, and supersingular and superspecial abelian varieties; his interest in geometry over arbitrary fields his works on p-divisible groups (Cayley- crystallized. This is witnessed in one of his Hamilton and Catalogues); his study of special earliest works: Commutative group schemes loci (hyperelliptic, Torelli, etc.) and lifting (LNM 15). problems (CM, endomorphism, Jacobians), and The next sixteen years were spent at the his work on group schemes and deformation University of Amsterdam, where he became a problems. His works are always characterized in full professor in 1967. In 1977 he moved to their balance between general theory and Utrecht University, where he remains to this concrete questions. An interplay that was day. Professor Oort has traveled widely instrumental in his contribution to making those andvisited deparments and institutes all over the objects and the special attributes they have, mathematical world, including his receiving the familiar and understood. Besides his direct 1999 Aisenstadt Chair from the CRM in contributions to mathematical knowledge, Montreal. From 1966 to 1982 he was managing Professor Oort is well known for producing a editor of Compositio Mathematica, and is currently line of leading mathematicians, and for his an editor of several others. tremendous influence on the development of Frans Oort is an algebraic geometer. The bulk mathematics in The Netherlands. of his work pertains to the study of geometry over fields of positive characteristic and of In his Montreal Notes, Grothendieck included a moduli spaces. Continuing the work of letter to Barsotti in which he announces a conjecture. Grothendieck, Mumford and Deligne, he was a In this course I will present a proof for this conjecture. To every p-divisible group (also called a Barsotti-Tate group) in characterstic p one can attach

20 Annual Report 1998-1999 CRM S C I E N T I F I C A C T I V I T I E S a discrete invariant, its Newton Polygon. theory. Moduli of abelian varieties. A conjecture by Grothendieck showed that under specialization Manin ("every symmetric Newton Polygon is Newton Polygons "go up"; his conjecture says that, algebraizable"). This conjecture by Grothendieck. conversely, for a given p-divisible group, and a given Techniques involving "catalogues" (a new, useful "lower" Newton Polygon such a specialization should notion). Study various strata in many different be possible. moduli spaces and catalogues. Determine the My main interest comes from the study of moduli structure of Newton Polygon strata (dimension, spaces of abelian varieties in positive characteristic. irreducibility, etc.). These spaces have an incredibly rich structure. In my first course (May 14) I shall review Several properties can be studied by "going to the definitions and results. In my second (May 18) I shall boundary" (a useful method in algebraic geometry), sketch ingredients used and the main lines of the by which we mean in this case that the abelian variety proofs. The first two lectures give a complete survey does not degenerate at all, but that the p-structure of methods and results. I shall try to make these 6 becomes more special. The Grothendieck conjecture lectures accessible for a wide audience (although, on (in the polarized case) tells us exactly which strata some occasions I am using advanced methods). should be in the boundery of a given stratum. In each of the last four courses (May 20-28) I shall In proving this conjecture one encounters the concentrate on a particular, interesting aspect. problem that the variation of the Newton Polygon Catalogues will be introduced and discussed. Some under a deformation is very difficult to follow (this is combinatorial problems have to be solved. A mixture why it took us so long to give a proof for this of deep algebraic geometry and easy computations reasonable conjecture). I shall explain this in several will be presented, eventually leading to a complete ways in my course. This causes that a direct approach understanding of this complex of problems, giving a to the problem does not seem to lead anywhere. My rather precise description of the spaces involved. A. proof consists of several very different stages, each of Grothendieck, Groupes de Barsotti-Tate et cristaux de them developing very interesting new techniques. Dieudonné. Sém. Math. Sup., Univ. Montréal, In my course I shall define, study and prove : Finite (Presses Univ. Montréal, 1974.) group schemes, p-divisible groups and deformation

CRM Annual Report 1998-1999 21 S C I E N T I F I C A C T I V I T I E S

General Program

The CRM’s general program funds a wide variety of scientific events, both on-site and around the country. The program is quite flexible, to allow for opportunities as they arise. Following the cancellation of the NSERC conference grant program, the CRM, along with the other Canadian mathematics institutes, is responsible for funding conferences across Canada.

Congress of the Statistical Society of Formal Power Series and Algebraic Canada Combinatorics’98 31 May-3 June 1999, Univ. of Sherbrooke 15-19, June 1998. Org. : L-P Rivest (Univ. Laval) Org. : N. Bergeron, Walter Whiteley (York) and Frank The CRM was the official sponsor of a session Sottile (Univ. of Toronto) entitled "Special session of the Centre de The Formal Power Series and Algebraic recherche mathematiques: Analysis of Shape" Combinatories Conference (FPSAC) was held in featuring H. Le (University of Nottingham), I. Toronto on the University of Toronto campus Dryden (University of Leeds) and K. Worsley with talks at the Koffler Institute, and poster (McGill University). sessions and software demonstrations at the Fields Institute. Summer Meeting of the Canadian The conference had financial assistance from Mathematical Society: Special a number of sources including the centre de sessionÊ: Relativity & Geometry recherche mathematiques in Montreal, the 13 - 15, June 1998 Univ. of New Brunswick, Saint Connaught fund of the University of Toronto, John the Fields Institute, York University, and Org. : Jacques Hurtubise and Niky Kamran individual NSERC research grants. Logistical (McGill) support for the conference was provided by the This special session consisted of 12 lectures. Fields Institute and it was organized by Nantel Bergeron and Walter Whitely of York University Maung Min-Oo (McMaster University), Mass, scalar and Frank Sottile of the University of Toronto. curvature and K-area. The Scientific program consisted of 9 hour Charles P. Boyer (University of New Mexico), long invited addresses by P. Diaconis (Stanford), Contact geometry and Einstein manifolds. Roger Bielawski (Max Planck Institute, Germany), P. Dehornoy (Paris), C. Godsil (Waterloo), J. Y. Tn-invariant hyperkähler 4n-manifolds. Thibon (Paris), B. Sturmfels (Berkeley), K. Ono Andrew Dancer (McMaster University), Einstein (Penn. State), B. Derrida (Paris), G. Benkart metrics of cohomogeneity one. (Wisconsin) and P. Cameron (England). There Paul Ehrlich (University of Florida), Bochner's was also 27 contributed talks, 24 posters technique for compact Lorentzian manifolds (after A. presented in 2 sessions, and 3 software Romero and M. Sanchez). demonstrations. Marek Kossowski (University of South Carolina), The invited speakers were from the USA, Characteristic classes for pseudo Riemannian manifolds France, England, and Canada, and represented with volume-resolvable metric singularities. Hans-Peter Künzle (University of Alberta), SU(n)- areas of mathematics, statistics, and physics Einstein-Yang-Mills fields in sphericaly symmetric and related to the themes of the conference. The cosmological space-times. contributed talks, posters, and software McKenzie Y. Wang (McMaster University), The demonstrations were refereed by the program cohomogeneity one Einstein equations. committee, which also selected the invited Rob Milson (McGill University), Realization of speakers. The program committee was chaired reflection quotients by singular metrics. by Ian Goulden of the University of Waterloo Conrad Hewitt (St Jerome's University), Three and included Bergeron and Sottile, as well as 20 dimensional symmetry groups in cosmology. others from Europe, North America, and Asia. Two lectures were given by G. Weinstein and A. There were 136 registered participants from Coley as well. many countries, including Canada, Russia, the USA, Japan, France, Switzerland, Hong Kong, England, Korea, Italy, Germany, Australia, Austria, Israel, Slovenia, Sweden, and Mexico. This included 44 graduate students. Over all, the organizing committee feels the conference was a success. We had a strong scientific program, due in part to the extensive refereeing of contributions. The facilities of the

22 Annual Report 1998-1999 CRM S C I E N T I F I C A C T I V I T I E S

Fields Institute and the lecture room at the ISMB is well known for its poster session and Koffler Institute facilitated the presentations. The its introductory tutorial program. There were 11 financial assistance we received enabled us to tutorials, with a total enrollment of 559 (note that invite distinguished speakers and help support a some participants attended more than one large number of young mathematicians. tutorial). Tutorial topics included protein evolution, comparative genomics, molecular ISMB '98: Sixth International phylogenetics, machine learning and knowledge Conference on Intelligent systems discovery. In total, there were 96 posters for Microbiology presented during an afternoon session on the 28 June-1 July, 1998 second day of the conference. The conference Org. : Janice Glasgow, (Queen's) was held concurrently with a workshop on Ontologies for Molecular Biology. This meeting The Sixth International Conference on focussed on several aspects of the schemata, Intelligent Systems for Molecular Biology controlled vocabularies and ontologies for (ISMB '98) was held in Montreal, Canada from bioinformatics. June 28-July 1, 1998. As with the previous ISMB In order to encourage and reward student conferences, this meeting provided a general participation in the conference, student awards forum for disseminating the latest developments were introduced. Malcolm Casale, from the in bioinformatics. ISMB is a multidisciplinary University of California, Irvine, was presented conference that brings together scientists from with the Best Student Paper Presentation and computer science, molecular biology, Carolyn Allex, from the University of Wisconsin, mathematics and statistics. Its scope includes won for the Best Student Poster Presentation. the development and application of advanced These awards were made possible by a donation computational methods for biological problems. from Glaxo Wellcome. The conference also The relevant computational techniques included facilitated student participation by making machine learning, pattern recognition, available travel awards that were made possible knowledge representation, databases, string by the generous sponsorship of several algorithms, statistical analysis, genetic industrial and government agencies. algorithms, information theory, hidden Markov Three keynote addresses were presented by models, logic programming, linguistic methods, eminent scientists: Robert Cedergren, from the constraint satisfaction, and data compression. University of Montreal, gave a talk on "Fishing Biological areas at the forefront of the conference for Function in RNA Form and Features"; were molecular structure, gene prediction, Michael Waterman, from the University of sequence alignment and analysis, molecular Southern California, spoke on the topic of function, simulation environments, modeling "Constructing Restriction Maps", and Shoshana protein repeats, docking, threading and and Wodak, from the European Bioinformatics phylogenetics. The emphasis of the conference Institute, gave a presentation on "Database was on the validation of methods using real data Derived Potentials for Prediction of Protein sets, on practical applications in the biological Structure and Stability". sciences, and on the development and For the first time, ISMB was under the official application of novel computational techniques. sponsorship of the International Society for The level of interest in ISMB '98 was high. The Computational Biology (ISCB). The mission of call for papers produced a record number of 92 this society is the advancement of the scientific submissions. All papers were rigorously understanding of living systems through reviewed by members of a distinguished computation; its emphasis is on the role of program committee, and the program was computing and informatics in advancing assembled based on their recommendations. molecular biology. Information on ISCB can be This selection process was very competitive and found at its web site (http://www.iscb.org). The resulted in 25 high-quality papers that appear in conference was also held in cooperation with the the proceedings, which were published by AAAI American Association for Artificial Intelligence Press. The conference was truly international (AAAI). with authors of accepted papers representing 12 Along with the high quality program of the countries and 4 continents. There was also conference, attendees were able to enjoy social record breaking attendance at ISBM '98: 413 events that included a welcoming reception and attendees registered including representatives a boat cruise on the St-Lawrence River. The from government and university (176), conference was timed so that many of the industrial participants (135), students (96) and participants could attend the world famous exhibitors (6). Montreal Jazz festival, which took place immediately following the meeting.

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The IIMS (Institute of Industrial International Conference on Mathematical Sciences) at the University of Operator Theory and its Applications Manitoba organized the Conference, and its to Scientific and Industrial Problems Director, Dr. P.N. Shivakumar, was the chair of October 7 - 11, 1998, Winnipeg the local organizing committee and the chairman Org. : P.N. Shivakumar (Univ. of Manitoba) of the conference. The participants expressed The scope of the conference topics was broad: gratitude to the NSF, the Fields Institute, CRM it included theoretical aspects of linear and and IMA and to the organizers of the conférence nonlinear operator theory and its applications to at the closing of the conférence on October 11, numerical analysis, biology, physics and 1998. A follow up Conference on Inverse engineering sciences. Scientific and industrial Problems was discussed and is expected to take problems can often be formulated in terms of place in 2000. differential and integral equations. There were many talks on various aspects of the theory and Atelier sur les méthodes algébriques applications of such equations. At the suggestion et géométriques en théorie des of the National Science Foundation (USA), champs de vecteurs sessions were held to discuss directions of 13-19 January 1999 research in the field as well as to formulate some Org. : C.Rousseau and D. Schlomiuk (UdeM) open problems. Cet atelier a regroupé plusieurs chercheurs Among the participants were internationally oeuvrant sur différentes méthodes algébriques et known specialists: D. Alpay, Y. Alber, J. Ball, G. géométriques en théorie des champs de vecteurs Elliott, F. Gesztesy, E. Khruslov, A. Ramm, P. et permis des échanges sur le sujet. Parmi les Rejto, F. Rofe-Beketov, B. Silbermann, H. de thèmes abordés les problèmes de finitude du Snoo, V. Strauss, V. Trenogin, N. Voitovich, N. nombre de cycles limites d'un champs de Young, and many other prominent specialists vecteurs ont reçu une attention particulière, tant and young researchers. au niveau des champs de vecteurs du plan There were several mini-symposia organized (conférences de F. Dumortier, V.Kaloshin, A. by internationally known specialists: on Mourtada, R. Roussarie, C. Rousseau, D. biomathematics, on ill-posed problems, on Schlomiuk et H. Zhu) que des champs de mathematical problems in solid mechanics, on vecteurs dans l'espace (conférences de L.-S. operator evolution equations, on non-standard Guimond et V. Kaloshin). Le thème de l'étude inverse problems arising in electrodynamics. des points singuliers en dimension supérieure a The participants of the conférence came from été couvert avec la conférence de P. Mardesic et North and South America, Europe and Asia. le colloque de X. Gomez-Mont auquel ont assisté Large groups came from the fSU (Russia, beaucoup d'étudiants. Le dernier thème majeur Ukraine, Armenia), Japan, Israel and Spain. de cet atelier a été celui de l'intégrabilité avec les There were also groups of participants from conférences de C. Christopher et J.-P. Françoise. Germany, Great Britain, The Netherlands and Les conférences les plus marquantes de Italy. There were several junior participants and l'atelier ont été la conférence d'A. Mourtada et Ph.D students among the participants and les conférences de V. Kaloshin, ces conférences financial help was given to them. témoignant d'une percée de premier plan dans le Due to the financial crisis in Russia, it was sujet et les participants de l'atelier ont beaucoup necessary to buy air tickets for some of the discuté avec ces deux conférenciers des détails Russian participants. The Conference was des résultats présentés. L'atelier a accueilli la supported by the Fields Institute ($5,000), CRM soutenance de thèse de L.-S. Guimond, thèse ($5,000) and the National Science Foundation effectuée en cotutelle entre l'université de (US $15,000) . Montréal et l'université de Bourgogne (Dijon). There is an agreement with the Fields L'étudiant Zhu a pu profiter de l'expertise de F. Institute that a volume with these papers will be Dumortier et R. Roussarie pour la poursuite de published by the Fields Institute jointly with the sa thèse. Enfin la présence de tous ces visiteurs a American Mathematical Society. P.N. permis de nouvelles collaborations entre A. Shivakumar, A.G. Ramm and A. Strauss are the Mourtada et D.Schlomiuk d'une part et entre C. Editors for the Proceedings. Christopher, P. Mardesic et C. Rousseau d'autre part.

24 Annual Report 1998-1999 CRM S C I E N T I F I C A C T I V I T I E S

VI/QCAV’99 Conference: Vision • Les aspects formels de la répartition Interface and Quality Control by • Architectures et développements d'appli- Artificial Vision cations réparties dans des domaines spé- 18-21 May 1999, Trois-Rivières cifiques Org. : F. Nouboud (UQTR) • Aspects spécifiques de la gestion des applications réparties La 12ième édition de la conférence Vision • Ingénierie d'applications réparties: Interface (VI) a eu lieu à Trois-Rivières, Québec, • Applications distribuées dans les Canada, du 18 au 21 mai 1999 conjointement environnements mobiles. avec la 5ième édition de la conférence Quality Control by Artificial Vision (QCAV). th VI/QCAV'99 a été un grand succès avec 220 27 Annual Canadian Conference on participants provenant de plus de 23 pays et 150 Operator Theory and Operator présentations arbitrées par deux comités Algebras internationaux. En plus des sessions orales et 20-24 May, 1999, Prince Edward Island d'affiches arbitrées, une session poster spéciale a Org. : Gordon MacDonald été organisée pour les étudiants de deuxième et The 27th Canadian Operator Theory troisième cycles. Symposium was held May 20-May 24, 1999 at La participation du milieu industriel à ces the University of Prince Edward Island in deux conférences fût importante et s'est traduite Charlottetown, Prince Edward Island. Over 50 par la tenue de deux ateliers spéciaux durant cet researchers were in attendance. The following événement. Le premier atelier, Industry papers were presented: Researchers Link Up, était parrainné par CIPPRS Blecher, David, Univ. of Houston (Canadian Image Processing and Pattern Noncommutative functional analysis and Recognition) et le NRC (National Research noncommutative spaces Council of Canada). Le second atelier, relié au Choi, Man-Duen, Univ. of Toronto projet international HUTOP (Human Sensory Re-encounters with numerical ranges Factors for Total Production Life Cycle) a été Davidson, Ken, Univ. of Waterloo organisé par une équipe de chercheurs Isometric dilations of non-commuting n-tuples and universitaires et industriels du Japon. representations of the Cuntz algebra Deux comptes-rendus arbitrés (VI et QCAV) Dean, Andrew J., Univ. of Toronto Stable relations and continuous fields ont été publiés ainsi qu'un disque compact. Les Drissi, Driss, Kuwait Univ. conférences VI/QCAV'99 se sont avérées être un On operators satisfying Kreis-Ritt resolvent condition succès grâce au support et la collaboration des Elliot, George, Univ. of Toronto nombreux partenaires impliqués dans ces On the possible role of algebraic K-theory in classification conférences. theory Fialkow, Lawrence, SUNI-New Paltz The quartic complex moment problem Colloque NOTERE’ 98 (Nouvelles Rulman, Igor, Univ. of Calgary Technologies de la Répartition) Ideals in non-selfadjoint algebras associated to 20-24 October, Univ. de Montréal semidynamical systems Org. : Rachida Dssouli (UdeM), Petre Dini ( CRIM), Ge, Liming, Univ. of New Hampshire Michel Kadoch (Université du Québec ETS) Convex bodies, covering numbers and free entropy C'est la deuxième édition du Colloque Gong, Guihua, international sur les Nouvelles Technologies de Classification of simple inductive limit C*-algebras Han, Deguang, McMaster Univ. la Répartition. La première édition a eu lieu à Adensity result for projective unitary representations Pau (Novembre 97). Après l'ère de la program- Hadwin, Don, Univ. or New Hampshire mation structurée, des modèles en couches et Completely rank-nonincreasing linear maps des réseaux de communication, l'informatique Handelman, David, Univ. or Ottawa répartie est déjà bien rentrée dans une autre ère, Matrices of positive polynomials celle des objets, des plates-formes, de la Haworth, Paul, Lancaster Univ. transparence et de la banalisation des réseaux de Characterisation of separable operator algebras communication. Après un règne florissant et Holbrook, John, Univ. of Guelph riche en production scientifique, normative et Big problems with small matrices Kribs, David, Univ. or Waterloo technologique, le modèle OSI et ses diverses Isometric dilations of non-commuting finite rank n-tuples variantes, ont déjà fait place à de nouveaux Kumjian, Alex, Univ. of Nevada modèles, architectures et environnements, pour C*-Algebras of higher rank graphs le développement d'applications réparties: DCE, Larson, David, Texas A & M Univ. ODP, CORBA, OLE, JAVA, WEB, etc. Operator algebras and wavelets • Les thèmes spécifiques à cette édition sont: Livshits, Leo, Colby College

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On band algebras Tang, Wai Shing, National Univ. of Singapore Marcoux, Laurent, Univ. of Alberta Multiwavelets in Hilbert spaces Lie structures in operator algebras Toms, Andrew,

Mohebi, Hossein, Dalhousie Univ. On perforated ordered K0 groups of simple and Best approximation in reflexive subspaces of commutative C*-algebras L (X, Y) Vasilevski, Nikolai, CINVESTAV del I.P.N. Nikolaev, Igor, CRM, Univ. de Montréal Toeplitz operators on the unit disk with radial symbols Glimm algebras over S1 Yahaghi, Reza, Dalhousie Univ. Power, Stephen, Lancaster Univ. On simultaneous triangularization of commutants Approximately finitely acting operator algebras Zorboska, Nina, Univ. of Manitoba Radjavi, Heydar, Dalhousie Univ. Essentially normal composition operators On semigroups of non-negative operators (in other sense) Rosenthal, Peter, Univ. of Toronto Inequalities for spectral radII of products

26 Annual Report 1998-1999 CRM S C I E N T I F I C A C T I V I T I E S

CRM Prizes

CRM/Fields Prize Professor Cook has also made significant In 1994 the Centre de Recherches contributions to the fields of the structure of Mathematiques (CRM) and the Fields Institute abstract complexity classes, models of parallel announced the creation of a new prize to be computation, and mathematical logic. awarded for exceptional contributions to the mathematical sciences. The recipient of the Stephen A. Cook received his doctorate from prize is chosen by the Comite consultatif of the Harvard University in 1966. After a four year CRM and the Scientific Advisory Committee stay at the University of California at Berkeley, of the Fields Institute according to the criterion as assistant professor, he joined the faculty of the of excellence in research. The prize consists of University of Toronto where he is currently both a $5 000 award and a medal, and the Professor in the Department of Computer winner is required to give a lecture at the CRM Science, Honorary Professor in the Department and the Fields Institute. The past recipients are: of Mathematics and "University Professor". To H.S.M. Coxeter, G.A. Elliot, J. Arthur, and R.V. mention just a few of his numerous honours, he Moody; this year's winner is Stephen A. Cook. has held Steacy and Killam Fellowships, he is a member of the Royal Society of Canada and the The CRM/Fields Prize for 1998 was awarded National Academy of Sciences of the United to Professor Stephen A. Cook of the University States, as well as numerous other honorary of Toronto. Professor Cook works primarily in societies both foreign and domestic. Professor the field of computational complexity which is Cook has given many invited addresses the study of the inherent difficulties in computer including a plenary lecture at the International calculation. He is probably most well known for Congress of Mathematicians in 1998. a result which first appeared in his 1971 paper "The Complexity of Theorem Proving The following is Professor Cook's resume of Procedures" and which is now known simply as the CRM/Fields Prize Lecture which he gave at "Cook's Theorem". This result established, by the CRM on November 19, 1999: means of an elegant construction, the existence of the first NP-complete problem. It stimulated "We present an historical overview of considerable further research, much of it by R.M. computational complexity theory. The emphasis is on Karp. For their efforts Professors Cook and Karp the importance, plausibility, and difficulty of the were both awarded the Turing Prize. conjecture that P is not equal to NP, which Steve Smale listed as one of the top three mathematical problems for the next century."

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André-Aisenstadt Prize devoted to this question principally in terms of trace formulae for the reduced wave operator, U(t)= exp (it√∆) and the related Weyl asymptotics for the Created in 1991, the André-Aisenstadt λ λ ∈ ∆) spectral counting function, N( ) = # { j Spec( ; Mathematics Prize is intended to recognize and λ ≤λ} as λ→∞. However, comparatively little is reward talented young Canadian j known about the asymptotics of the corresponding mathematicians. The Prize, which is given for eigenfunctions. In the first part of the talk, I discussed research achievement in pure and applied recent results on the asymptotic concentration of mathematics, consists of a $3000 award. The Laplace eigenfunctions in the case where ∆ is recipient is chosen by the CRM Advisory quantum completely integrable. I then gave some Committee. At the time of nomination, implications for inverse spectral theory. candidates must be Canadian citizens or In the second part, I linked semiclassical analysis permanent residents of Canada, and no more to a geometric ``Law of Large Numbers'' for families than seven years from their Ph.D. The previous of Riemannian manifolds of increasing dimension and winners of the André-Aisenstadt Prize were: positive Ricci curvature. To do this, I showed how Niky Kamran(1991); Ian Putnam (1992); questions involving semiclassical concentration Michael Ward and Nigel Higson (1994); Adrian phenomena arise naturally when considering the S. Lewis (1995); Henri Darmon and Lisa Jeffrey dimensional limits of Gromov and Milman. (1996) ; Boris Khesin (1997).

The CRM took great pleasure in awarding the 1998 Andre Aisenstadt Prize to Professor John Toth from McGill University.

Professor Toth is one of the leading young microlocal analysts in the world. His has done fundamental work on the asymptotic concentration of eigenfunctions of quantum completely intégrable Laplacians. This work has important implications for inverse spectral theory on Riemannian manifolds. He has also developed a deep and fascinating link between semiclassical analysis and a geometric "law of large numbers" for parametrized families of Riemannian metrics of positive Ricci curvature.

John Toth obtained his B.Sc in 1988 and his M.Sc in 1989, both from McMaster University.

He then moved on to MIT where he obtained his Ph.D. under the direction of Victor Guillemin in 1993. From 1993 to 1995, he was a Benjamin Peirce Instructor at Harvard. He joined McGill University as an Assistant Professor in the Fall of 1995.

Professor Toth presented a lecture at the CRM on October lst 1999, entitled, Concentration phenomena in semiclassical analysis. A summary of his talk follows :

Let (M,g) be a compact, C∞ Riemannian manifold and ∆, the associated Laplace-Beltrami operator. One of the main objectives of semiclassical analysis is the study of the connection between the spectral asymptotics of ∆ and the geometry of the geodesic flow on the cosphere bundle, S*M. Over the past thirty years, there has been a great deal of work

28 Annual Report 1998-1999 CRM S C I E N T I F I C A C T I V I T I E S

CRM-CAP Prize

The CRM-CAP Prize is given for outstanding Prof. Rowe received B.A.s in 1959 from contributions to theoretical and mathematical Cambridge University and Oxford University. In physics. Previous winners were Werner Israel 1962, he obtained his M.A. from Oxford of the University of Alberta (1995), William G. University as well as a D. Phil (Thesis: "Studies Unruh of the University of British Columbia of Nuclear Structure using Medium Energy (1996), Ian Affleck of the University of British Protons"). After spending a year as a lecturer at a Columbia (1997), and J. Richard Bond of CITA Royal Air Force Radio School, Dr. Rowe worked of the University of Toronto (1998).The 1999 as a Ford Foundation Fellow at the Neils Bohr CRM-CAP prize has been awarded to David Institute followed by a three years with the J.Rowe. Atomic Energy Research Establishment (Harwell). He was a Research Associate at the The Canadian Association of Physicists University of Rochester from 1966-68 and joined (CAP) and the Centre de recherches the faculty at the University of Toronto as an mathématiques (CRM) are pleased to announce Associate Professor in 1968. He became full that the 1999 CAP-CRM Prize in Theoretical and Professor in 1974. He was elected a Fellow of the Mathematical Physics will be awarded to David Royal Society of Canada in 1986. J. Rowe, Professor at the University of Toronto, for developing a microscopic foundation for the Dr. Rowe has received a number of honours, models and theories of nuclear collective states including an A. P. Sloan Fellowship (1972), the by the application of elegant techniques from Rutherford Memorial Medal (1983) of the Royal group theory and mathematical analysis. Society of Canada, Fellowship in the Royal Society of Canada (1986) and an Isaac Walton Together with his students and associates, Killam Senior Research Fellowship from 1990-92. Dr. David J. Rowe has been able to develop a detailed picture of important system, based on The annual CAP-CRM Prize in Theoretical the underlying properties of the protons and and Mathematical Physics was first introduced neutrons that form the nucleus. In doing so, he in 1995. Dr. Rowe will receive the 1999 Prize also developed a number of new mathematical during the CAP's awards banquet to be held at tools that have used to explain other classes of the University of New Brunswick on June 8th, phenomena. 1999. Rowe's research has introduced many techniques of modern mathematics into physics, a strategy that allowed him to make significant steps in the development of modern nuclear theory. Understanding the atomic nucleus has been considered an intractible problem, as it involves simultaneously describing the behaviour of hundreds of particles, all interacting strongly under the force that binds together the nucleus. Rowe's contributions have enabled us to view this system as literally a fluid, albeit one with unusual properties. The mathematical techniques he has introduced have found application in many other areas of physics, especially in those cases where the underlying patterns or symmetries of the system change. Rowe's impact on theoretical physics has therefore extended far beyond the original scope of his work on the structure of the atomic nucleus.

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English or in French in peer-reviewed statistical Statistical Society of Canada Prize journals, but he also co-authored publications in actuarial science, finance, management, mathematical psychology and other areas. A The CRM-SSC Prize in Statistics is a new joint complete list of his writings may be found at prize awarded yearly by the Centre de www.mat.ulaval.ca/pages/genest. recherches mathématiques (CRM) and the Statistical Society of Canada in recognition of outsanding contributions to the Statistical Sciences during the recipient’s first 15 years after earning a doctorate. The CRM-SSC Prize in Statistics consists of a $3000 award and a medal. The recipient is chosen by a joint In recognition of his contributions to CRM/SSC advisory committee, consisting of research, Dr Genest received the 1999 Summa three members named by the SSC and two, Award from Laval University's Faculty of including a president, by the CRM.The Science and Engineering; he was also promoted Statistical Society of Canada and the CRM to the rank of fellow of the American Statistical took great pleasure in awarding the 1999 Association (1996) and the Institute of Statistical Society of Canada Prize to Professor Mathematical Statistics (1997). Also recognized Christian Genest from Laval University. for the quality of his teaching and for his careful supervision of some fifteen graduate students he Born in Chicoutimi (Quebec), Christian advised over the years, Dr Genest was awarded Genest received his mathematical education at the SSC Plaque for Services to the profession in the University of Quebec at Chicoutimi (B. Sp. 1997. He served on many thesis committees and Sc., 1977) and at the University of Montreal (M. national orinternational selection committees Sc., 1978). He then specialized in statistics at the (NSERC, FRSQ, COPSS Fisher Award, ISI Jan University of British Columbia, where he Tinbergen Award, etc.), in addition to being completed in 1983 a doctoral thesis for which he actively involved in the scientific and local was selected as the winner of the Pierre organization of several international meetings, Robillard Award of the Statistical Society of most notably the memorable 1996 meeting of Canada (SSC). He held teaching and research French-speaking statisticians in Quebec City. positions at Carnegie-Mellon University, in Christian Genest is currently Editor in Chief of Pittsburgh (1983-4), and at the University of "The Canadian Journal of Statistics." In recent Waterloo, in Ontario (1984-7), before joining the years, he has also been responsible for several Department of Mathematics and Statistics at quality insurance workshops in industry, in Laval University in June 1987, where he was addition to being a regular consultant for the promoted to professorship in 1993. Author or co- Quebec Institute of Statistics and Statistics author of over forty research papers in Canada's Committee on Statistical Methodology. fundamental and applied statistics, Professor Genest has developed expertise in opinion pooling methods, multicriteria decision making techniques, concepts and non parametric measures of dependence, as well as inference for multivariate stochastic models derived from copulas. Most of his work has been published in

30 Annual Report 1998-1999 CRM S C I E N T I F I C A C T I V I T I E S

Member’s Seminars & Special Events

The members of the CRM are encouraged to organise seminars and other scientific activities during their stay at the CRM. These activities take the form of a course, a workshop, of a research seminar.

Éric Renault, CREST-INSEE (Paris) Seminar in statistics Composantes principales non linéaires et Org. : Christian Léger (UdeM) inférence sur un opérateur d'espérance conditionnelle • 8 October 1998 • 18 February 1999 Keith Worsley, Univ. McGill Christian Gouriéroux , CREST, Paris Detecting shape changes via non-isotropic Kernel Based Nonlinear Canonical Analysis random fields • • 10 March 1999 15 October 1998 Mark Glickman, Boston Univ. David Bellhouse, Univ. of Western Ontario Density Estimation from Complex Surveys Parameter Estimation in Large Dynamic Paired • Comparison Experiments 29 October 1998 • Michael Newton, Univ.du Wisconsin à Madison 18 March 1999 Statistical methods for a cancer mutagenesis Michael Evans, Univ. de Toronto experiment Concepts of Surprise Used to Derive Inferences • 5 November 1998 Jean-François Angers, Univ. de Montréal Seminar in statistics Transformée de Fourier et l’estimation bayesienne Org.: Roch Roy (UdeM) d’un paramètre de position • 3 June 1999 • 12 November 1998 Ian McLeod, Univ. of Western Ontario Celia Greenwood, Univ. McGill Misspecification in Hyperbolic Time Series Affected sib pair models with covariates and constraints • Seminar in nonlinear Analysis 19 November 1998 Org.: Marlène Frigon (UdeM) Renate Meyer, Univ. d'Auckland • Bayesian Stock Assessment Using a Nonlinear 28 September 1998 State-Space Model Frédéric Picard, Univ.de Montréal Introduction aux espaces de Sobolev • 26 November 1998 • 5 October 1998 James Ramsey, New York Univ. Frédéric Picard, Univ. de Montréal The role of time scale in the analysis of aggregated Introduction aux espaces de Sobolev, II relationships using wavelets • • 19 October 1998 3 December 1998 Frédéric Picard, Univ.de Montréal Don Fraser, Univ. de Toronto Some useful integrals for asymptotic densities: the Introduction aux espaces de Sobolev, II • 26 October 1998 mystery of hyperaccuracy in inference Isidore Fleischer, Fleischer Foundation • 14 January 1999 Comment présenter le théorème de point fixe de Christian Genest, Univ. Laval À propos de l'estimation de la fonction de Brouwer en analyse III • 9 November 1998 dépendance d'une loi de valeurs extrêmes bivariée Alexandre Girouard, Univ.de Montréal • 28 January 1999 Points critiques multiples de fonctionnelles Angelo Canty, Univ. Concordia Hypothesis Testing for Convergence of the Gibbs symétriques • 16 novembre 1998 Sampler Alexandre Girouard, Univ. de Montréal • 4 February 1999 Points critiques multiples de fonctionnelles Pierre L'Ecuyer, Univ.de Montréal Interaction des tests sériels avec la structure de symétriques II • 23 November 1998 certaines familles de générateurs pseudo-aléatoires Alexandre Girouard, Univ. de Montréal • 8 February 1999 Points critiques multiples de fonctionnelles Annie Morin, IRISA Univ. de Rennes 1 symétriques III Présentation de deux méthodes d'analyse des • 30 November 1998 données textuelles pour la recherche Nicolas Beauchemin, Univ. de Montréal documentaire Théorème du point de selle généralisé pour des fonctionnelles multivoques paires • 14 December 1998 Nicolas Beauchemin, Univ. de Montréal • 11 February 1999

CRM Annual Report 1998-1999 31 S C I E N T I F I C A C T I V I T I E S

Théorème du point de selle généralisé pour des • 3 November1998 fonctionnelles multivoques paires II Z. Masakova, Univ.Technique de Prague et • 18 January 1999 CRM Nicolas Beauchemin, Univ. de Montréal Autosimilarités des quasicristaux basés sur des Théorème du point de selle généralisé pour des nombres de Pisot quadratiques unitaires fonctionnelles multivoques paires III • 5 November 1998 • February 1, 1999 Bernard Champagne, CRM Marlène Frigon, Univ.de Montréal Méthodes de Coxeter pour la génération de Quasi- La notion d’enlacement en théorie des points Réseaux • critiques 10 November 1998 • 8 February 1999 C. Doran, Harvard Univ. Ron Stern, Concordia Univ. Algebraic and Geometric Isomonodromic Some current issues in feedback control Deformations • 15 February 1999 • 17 November 1998 Frédéric Picard, Univ.de Montréal D.Korotkin, Max Planck Institute Enlacement local Isomonodromic Deformations and Theta • 8 March 1999 Functions in Dimensionally Reduced Einstein Emmanuel Montoki, Univ. de Montréal Equations Problème elliptique résonnant • 23 November 1998 • 15 March 1999 V. Dorodnitsyn, Keldysh Institute of Applied Emmanuel Montoki, Univ. de Montréal Mathematics, Moscow Problème elliptique résonnant II Lie point symmetries of second order ordinary • 29 March 1999 difference equations and of a nonlinear discrete D. Anosov, Univ. of Moscow heat equation Some achievements in the theory of Dynamical • 24 November 1998 Systems during the last 25 years Myriam Caprioglio, CRM Reconnaissance de contours: Application en Seminar in Mathematical Physics vidéokératographie Org.: Pavel Winternitz (UdeM) • December 1,1998 Roman Grodzicky, CRM • 11 August 1998 I. Mindlin, Technical Univ. Un quasi-cristal vu comme un ensemble modèle • New Analytic Methods for Solutions of Nonlinear 8 December 1998 George Pogosyan, Institut international de Problems of Vortex and Wave Dynamics in physique nucléaire, Dubna, Russie Heavy Liquids with Piecewise Constant Density • Coulomb Oscillator Duality on Spaces with 18 August 1998 Constant Curvature D. Levi, Univ. of Roma III • 16 December 1998 Solitons on a Free Electron Laser Anatol Odzijewicz, Univ.de Bialystok, Pologne • 25 August 1998 Quantum Algebras and q-special functions Luigi Martina, Univ.Lecce Bright Solitons and Black Holes related to coherent state map • 7 January 1999 • 15 September 1998 N.M. Atakishiyev, Instituto de Matematicas, Iadh Ayari, Univ.de Montréal Unam (Mexico) Symétries conditionnelles pour les équations de Fourier-Gauss Transforms of some q-special Sawada-Kotera et Tzitzéica functions • 22 September 1998 • 12 January 1999 D. Richter, Univ. McGill Zora Thomova, SUNY (Utica) Z-Gradations of Simple Lie Algebras and Maximal Abelian subalgebras of the e(p,q) Infinitesimal Generators algebras and their application • 28 September 1998 • 19 January 1999 Jean-Marie Souriau, Univ. de Provence • Paul Bracken, CRM DE MOTU The Weierstrass-Enneper System for Constant • 29 September 1998 Jean-Marie Souriau, Univ. de Provence Mean Curvature Surfaces the Completely DE MOTU II Integrable Sigma Model, and Certain Classes of • 13 October 1998 Solutions • John Harnad, Univ. Concordia et CRM 26 January 1999 Les équations de Picard-Fuchs, les fonctions Stéphane Lafortune, CRM modulaires et les systèmes intégrables Schlesinger Transformations for linearisable • equations 21 October 1998 • Alexei V. Penskoï, DMS et CRM 9 February 1999 Les crochets de Poisson algébro-géométriques et le Philippe Roche, MIT (Cambridge) et École Polytechnique (Palaiseau, France) système de Volterra

32 Annual Report 1998-1999 CRM S C I E N T I F I C A C T I V I T I E S

Analyse harmonique sur le groupe quantique de Working Group on Frobenius Lorentz et polynômes d’Askey-Wilson Manifolds, Seiberg-Witten Theory and • 22 February 1999 Integrable Systems Robert Conte, Saclay Correspondance birationnelle entre les deux Org. : John Harnad (Concordia et CRM) fonctions entières de la transformation de • 16 October 1998 Bäcklund: le cas de l’équation de Kaup- Introduction to Frobenius Manifolds I Kupershmidt • 23 October 1999 • 23 February 1999 Introduction to Frobenius Manifolds. II Philippe Zaugg, CRM, CNRS et LAPP • 30 October 1998 Le modèle de Schrodinger non-linéaire et algèbre Frobenius Manifolds and Isomonodromic de Yangien Deformations • 2 March 1999 • 6 November 1998 Jean-Pierre Gazeau, Univ.Paris VII Frobenius Manifolds and Isomonodromic États cohérents pour des systèmes à spectre Deformations, II discret et/ou continu • 13 November 1998 • 9 March 1999 Frobenius Manifolds and Isomonodromic Stephen Anco, Univ.Concordia Deformations, III Complete conservation laws and symmetries of Frobenius Manifolds Seiberg-Witten Maxwell’s equations Theory and Integrable Systems • 30 March 1999 • 20 November 1998 Alexei V. Penskoi, CRM et DMS Hurwitz Spaces Les opérateurs aux différences finies algébro- géométriques • 13 April 1999” Special Lectures Paul Sorba, LAPTH, CNRS, Annecy (France) Org. : Ram Murty (Queen’s) A (Quantum) Group Theoretical Model for the • 25 November 1998 Genetic Code Dmitry Jackson, Caltech • 20 April 1999 Limits of eigenfunctions Pierre Mathieu, Univ. Laval • 25 November 1998 Bases de fusion Nathan Ng, Univ. of British-Columbia • 27 April 1999 Zeros of L-functions on the critical line J.A. Tuszynski, Univ.of Alberta • 25 November 1998 Model of Motor Protein Motion Along Mark David Coleman, UMIST Microtubule Filaments Chens Theorem, Linniks Theorem • 4 May 1999 • 19, 21, 25 and 26 May 1999 Pavel Winternitz, CRM et DMS, Univ. de Montréal Mark Goresky, IAS Classification des équations à différences finies Chern classes of modular varieties selon leurs symétries de Lie • 21, 25 and 26 May 1999 • 11 May 1999 Mark Goresky, IAS Paul Sorba, LAPTH, CNRS et CRM Lefschetz fixed point for Hecke correspondances Remarques sur les algèbres de symétrie déformées : propriétés et relations Workshop in Industrial and Applied • 13 May 1999 Mathematics Stephen Anco, Concordia Univ. Classification of Symmetries and Conservation Org.: Michel Delfour (UdeM) Laws of Maxwell’s Equations • 30 March 1999 • 18 May 1999 Mohammed Aassila, CRM Lubomir T. Dechevsky, DMS Nouvelle approche à la stabilisation forte des Integral Represenations of Local and Gobal systèmes distribués Diffeomorphisms and Applications • 29 April 1999 • 20 May 1999 Jacques Henry, INRIA Rocquencourt, France E.V. Ferapontov, Moscow, Landau Institute for Factorisation d’opérateurs elliptiques du 2ème ordre Theor. Phys. par programmation dynamique Systems of conservation laws and projective • 29 April 1999 theory of congruences Patrick Giroud, IMAG, Grenoble, France • 25 May 1999 Analyse asymptotique de coques inhomogènes en A. Zhedanov, Donetsk Univ.et CRM lasticité linéarisée anisotrope Orthogonal polynomials satisfying higher order differential equations Seminar of the PHYSNUM Group Org.: Jean-Marc Lina (UdeM)

CRM Annual Report 1998-1999 33 S C I E N T I F I C A C T I V I T I E S

• 11 June 1998 Workshop in Industrial and Applied Rita Noumeir, École de technologie supérieure Mathematics Reconstruction de Surface en Tomographie Org. : Noriko Yui (Queen’s) • 16 June 1998 • Emmanuel Bacry , CMAP, École Polytechnique, 27 November 1998 Paris James Lewis, Univ. of Alberta Récents développements en analyse du signal: de Chow Groups, Hodge Theory and (higher) l'analyse en ondelettes au "matching pursuit regulartors • 18 June 1998 • 27 November 1998 Kalid Daoudi, MIT Brent Grodon, Univ.of Oklahoma Construction de modèles autogressifs muti-échelles Chow-Künneth decompositions for some degenerating families of abelian varieties ayant des coéfficients en ondelettes • comme variables d'état 27 November 1998 • October 1,1998 Hiroyuti Ito (Tôhoku Univ.and Harvard Univ.) Bernard Picinbono, Laboratoire des Signaux et Extremal and elliptic modular surfaces • Systèmes, École Supérieure d'Électricité et 27 November 1998 Université de Paris-Sud Abdella Sebbar, CRM Du réel au complexe en traitement du signal Discrete subgroups of SL (2,R) and Schwarzian • 8 October 1998 differential equations Jean-Charles Côté, U de M et Hôp. Notre-Dame • 27 November 1998 (CHUM) Noriko Yui, Queen’s Univ. and CRM Nouveau concept d'excitation RF en Imagerie de The modularity conjecture for rigid Calabi-Yau Résonance Magnétique Nucléaire threefolds over number fields • 12 November 1998 Jean-Louis Merrien, INSA-Rennes (France) Workshop on Algebraic and Interpolants d’Hermite par subdivison et rayons Geometric Methods in the Theory of spectraux généralisés Vector Fields • 17 February 1999 Kaleem Siddiqi, Univ. McGill Org. : C. Rousseau and D. Schlomiuk (UdeM) Geometric flows for shape segmentation 13 - 19 January 1999 • 11 May 1999 • 13 January 1999 G. Oppenheim, Equipe de probabilité et J.-P. Françoise,Paris VI Statistique d’Orsay et Univ. De Marne la Vallée The classical Bautin method Une façon simple de créer de la mémoire longue V. Kaloshin, Princeton An estimate for cyclicity of elementary polycycle I Seminar on Probability Theory (Il’yashenko-Yakovenko theorem with an explicit Org. : Dana Schlomiuk (UdeM) and Martin estimate) Goldstein C. Christopher, Plymouth, UK • 12 November 1998 Liénard systems with linearisable centres Ioan Cuculescu, Univ. de Bucarest V. Kaloshin (Princeton) An estimate for cyclicity of elementary polycycle II Représentations des mesures de probabilité • préservant la moyenne et leur application à la 14 January 1999 positivité des moments fonctionnels D. Schlomiuk, CRM Théorèmes de finitude pour les cycles limites et en géométrie diophantienne Special Lectures R. Roussarie, Dijon, France Org.: Paul Arminjon (UdeM) Unfolding hyperbolic polycycles • 17, 19 and 22 June 1998 X. Gomez-Mont, Guanajuato, Mexique Marie-Claude Viallon, Univ. de Saint-Etienne Dissipative and Conservative Components in Principe de convergence d’une méthode de Transversely Conformal Foliations volumes finis pour la résolution d’une équation de L.-S. Guimond,Univ. de Montréal, (soutenance de conservation hyperbolique. Introduction aux thèse) mesures de Young. Cyclicité finie des boucles homoclines dans R3 Applications à la convergence d’une généralistion non dégénérées avec valeurs propres principales des schémas aux différences de Lax-Friedrichs et en résonance 1:1 Nessyahu-Tadmor à uneméthode de volumes finis • 15 January 1999 d’ordre 2 sur des maillages non-structurés F. Dumortier, Diepenbeek, Belgique Application à la convergence de la méthode Hamiltonian bifurcations in Liénard equations of Arminjon-Viallon pour une équation de type (3,2) conservation hperbolique non linéaire V. Kaloshin, Princeton

34 Annual Report 1998-1999 CRM S C I E N T I F I C A C T I V I T I E S

Bifurcation of spatial polycycles and the Newton • 18 January 1999 Interpolation polynomials (multidimensional J.P. Françoise, Paris VI extension of Il’yashenko-Yakovenko theorem) « A global complex analytic version of Bautin’s Mourtada, Dijon, France theorem » Déploiement analytique de polycycles P. Mardesic, Dijon, France hyperboliques. Un cas localement noethérien Indice des champs de vecteurs tangents aux X. Gomez-Mont, Guanajuato, Mexique variétés singulières Computing Topological Invariants with Linear C. Rousseau, CRM Algebra Finite cyclicity of graphics through a nilpotent point of saddle or elliptic type I • 19 January 1999 J.P. Françoise, Paris VI The successive derivatives method and its comparison to the classical Bautin’s approach. The Abel equation approach. H.-P. Zhu , Université de Montréal Finite cyclicity of graphics through a nilpotent point of saddle or elliptic type II

CRM Annual Report 1998-1999 35 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 1998 winter 1998 • 24 September 1998 • 15 January 1999 Jean-Marie Souriau, Univ. de Provence Xavier Gomez-Mont, CIMAT, Guananjuato DE MOTU (Mexique) • 2 October 1998 Computation of topological numbers via linear Herbert Hetchcote, Univ.of Iowa algebra Periodicity and Stability in Epidemiological • 29 January 1999 Models Keith Worsley, McGill Univ. • 23 October 1998 Shape analysis and the geometry of random fields Ram Murty, Queen’s Univ. • 5 February 1999 Artin L-functions Alexander Zvonkine, Univ.de Bordeaux I • 30 October 1998 Combinatoire des polynomes complexes Paul Koosis, McGill University • 12 February 1999 Relations between two results about entire Changfeng Gui, Univ. of British Columbia functions of exponential type On a conjecture of de Giorgi and related problems • 6 November 1998 • 19 February 1999 Brian Steer, Oxford Univ. Donald Dawson, The Fields Institute Knots and some (uncalculable) invariants Local and global random structures in nonlinear • 13 November 1998 stochastic partial differential equations Mark Sapir, Vanderbilt Univ. • 26 February 1999 Dehn functions on groups and computational Israel M. Sigal, Univ. of Toronto complexity Some mathematical problems in quantum field • 20 November 1998 theory Yuri Berest, Univ. of California at Berkeley • 5 March 1999 Differentially Isomorphic Curves Andrew Granville, Univ. of Georgia • 27 November 1998 Locating zeros of Fekete polynomials Alexandru Buium, Univ. of Illinois • 12 March 1999 Elementary adeles and differential modular forms Michel Delfour, Univ. de Montréal • 4 December 1998 L’optimisation de forme via l’analyse fonctionnelle Nancy Reid, Univ. of Toronto • 19 March 1999 Approximate ancillarity and accurate p-values Jean-François Mestre, Univ.de Paris VII • 11 December 1998 Capacités, courbes hyperelliptiques et moyennes Idun Reiten, Norwegian Univ.of Science arithmético-géométrique Finite dimensional algebras and commutative • 26 March 1999 rings Fred Gehring, Univ.of Michigan Quasiconformal mappings and their role in mathematics • 9 April 1999 A. Johan de Jong, M.I.T. The fundamental group of a curve over a finite field • 16 April 1999 Sylvain Cappell, Courant Institute, NYU New geometrical comparisons of integration and lattice summation • 23 April 1999 Karen Parshall, Univ.of Virginia The Mathematical Legacy of James Joseph Sylvester (1814-1897)

36 Annual Report 1998-1999 CRM S C I E N T I F I C A C T I V I T I E S

COMING EVENTS

Theme Year 1999-2000Ê: Mathematical Physics

Organizing Committee 9th CRM Summer School Theoretical Physics at the End of the Philippe Di Francesco (North Carolina) XXth Century Lisa Jeffrey (Univ. of Toronto) June 27 - July 10, 1999, Banff, Alberta, André LeClair (Cornell) Org. : Yvan Saint-Aubin (UdeM & CRM), Luc Vinet Yvan Saint-Aubin (UdeM, CRM) (McGill & CRM) Luc Vinet (UdeM, CRM) Invited Speakers : Ian Affleck (UBC), Gilles Brassard (Montréal), Eric D'Hoker (UCLA ), Michael Duff Overview (Texas A&M), Krzysztof Gawedzki (IHES), Brian R. Greene (Columbia), Allan Griffin (Toronto), Satoru Many sectors of mathematics and physics Odake (Shinsu), José N. Onuchic (UCSD), Marc have been tightly interwoven in the last decades. Potters (Science & Finance, Paris), Ben Simons The interactions have triggered some important (Cambridge), Frank Wilczek (Institute for Advanced developments that turned out to be fruitful for Study) both disciplines: to name only a few, conformal field theory, vertex operators and representation The School will cover a large spectrum of theory; string theory, duality, non-commutative active topics in theoretical physics such as geometry and mirror symmetry; classical and conformal field theory and its applications, quantum integrable systems and quantum string theory and duality, mesoscopic systems, groups. integrable models, disordered systems, These links make a theme year in mathe- cosmology, Bose-Einstein condensation as well matical physics particularly appealing. Several as new fields of interest to physicists like other reasons make it compelling. Canada can quantum information processing and statistical boast of an impressive number of first-class physics in finance. mathematical physicists, a number which is even larger if one includes theoretical physicists Aisenstadt Chair Lecture Series whose research interests have been influenced Renormalization Group and Fermionic Functional by mathematical developments. Through its Integrals various events and minicourses, it will also Joel Feldman (UBC) provide excellent opportunities for (pure) August 22-25, 1999 mathematicians to learn how recent Nonlinear (fluid dynamical) equations and d-Branes developments in some of their disciplines are Roman Jackiw (M.I.T) being used in physical theories. The summer March 2000 school, the longer workshops, and the winter concentration period are designed to welcome Supersymmetric Gauge Theories, Symplectic Forms, advanced graduate students and postdoctoral and Integrable Models fellows in both mathematics and physics and Duong H. Phong (Columbia) give them a chance to interact among themselves May 2000 and with the leaders of these disciplines. Two of Fermi surfaces and infinite genus Riemann surfaces the workshops draw not only from mathematics Joel Feldman (UBC) and physics but from yet a third discipline May 2000 (finance and computer science, respectively). Finally the theme year will enhance links between the mathematics and theoretical physics communities in Canada.

CRM Annual Report 1998-1999 37 C O M I N G E V E N T S

Workshop on Theoretical Methods (Montréal), F. Pempinelli (Lecce), O. Ragnisco (Roma for Strongly Correlated Fermions 3), S. Rauch (Linköping), E.G. Reyes (Utah State), C. 26-30 May 1999 Rogers (New South Wales), P. Santini (Roma 1), W. Org. : André-Marie Tremblay (Univ. of Schief (UNSW), R. Schmid (Emory), H. Steudel Sherbrooke), Andrei Ruckenstein (Rutgers) (Max-Planck Institute), A. Sym (Warsaw), K. Tenenblat (Brasilia), Z. Thomova (SUNY, Utica) A. Invited Speakers : I. Affleck (UBC), N.E. Bickers Turbiner (UNAM, Mexico), P. Wiegmann (Chicago), (USC), C. Bourbonnais (Sherbrooke), A. Chubukov P. Winternitz (CRM), W. Zakrzewski (Durham) (Wisconsin, Madison), A. Deppeler (Rutgers), V. Dobrosavljevic (NHMFL, FSU), M.P. Fisher (UC The objective of this workshop is to bring Santa Barbara), R. Frésard (Institut de Physique), T. together active researchers in the general field Giamarchi (Paris-Sud), S. Haddad (Sherbrooke), K. Hallberg (Nacional de Energia Atomica), M. Imada of soliton science to present original results and (Tokyo), B. Kyung (Sherbrooke), S. Kehrein reviews concerning the development and (Harvard), G. Kotliar (Rutgers), A. Rosch (Rutgers), applications of Bäcklund and Darboux A. Ruckenstein (Rutgers), S. Sachdev (Yale), D. transformations. Sénéchal (Sherbrooke), N. Shah (Rutgers), R. Shankar (Yale), S.R. White (UC Irvine), P. Wölfle (Karlsruhe), Soucheng Zhang (Stanford) Conference on General Relativity, Astrophysics and Cosmology The quest to understand the physics of high- 6-12 June 1999 temperature superconductors, organic conductors, heavy-fermion alloys and giant This large conference will group two major magneto resistance materials, has led to workshops covering closely related subjects that remarkable advances in the theory of strongly are usually isolated. correlated electrons. Some of the recent theoretical achievements as well as open Workshop on Black Holes II : Theory and questions will be discussed in a number of Mathematical Aspects tutorial lectures, contributed presentations and 6-9 June 1999, Val Morin, Québec poster sessions. Co-sponsors : Canadian Institute for Advanced Research (CIAR) Canadian Institute for Theoretical Astrophysics (CITA) Workshop on Bäcklund & Darboux Org. : Valeri Frolov (Univ. of Alberta), Werner Transformations : The Geometry of Israel (Univ. of Victoria), Robert Myers (McGill), Soliton Theory Don Page (Univ. of Alberta), Eric Poisson (Guelph) 4-9 June 1999, Halifax, Nova Scotia Invited Speakers : A. Ashtekar (Pennsylvania State), Org. : Mark J. Ablowitz (Colorado), Alan Coley S. Carlip (UC Davis), V. Frolov (Alberta), W. Israel (AARMS, Dalhousie), Athanassios S. Fokas (Victoria), T. Jacobson (Maryland), R. Kallosh (Imperial College), Decio Levi (Roma 3), Peter J. (Stanford), G. Kunstatter (Winnipeg), J. Maldacena Olver (Minnesota), Colin Rogers (New South (Harvard), R. Mann (Waterloo), E. Martinec Wales), Pavel Winternitz (UdeM, CRM) (Chicago), D. Page (Alberta), L. Susskind (Stanford), Invited Speakers : M.J. Ablowitz (Colorado), Y.A. B. Unruh (UBC), B. Wald (Chicago) Aminov (Kharkiv), I. Anderson (Utah State), N. Atakishiyev (UNAM, Mexico), Y. Berest (Berkeley), This workshop will focus mostly on recent O. Bogoyavlenskij (Queen's), M. Boiti (Lecce), J. developments regarding the statistical Cieslinski (Warsaw), P. Clarkson (Kent), A. Coley mechanics of black-holes, and is meant to bring (AARMS, Dalhousie), R. Conte (CEA-Saclay), F. together relativists and string theorists who are Estabrook (Caltech), M. Fels (Utah State), E. interested in this exciting topic. It is the second Ferapontov (Steklov Math. Inst., Moscow), D. Finley (New Mexico), A.S. Fokas (Imperial College), J. installment in a series of similar workshops; the Gegenberg (New Brunswick), V.I. Gromak first one was held in Banff (Alberta) in June 1997. (Bielorussian State), A. Grünbaum (UC Berkeley), M. Grundland (CRM), M. Gurses (Bilkent), M. Havlicek 8th Canadian Conference on General Relativity (Faculty of Nuclear Science, Prague), J. Hietarinta (Turku), L. Hlavaty (Czech Technical Univ.), C. and Relativistic Astrophysics Hoenselaers (Loughborough), N. Joshi (Adelaide), N. 10-12 June 1999,McGill University Kamran (McGill), A. Kasman (MSRI), B. Co-sponsor : Canadian Institute for Theoretical Konopelchenko (Lecce), M. Kruskal (Rutgers), V. Astrophysics (CITA) Kuznetsov (Leeds), S. Lafortune (CRM), M. Legaré Org. : C.P. Burgess (McGill), J. Gegenberg (New (Alberta), D. Levi (Roma 3), Wen-Xiu Ma (City Univ., Brunswick), D. Hobill (Univ. of Calgary), G. Hong Kong), P. Mathieu (Laval), O. Mokhov (Steklov Kunstatter (Univ. of Winnipeg), R.G. McLenaghan Math. Inst., Moscow), M. Musette (Brussel), G. (Univ. of Waterloo), R.C. Myers (McGill) Neugebauer (Friedrich-Schiller), J. Nimmo Invited Speakers : A. Ashtekar (Pennsylvania State), (Glasgow), P.J. Olver (Minnesota), M. Paranjape G. Fontaine (Montréal), T. Jacobson (Maryland),

CRM Annual Report 1998-1999 38 C O M I N G E V E N T S

Vicky Kaspi (MIT), L. Kofman (CITA, Toronto), S. (Toronto), H. Nawa (Nagoya), D. Pelinowsky Morsink (Wisconsin-Milwauke), D. Page (Alberta), P. (Toronto), G. Perelman (École Polytechnique, Paris), Saulson (Syracuse), L. Susskind (Stanford), W. Unruh G. Ponce (Santa-Barbara), J. Quastel (Toronto), Y. (UBC), J. Winicour (Pittsburgh Saint-Aubin (Montréal, CRM), S. Serfaty (ENS), J. General Relativity and Relativistic Shatah (Courant), A. Soffer (Rutgers), T. Spencer Astrophysics are both fields which are seeing (IAS), B. Vasiljevic (Toronto) exciting new progress in several directions, e.g., black hole physics, gravitational wave detectors The workshop is devoted to two relatively and new cosmological data. This conference young and fast developing areas of will be the eighth in an ongoing series of mathematical physics-nonlinear dynamics and biannual Canadian meetings, which bring renormalization group, the former being together researchers working on various understood as a qualitative theory of nonlinear aspects of gravitational physics. evolution partial differential equations. Some of the questions addressed are: the dynamics of Frontiers of Mathematical Physics : particle-like structures (e.g solitons and Summer Workshop on Particles, vortices) and interface boundaries, blow-up profiles, universal features of large-time Fields and Strings '99 behavior, and the application of renorma- 2-20 August, 1999, Univ. of British Columbia, Vancouver lization group methods to the dynamical Co-sponsors : Pacific Institute for Mathematical phenomena in nonequilibrium statistical Sciences (PIms) Asia Pacific Center for Theoretical mechanics and in particular to nonlinear PDEs. Physics (APCTP) The workshop will have review talks Org. : Taejin Lee (Kangwon National University), summarizing recent advances, talks on current Yuri Makeenko (ITEP, Moscow & NBI, progress and discussions on promising Copenhagen), John Ng (TRIUMF), Soonkeon Nam directions. (APCTP, Seoul), Chaiho Rim (APCTP, Seoul), Alexander Rutherford (PIms), Gordon Semenoff (UBC), K.S. Viswanathan (SFU), Ariel Zhitnitsky Workshop on Aspects of (UBC) Quantization Invited Speakers : R. Dijkgraaf (Amsterdam), D. 23-28 September, 1999 Gross (UC Santa Barbara), J. Harvey (Chicago), I. Org. : Lisa Jeffrey (Univ. of Toronto) Klebanov (Princeton), J. Maldacena (Harvard), J. Invited Speakers : S.T. Ali (Concordia), S. Berceanu Polchinski (UC Santa Barbara), A. Polyakov (NIPNE, Romania), M. Brion (Grenoble), C. Duval (Princeton), H. Verlinde (Princeton) (Marseille), H. Fuehr (INRIA/LATP), M. Gotay (Hawaii), B. Hall (Notre-Dame), J. Hurtubise The workshop is devoted to modern (McGill), Y.-H. Kiem (Yale), B. Kostant (M.I.T.), E. developments in mathematical physics, gauge Lerman (UIUC, Illinois), E. Meinrenken (Toronto), and string theories. The subject of the P.-E. Paradan (Grenoble), R. Sjamaar (Cornell), J. Sniatycki (Calgary), A. Szenes (M.I.T.), C. Teleman workshop includes in particular : non- (Texas, Austin), A. Uribe (Michigan), M. Vergne perturbative string and superstring theory; (Paris VII), C. Blas Villegas (UNAM), J. Weitsman anti-de-Sitter space and conformal field theory; (UC Santa Cruz), C. Woodward (Rutgers) large-N QCD, confining strings; MQCD, duality; M(atrix) theory. Quantization describes a mathematical procedure which associates a vector space (the Workshop on Nonlinear Dynamics "physical Hilbert space") to a symplectic and Renormalization Group manifold (the "classical phase space"). The 22-27 August, 1999 workshop will focus on three aspects of Org. : Catherine Sulem (Univ. of Toronto), Michael quantization: geometric quantization, coherent Sigal (Univ. of Toronto) state quantization and the behaviour of Invited Speakers : S. Alama (McMaster), N. Alikakos quantization under symplectic reduction (which (Tennessee & Athens), F. Bethuel (Orsay), O. was the subject of a celebrated conjecture of Bogoyavlenski (Queen's), L. Bronsard (McMaster), P. Guillemin and Sternberg, recently proved under Constantin (Chicago), P. Deift (Courant), J. Dimock very general hypotheses). (Buffalo), Weinan E. (Courant), J.P. Eckmann (Geneva), J. Feldman (UBC), G.M. Graf (Zurich), S. Gustafson (Toronto), T. Hurd (McMaster), V. Jaksic (Ottawa), R. Jerrard (Illinois), L. Kapitanski (Kansas), N. Kevlahan (McMaster), M. Kiessling (Rutgers), J. Lebowitz (Rutgers), M.-A. Lewis (Paris VI), C.-K. Lin (National Cheng-Kung University), F.H. Lin (Courant), R. McCann (Toronto), M. Merkli

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B. Lian (Brandeis), A. Libgober (Illinois, Chicago QIP 2000 Circle), K. Liu (Stanford), S. Mathur (Ohio State), J. Morgan (Columbia), S. Naculich (Bowdoin), L. Third Workshop on Quantum Rastelli (M.I.T.), C. Pioline (École Polytechnique, Information Processing France), W. Ruan (Columbia), M. Porratti (New 6-11 December, 1999 York), H. Schnitzer (Brandeis) Org. : Gilles Brassard (UdeM), Richard Cleve (Univ. of Calgary) This one-week workshop, to be held during Invited Speakers : Dorit Aharonov (Berkeley), the month of March 2000, will concentrate on Charles H. Bennett (IBM Yorktown), Thomas Beth recent progress in non-perturbative aspects of (Karlsruhe), Eli Biham (Technion), Gilles Brassard both field and string theories. (Montéal), Harry Buhrman (Amsterdam), Isaac Chuang (IBM Almaden), Richard Cleve (Calgary), Claude Crépeau (McGill), David DiVincenzo (IBM Workshop on Mathematical Yorktown), Artur Ekert (Oxford), Christopher Fuchs Physicists in Finance and Industry (Los Alamos), Daniel Gottesman (Microsoft), Lov 12-17 June, 2000 Grover (Lucent), Richard Jozsa (Bristol), Raymond Org. : Luis Seco (Univ. of Toronto), Stathis Laflamme (Los Alamos), Hoi-Kwong Lo (MagiQ Tompaidis (Texas) Technologies), Dominic Mayers (NECI), Tal Mor Invited Speakers : C. Albanese (Morgan Stanley & (UCLA), Michele Mosca (Waterloo), Michael Nielsen Toronto), M. Avellaneda (Courant), J. Bona (Austin), (Caltech), John Preskill (Caltech), Vwani J. Chadam (Pittsburgh), C. Fefferman (Princeton), R. Roychowdhury (UCLA), Louis Salvail (Aarhus), Garcia (Montréal), I. Karatzas (Columbia), R. Peter Shor (AT&T), Umesh Vazirani (Berkeley), John McCann (Toronto), G. Papanicolau (Stanford), S. Watrous (Calgary) et Ronald de Wolf (Amsterdam). Tompaidis (Austin)

Quantum information processing is a new Since the work of Nobel Laureates Merton, and exciting field that studies the implication of Scholes and Black, basic issues in Mathematical quantum mechanics for information processing Finance show a remarkable analogy with others purposes. This includes quantum computing, in Mathematical Physics. This workshop brings quantum cryptography, quantum teleportation together mathematical physicists who are and other forms of quantum communication that dealing with financial issues, in combination hinge upon quantum entanglement. QIP 2000, with experts in different areas of finance and which takes place just slightly before year 2000, economics. is part of the 1999-2000 special year on Mathematical Physics, sponsored by the CRM. It is also the natural continuation of the workshops Concentration Period on Algorithms in Quantum Information Quantum Integrability 2000 Processing (AQIP '98 in Aarhus and AQIP '99 in April 2 - June 11, 2000 Org. : Philippe Di Francesco (North Carolina), Chicago). Like these workshops, QIP 2000 will André LeClair (Cornell), Nicolai Reshetikhin put emphasis on the computer science aspects of (Berkeley), Hubert Saleur (USC) the discipline, focusing on algorithms and information theory. The first day, 6 December, The CRM will host a semester-long will be a day of tutorials aimed at nonspecialists concentration period with several specialists in who may have had no previous acquaintance residence. The program is organized around two with quantum mechanics. The technical sessions 4-week periods described below and a will start on Tuesday, 7 December, and continue workshop. through Saturday, 11 December. There will be ample time and facilities for informal interaction Quantum Algebras and Integrability among participants. April 2-30, 2000 Org. : André LeClair (Cornell), Nicolai Reshetikhin Workshop on Strings, Duality and (Berkeley) Geometry Invited Speakers : O. Babelon (Jussieu), V. Bazhanov March 22-25 2000 (Canberra), D. Bernard (Saclay), E. Corrigan Org. : Eric D'Hoker (UCLA), Duong H. Phong (Durham), E. D'Hoker (UCLA), P. Dorey (Durham), (Columbia), Shing-Tung Yau (Harvard) Vl. Drinfeld (*) (Kharkov), P. Etingof (*) (M.I.T.), V. Invited Speakers : L. Chien-Hao (Harvard), F. Denef Fateev (Montpellier), E. Frenkel (Berkeley), I. Frenkel (Columbia), M. Faux (Columbia), D.S. Freed (Texas, (Yale), G. Felder (Zurich), J. Harnad (Concordia, Austin), D. Freedman (M.I.T.), J.-L. Gervais (ENS, CRM), A. Its (Indiana), N. Jing (North Carolina), S. Paris), B. Greene (Columbia), M. Gross (Cornell), R. Khoroshkin (ITEP, Moscow), V. Korepin (Stony Jackiw (M.I.T.), B. Julia (ENS, Paris), D. Kabat Brook), S. Lukyanov (Rutgers), N. MacKay (I.A.S.), A. Klemm (I.A.S.), I. Krichever (Columbia), (Sheffield), P. Mathieu (Laval), B. McCoy (Stony

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Brook), L. Mezincescu (Miami), T. Miwa (Kyoto), G. May 14 - June 11, 2000 Mussardo (Trieste), A. Nakayashiki (Kyushu), R. Org. : Philippe Di Francesco (North Carolina), André Nepomechie (Miami), S. Pakuliak (Dubna), N. LeClair (Cornell), Hubert Saleur (USC) Reshetikhin (Berkeley), F. Smirnov (Jussieu), Y. Invited Speakers : I. Affleck (UBC), J. Cardy (Oxford), Saint-Aubin (Montréal, CRM), L. Takhtajan (*) (Stony J.-S. Caux (Oxford), J. Chalker (Oxford), C. Chamon Brook), V. Tarasov (*) (St. Petersburg), C. Tracy (UC (Boston), F. David (Saclay), M. den Nijs (Washington), Davis), A. Varchenko (North Carolina), L. Vinet B. Derrida (École Normale), P. DiFrancesco (North (Montréal, CRM), R. Weston (Durham), H. Widom Carolina), V. Dotsenko (Jussieu), P. Fendley (Virginia), (UC Davis), A. Zamolodchikov (*) (Rutgers) M. Fisher (ITP, UC Santa Barbara), E. Fradkin (Illinois), (*) To be confirmed V. Gurarie (ITP, UC Santa Barbara), D. Haldane (*) (Princeton), R. Konik (UC Santa Barbara), M. Lassig Topics : Quantum affine algebras in lattice (Max-Planck Institute, Teltrow), F. Lesage (Montréal, models and quantum field theory; vertex CRM), A. Ludwig (UC Santa Barbara), S. Maslov operators and form-factors; deformed Kniznick- (Brookhaven), C. Mudry (Harvard), B. Nienhuis Zamolodchikov equations and other finite- (UVA), M. Oshikawa (Tokyo Inst. Of Technology), V. difference equations; elliptic algebras; deformed Pasquier (Saclay), N. Read (Yale), V. Rittenberg (Bonn), Virasoro algebras; exact results for correlation V. Rupasov (Toronto), H. Saleur (USC), D. Sénéchal functions; finite temperature; boundary field (Sherbrooke), G. Sierra (IMFF, Madrid), M. Stone (Illinois), A.-M. Tremblay (Sherbrooke), A. Tsvelik theory; integrable perturbations of conformal (Oxford), X.G. Wen (MIT), P. Wiegmann (Chicago), A. field theories; quantum affine algebras and exact Zee (ITP, UC Santa Barbara), M. Zirnbauer (Koeln) S-matrices. (*)To be confirmed

Workshop on Isomonodromic Deformations Topics: Disordered systems; random and Applications in Physics matrices; impurity problems; quantum Hall May 1-6, 2000 systems; integrability in stochastics processes; Org.: John Harnad (Concordia, CRM), Alexander Its cellular automata; biological evolution models; (IUPUI, Indianapolis) scaling in far from equilibrium systems; Invited Speakers : P. Bleher (IUPUI, Indianapolis), A. turbulence; self-organized criticality. Bolibruch (Steklov Institute, Moscow), P. Deift (Courant Institute), B. Dubrovin (*) (SISSA, Trieste), H. Mini-courses Flaschka (*) (Arizona), T. Fokas (Imperial College), H. Hitchin (*) (Oxford), A. Its (IUPUI, Indianapolis), M. Several mini-courses are planned during the Jimbo (*) (Kyoto), N.A. Kapaev (Steklov Institute, St. year to prepare graduate students for the Petersburg), A. Kitaev (Steklov Institute, St. workshops and the concentration period. Petersburg), V. Korepin (ITP, SUNY, Stony Brook), D. Korotkin (Max-Planck Institute, Potsdam), A. Orlov (Oceanology Institute, Moscow), J. Palmer (Arizona), Orthogonal polynomials and Random N.A. Slavnov (Steklov Institute, Moscow), C. Tracy Matrices: A Riemann-Hilbert approach (UC Davis), P. Van Moerbeke (Université Catholique Fall 1999 de Louvain), H. Widom (UC Santa Cruz), X. Zhou Lecturer : John Toth (McGill) (Duke) (*) To be confirmed Informal seminar covering (parts of) Percy Deift's book "Orthogonal polynomials and The study of isomonodromic deformation Random Matrices: A Riemann-Hilbert equations is currently in very active approach", which is available directly from the development, motivated by the central role of Courant Institute website (www.courant.edu). such equations in a number of areas of quantum and statistical physics. The main domains to which this approach is applicable are: L'intégrabilité des systèmes discrets, entropie computation of correlation functions in quantum algébrique, lien avec les équations de Yang- integrable systems and lattice models of Baxter et l’intégrabilité quantique statistical physics; the spectral theory of random November 2, 3 and 11, 1999 matrices, with applications to quantum gravity; Lecturer : Claude Viallet (Université Pierre et Marie topological field theory, with applications to Curie et CNRS) solution of the DVVW equations through the theory of Frobenius manifolds; Scaling reductions of classical integrable systems. Mathematical foundations of second quantization Integrable Models in Condensed Matter and January - February 2000 Non-Equilibrium Physics Lecturer : Jan Derezinski (Warsaw)

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Various mathematical structures that are topological field theory, quantum gravity, used in quantum mechanics and quantum field integrable systems), as well as in number theory theory will be described. (Tentative) list of (distributions of zeros of zeta functions). The topics: topics to be covered are: the Gaussian ensembles 1. Canonical commutation relations. and circular ensembles (Orthogonal, Symplectic, a) Schrodinger representation; Unitary); ensembles related to the classical b) Weyl quantization; orthogonal polynomials; joint probability c) Fock spaces, Wick quantization; densities for eigenvalues; level densities, d) Metaplectic group; partition and correlation functions; level spacing e) Coherent states; distribution functions; scaling limits in the f) Inequivalent representations; "bulk" and "edge" of the spectrum; Fredholm g) Quasi-free states. determinant representations, univer-sality; 2. Canonical anticommutation relations. differential equations for correlation functions; 3. Simple models of quantum field theory. Hamiltonian structure and asymptotics. 4. Elements of axiomatic quantum field theory. Random Schrödinger operators Winter 2000 Selected Topics in Mathematical Physics: Lecturer : Vojkan Jaksic (Univ. of Ottawa) Random Matrices Winter 2000 Lecturer : John Harnad (Concordia, CRM) Isomonodromic deformations and twistor geometry This course is intended as an introduction to March 27-30, 2000 the spectral theory of random matrices. The Lecturer : Yousuke Ohyama (Osaka) subject is a remarkable one, with important applications and connections to a variety of areas of current research; in mathematical physics (statistical theory of nuclear spectra,

42 Annual Report 1998-1999 CRM C O M I N G E V E N T S

General Program 1999-2000

en 1980; elle contenait déjà une représentation CMS Summer Meeting graphique en plus de représentation textuelle. La Special Session in Harmonic Analysis dernière version est appelée SDL 2000. La May 29- June 1, 1999, St. Jean, Newfoundland particularité du forum est que les participants Org. : K. Hare (Univ. of Waterloo) and A. Broce (UdeM) proviennent pour les 2/3 de l'industrie et pour Speakers: J. Benedetto, M. Christ, C. Finet, 1/3 des universités. B.Forrest, J.-P. Gabardo, E. Granirer, H. Henig, z. Hu, R. Les thèmes du forum sont: Kerman, T. Korner, T. Lau D. Oberlin, J.-O. Ronning, G. 1. Les applications du langage LDS Sinnamon, S. Wainger 2. La dérivation systématique de LDS et génération de code Congress of the Statistical Society of 3. Les extensions au langage CanadaÊ: Special session on 4. La convergence avec UML directional statistics 5. Test, performance et simulation fondés 6-9 June 1999, Regina, Saskatchewan, sur LDS Org. : Louis-Paul Rivest, (Univ. Laval) International Conference and Un chercheur établi dans le domaine de la Workshop on Valuation Theory statistique directionnelle Nick Fisher de CSIRO 28 July – 4 August 1999, Saskatoon en Australie de même que deux chercheurs Org. : F.V, Kuhlmann (Univ. of Saskatchewan), Salma canadiens Peter Kim de l'Université Guelph et Kuhlmann and Murray Marshall Duncan Murdoch de Western seront les invités de cette séance spéciale. This conference is dedicated to Paul Ribenboim to honor his numerous contributions th 13 Annual International Symposium to the subject. The subject has experienced a on High Performance Computing rebirth in recent years and has been applied to Systems and Applications (HPCS’99) Galois theory, asymptotic analysis, model 13-16 June 1999, Kingston theory, and C*-algebras. The topics to be Org. : A. Pollard (Queen’s) discussed are: applications in algebraic geometry, in real algebraic geometry and This symposium will cover all aspects of high quadratic forms, non-commutative valuation performance computing, theoretical as well as theory, valuations and Galois theory, rigid practical. The applications covered in the analysis, o-minimality and Hardy fields, the program include: scientific and industrial com- theory of models of valuated fields, and ultra- puting, application to finance and economics, metric spaces. geographic-information processing, computing with the Web, performance evaluation, seismic- Winter Meeting of the signal processing and visualization. Besides Canadian Mathematical Society systems, we will discuss the technology of 11-13 December 1999, Univ. de Montreal compilers, architecture, user systems, and Org. : Michel Delfour (UdeM) parallel computing. Org. local : Véronique Hussin (UdeM)

th There will be a special session on algebraic 9 LDS Forum and geometric methods in differential equations: 21-25 June 1999, Montreal Celestial mechanics in the 20th century of work Org.: Rachida Dssouli (UdeM), Gregor von Bochmann th (Univ. of Ottawa), Yair Lahav (SDL Forum Society, ECI on Hilbert's 16 problem. Telecom LDT) et Nortel Networks The ncm2 (Network for Computing and Le Forum LDS se tient tout les deux ans, Mathematical Modeling) in conjonction with the celui-ci sera la 9ième occurrence de cette série. LACIM (laboratoire de combinatoire et Le langage normalisé LDS qui permet la d’informatique mathématique) and the CRM spécification et la description des systèmes will be sponsering two symposiums. communicants a évolué sur une vingtaine d’années à travers des versions successives du standard émanant de l'organisation de normalisation ITU-T. LDS est connu sous le nom "norme Z.100". La première version est apparue

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In the area of machine learning algorithms, Atelier CRM-MITACS Data Mining and there has recently been a lot of interest in new Machine LearningÊ: Selecting and ways to evaluate generalization error, to Combining Models with Machine optimize it, and to combine or select models, e.g, Learning Algorithms the Structural Risk Minimization approach along 12-14 April 2000 with Support Vector Machines, various Boosting Org. :Yoshua Bengio, Département d’Informatique algorithms and the Bagging algorithm (which et Recherche Opérationnelle, (UdeM) combine several models). These new approaches Invited Speakers : P. Bartlett (Australia National suggest that better generalization performance Univ.), L. Breiman (Berkeley Univ.), T. Dietterich can be obtained using certain rather general (Oregon State Univ.), Y. Freund (AT&T), R. Neal procedures. (Univ. of Toronto), M. Perrone (IBM), R. Schapire (AT&T), G. Wahba (Univ. of Wisconsin at Madison). Méthodes d’inférence statistique 28 April, 2000 It has been recognized in the last few years Org. : Christian Genest (Univ. Laval) by many corporations that they possess an almost untapped source of information to Tous les avis recueillis incitent à croire que improve themselves: the large amount of les résultats exposés dans l’article de Feifang et computerized data that they are collecting on John D.Kalbfleisch qui sera publié dans la Revue their processes and their customers. Machine canadienne de statistique contribuent de façon learning algorithms are becoming very importante au développement des méthodes important technological tools in many d’inférence statistique fondées sur le réé- applications such as data mining, in which one chantillonnage et le calcul numérique intensif. wants to extract useful information from large Comme le Canada compte plusieurs databases, and they are particularly important spécialistes des techniques d'auto-amorçage, ce when the probability distribution of that data is travail se prêterait bien, je crois, à un débat not known ahead of them. Machine learning scientifique dont les comptes rendus pourraient algorithms and their analysis focus on the être publiés en même temps que l'article lui- problem of generalization: it is not enough to même, vraisemblablement dans le numéro de extract some information from the data (e.g. to septembre 2000 de la revue. characterize the relation between some Ce genre de débat public, très prisé au variables), we want this information to Royaume-Uni où il est pratiqué depuis plus d'un generalize well to new data, so that it becomes siècle par la Société royale de statistique, really useful information. constituerait une première au Canada. In this regard, an old question is that of La liste des commentateurs pressentis s’établit «model selection», that is the choice of a class of comme suit : functions, or the ways to impose a preference • du Canada : Christian Léger (UdeM), Nancy over functions which make the learning problem M. Reid (Univ. of Toronto), James V. Zidek well-posed. For this, it would be very useful to (Univ. of British Columbia); estimate the expected generalization • des États-Unis : Thomas J. DiCiccio (Cornell performance that would be obtained with a Univ.), Robert J. Tibshirani (Stanford Univ.); particular preference of function class. One • d'Europe ou d'Asie : Anthony C. Davison could then pick the function class that is (Ecole polytechnique fédérale de Lausanne), expected to yield the lowest error, or combine Peter J. Hall (Australian National Univ.), functions from the functions classes with the Stephen M.-S. Lee (Univ. of Hong Kong). lowest expected error. For this purpose, many approaches have been proposed in the past, both in the statistics and the machine learning community.

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Theme Year 2000-2001Ê: Mathematical Methods in Biology and Medicine

Organizing Committee International Annual Meetings Combinatorial Pattern Matching Jacques Bélair (UdeM) (CPM 2000) Leon Glass (McGill) June 21-23, 2000 Brian Golding (McMaster) Org. : Raffaele Giancarlo (Univ. of Palermo), Leah Keshet (UBC) David Sankoff (UdeM) David Sankoff (UdeM) Keith Worsley (McGill) Invited speakers : A. Broder (Altavista), F. Pereira (AT&T Labs), I. Witten (Waikato, New Zealand)

Overview This meeting has a major computational The year 2000-2001 at the CRM will be biology component and includes fields which devoted to the rapidly developing field of share a common focus on the formulation, mathematical methods in biology and algorithmic recognition, analysis, commu- medicine. The application of mathematics nication and storage of patterns in diverse kinds contributes to the understanding of natural of data. processes both through mathematical models and their analysis, and through the 5th Annual International Conference development and application of mathematical on Computational Molecular Biology methods of inference. The year emphasizes (RECOMB 01) both aspects, with workshops covering various April 21-24, 2001 applications of nonlinear dynamics in biology Org. : David Sankoff (UdeM) and medicine, as well as genomics, and medical imaging. The premier annual meeting in computational molecular biology, featuring a 10th Summer SchoolÊ: highly competitive selection of the best research Nonlinear Dynamics in Biology and papers from cutting edge projects for Medicine presentation, its subject is computational and May 22 - June 3, 2000 mathematical in nature. Org. : Jacques Bélair (UdeM) Instructors : M. Courtemanche (Montréal), E. Doedel Workshops (Concordia), L. Glass (McGill), M. Guevara (McGill), Workshop on Novel Approaches in A. Longtin (Ottawa), M. C. Mackey (McGill), J. Milton (Chicago), A. Vinet (Montréal), J. Bélair RNA Informatics (NARI) May 18-19, 2000 (Montréal) Org. : François Major (UdeM) Offered jointly with the "Centre for Nonlinear Invited speakers : C. Duarte (Columbia), A. Ellington (*) (Texas), R. Hughey (*) (UCSC), V. Mohan (Isis), E. Dynamics in Physiology and Medicine", this is Rivas (Washington), B. Shapiro (NCI), C. Wilson an intensive introduction to the applications of (UCSC) nonlinear dynamics to biology and medicine, (*) to be confirmed with computer exercices and an introduction to numerical techniques. The goal of this symposium is to explore the current state of the art in RNA informatics and Aisenstadt Chair Lecture Series to look towards the future of the field. The Vortices in Motionless Media NARI symposium will provide a general forum Arthur T. Winfree (Arizona) for disseminating the latest developments, and September 2000 will bring together scientists from biochemistry, molecular biology, computer science, Mathematics for Reading and Understanding mathematics and statistics who will present an Genetic Sequences overview of novel approaches. Michael S. Waterman (USC) March 2001

Workshop on Bioinformatics May, 2000

CRM Annual Report 1998-1999 45 C O M I N G E V E N T S Org. : Nadia El-Mabrouk (UdeM) Workshop on Gene Order Dynamics, Invited speakers : G. Butler (Concordia), G. Drouin Comparative Mapping and Multigene (Ottawa), D. Forsdyke (Queen's), A. Kusalik Families (DCAF) (Saskatoon), M. Li (Waterloo), P. Rouzé (Ghent) September 22-25, 2000 Org. : David Sankoff (UdeM), Joseph H. Nadeau A workshop on diverse problem areas in (Case Western Reserve University) bioinformatics, in the context of the annual Invited speakers : S. Anderson (Uppsala), V. Barriel meeting of the Association canadienne- (Paris) & C. Gallut (Paris), B. Bed'Hom (Paris), M. française pour l'avancement des sciences. Blanchette (Seattle), J. Boore (Michigan), P. Bork (Heidelberg), D. Bryant (Montréal), G. Burger There will also be several colloquium style (Montréal), A. Caprara (Bologna) & G. Lancia lectures. (Padua), O. Cohen (Grenoble), K. Devos (UK), E. Invited participants: A. Gabrielov (*) (Purdue Eichler (Case Western Reserve), N. El-Mabrouk University), G.G. van der Hoeven (*) (CNRS, (Montréal), V. Ferretti (Montréal), A. Hughes, R. Université de Paris-Sud (Orsay)), N. Kamran (*) Irving (Glasgow), H.-P. Klenk (Gottingen), B. Koop (McGill University), A. Khovansky (*) (University of (Victoria), D. Liben-Nowell (Cornell), L.A. Lyons Toronto), M. Lodav-Richaud (*) (Université (NIH), S.R. McCouch (Cornell), A. McLysaght d'Angers), D. Marker (University of Illinois at (Dublin), S.M. McPeek (Chicago), J. Meidanis (Sao Urbana-Champlain), F. Menous (*) (Université de Paolo), A. Paterson (Georgia), J. Postlethwait Paris-Sud (Orsay)), Abderaouf Mourtada (Université (Oregon), D. Schoen (McGill), R. Shamir & I. Pe'er de Bourgogne), R. Moussu (*) (Université de (Tel Aviv), M. Turmel (Laval), B. Trask (Seattle), D. Bourgogne) A. Pillay (University of Illinois at Waddington (UK), J. Womack (Texas A&M) Urbana-Champlain), Ch. Rousseau (Université de Montréal), D. Schlomiuk (Université de Montréal), This meeting will bring together scholars in M. Singer, (University of North Carolina), P. the biological and mathematical sciences Speisegger (*) (Fields Institute), J.C Tougeron (*) working on genome rearrangement, mapping (Université de Rennes), B.Vallet (*) (Université de Paris-Sud (Orsay)). and the evolution of gene families in human, (*)to be confirmed animal, plant, other eukaryote, prokaryote, organellar and viral genomes. Workshop on Molecular, Metabolic, and Gene Control Networks Workshop on Nonlinear Dynamics September 9-13, 2000 and Biomathematics Org. : Michael C. Mackey (McGill) October 3-6, 2000 Org. : Pierre Auger (Lyons), Jacques Bélair (UdeM), Invited speakers : J. Collins (Boston), G. Church Jacques Demongeot (Grenoble), Christiane Rousseau (Harvard), I. Epstein (Brandeis), J. Ferrell (*) (UdeM), (Stanford), L. Glass (McGill), A. Goldbeter (Brussels), H. Herzel (Berlin), K. Kohn (NIH), R. Larter (Purdue), Invited speakers : O. Arino (Pau), P. Auger (Lyons), H. S. Leibler (*) (Princeton), J. Mahaffy (San Diego State), Benali (CHU Pitié Salpêtrière), A. Bourdou (INSERM), J. Reinitz (Mt. Sinaï), J. Ross (Stanford), M. Roussel R. Bravo de la Parra (Alacala), F. Clarke (Lyons), J.-L. (Lethbridge), M. Santillan (Mexico City), M. Savageau Coatrieux, J. Demongeot (Grenoble), A. Goldbeter (UL (Michigan), S. Scott (Leeds), K. Showalter (West Bruxelles), R. Roussarie (Dijon), R. Thomas (UL Virginia), P. Smolen (*) (Houston), R. Somogyi (Incyte), Bruxelles), P. Tracqui (Grenoble), J. Bélair (Montréal), J. Tyson (Virginia), D. Wolf (Lawrence Livermore) L. Gagnon (CRIM), L. Glass (McGill), B. Goulard (*) to be confirmed (Montréal), J.-M. Lina (Montréal), S. Lessard (Montréal), A. Vinet (Hôpital du Sacré-Coeur), N. Modeling in this field has recently considered Raissi (Maroc), D. Salahub (Institut Steacie), G. topics including regulation of progression Wolkowicz (McMaster) through the cell cycle as mediated by check points, control in the lactose and tryptophan The state of the art in the application of operons, and the integrated behaviour of large techniques from nonlinear dynamics to diverse coupled molecular/metabolic/gene networks. fields of biology (biochemistry, physiology, This workshop brings together both resources management, medical imaging) will be experimentalists and modelers to examine the covered. This workshop is part of the Entretiens current state of the field and the exciting future du Centre Jacques-Cartier. prospects.

46 Annual Report 1998-1999 CRM C O M I N G E V E N T S

Workshop on Memory, Delays and branching networks) have been given new Multistability impetus by the introduction of fractal concepts. October 12-15, 2000 This workshop will cover the latest theoretical Org. : André Longtin (Univ. of Ottawa) developments, their contributions in the Invited speakers : P. Bressloff (Loughborough), S.A. biomedical field and future directions of Campbell (Waterloo), C. Canavier (Nouvelles investigations. Orléans), G. Carpenter (Boston), A. Destexhe (Laval), M. Ding (Florida Atlantic), W. Gerster (Lausanne), L. Workshop on Mathematical Methods Glass (McGill), J. Guckehneimer (Cornell), A. Herz (Humboldt-Bremen), F. Hoppenstaedt (Arizona in Brain Mapping State), W. Mass (Tech. U. Graz), J. Milton (Chicago), December 10-11, 2000 K. Pakdaman (INSERM), X.-J. Wang (Brandeis) Org. : Keith Worsley (McGill) Invited speakers : J. Ashburner (UCL), J. Aston This workshop will focus on important (London), H. Benali (CHU Pitié Salpêtrière), E. current issues in the modeling of neural activity Brown (Harvard), A. Dale (Harvard), K. Friston in recurrent circuitry, such as recurrent activity (UCL), G. Glover (Stanford), L. K. Hansen (Tech. U. Denmark) , N. V. Hartvig (Aarhus), M. Hurdal thought to lie at the core of sensory information (Florida Atlantic), S. Kiebel (FSU jena), J.-F. Mangin processing. The emphasis will be on the (Service Hospitalier Frédéric Joliot, Orsay), J. Raz (U. mathematical issues which arise in the Penn.), J. Riera (Cuban Neuroscience Center), J. modeling of such activity in real biological Taylor (McGill), P. Thompson (UCLA) systems. Brain mapping is a rapidly growing research Workshop on Mapping and Control field that tries to understand human brain of Complex Arrhythmia function and anatomy using 3D images from October 29 - November 1, 2000 MRI, fMRI, PET, EEG and MEG using Org. : Leon Glass (McGill) geometry, topology, statistics and random Invited speakers : M. Allessie (*) (Holland), D. fields. This workshop is intended to bring Christini (New York), J. Collins (Boston), W. Ditto (*) together mathematicians and statisticians (Georgia), A. Garfinkel (Los Angeles), P. Guerra (*) interested in brain mapping, and medical (Montréal), R. Ideker (Alabama), J. Jalife (*) researchers interested in mathematical and (Syracuse), A. Karma (Boston), V. Krinsky (Nice), J. statistical methods for the analysis of brain Leon (*) (Montréal), M. Lesh (San Francisco), R. mapping data. Mehra (*) (Minneapolis), D. Nahon (*) (Montréal), S. Nattel (*) (Montréal), A. Panfilov (Holland), Y. Rudy (Cleveland), N. Trayanova (New Orleans), A. Vinet Workshop on Fractals and Wavelets (Montréal), A. Winfree (*) (Arizona), F. Witkowski (*) in Medical Imaging (Calgary) March, 2001 (*) to be confirmed Org. : Jean-Marc Lina (UdeM)

This workshop will bring together Workshop on Population Genetics at mathematicians, experimentalists, physicians, the Molecular Level and industrial representatives to present papers March 8-11, 2001 and discuss approaches to map and control Org. : Brian Golding (McMaster) complex arrhythmias. There would be a strong Invited speakers : J. Huelsenbeck (Rochester), A. focus on novel interdisciplinary approaches to Rzhetsky (Columbia), N. Goldman (*) (Cambridge), control atrial fibrillation. J. Thorne (NCSU), Z. Yang (U.C.London), L. Excoffier (Geneva), S. Kumar (Arizona State), B. Rannala (Stony Book), S. Muse (NCSU), M. Gouy Workshop on Fractal and Modeling (Lyons) in Structural and Dynamical Analysis November 11-14, 2000 The genes and alleles of classical genetics are Org. : Jacques Bélair, Fahima Nekka (UdeM) abstract notions. Now that these are increasingly Invited speakers : Q. Cheng (York), A. Einstein (Mt. understood in terms of particular sequences of Sinaï), B.H. Kaye (Laurentian), S. Lubkin (North DNA and protein, the mathematical foundations Carolina), H.E. Stanley (Boston), C. Tricot (Clermont- of the field must be revisited and expanded, Ferrand), E. Vrscay (Waterloo), G. West (Los Alamos) which is the object of this workshop. Classical problems in material sciences (surface characterization, description of Workshop on Mathematical Formalisms for RNA Structure April 25-26, 2001

CRM Annual Report 1998-1999 47 C O M I N G E V E N T S Org. : François Major (UdeM) In preparation for the workshop on brain Invited speakers : R. Altman (Stanford), J. Brown mapping, four series of introductory lectures (NCSU), D. Case (Scripps), D. Gautheret (CNRS- will be given, covering the geometry of random Marseille), R. Gutell (Texas), S. Harvey (Alabama), D. field, methods in functional magnetic resonance Haussler (*), E. Westhof (CNRS-Strasbourg), M. imaging and methods for EEG analysis. Zuker (*) (St. Louis) (*) to be confirmed Fractals and Wavelets in Medical Imaging This symposium will explore the current March, 2001 state of the art in computational RNA structure, Org. : Jean-Marc Lina (UdeM), Fahima Nekka (UdeM) and provide a look towards the future of the field Invited speakers : J. Levy-Vehel (INRIA, Rocquen- court), M. Unser (Swiss Federal Institute of Techno- logy, Lausanne) Courses and Seminars Combinatorial Pattern Matching Preceding the workshop, this tutorial will June 19-20, 2000 introduce the subject to nonspecialists. Org. : David Sankoff (UdeM) Invited speakers : D. Bryant (UdeM), N. El-Mabrouk Showcase for Competing Technologies for (UdeM), I. Witten (Waikato, New Zealand) and others Phylogenetics (SCOPH) April 18-20, 2001 Org.: David Bryant and David Sankoff (UdeM) Preceding CPM2000, this is a two-day tutorial on sequence analysis and other topics Invited speakers : D. Bryant (Montréal), A. Dress in computational biology and pattern matching. (Bielefeld), J. Felsenstein (Seattle), O. Gascuel (Montpellier), T. Hagedorn (College of New Jersey), K. Nixon (Cornell), M. Steel (Canterbury), D. Developing the Tools: A Canadian Swofford (Cornell), T. Warnow Bioinformatics Workshop June 26-July 1, 2000 This seminar is addressed to researchers, Org. : Christopher Hogue (Toronto), François Major teachers and students interested in current (UdeM) developments in phylogenetic analysis. The speakers will each address one or two major One of a series of training workshops areas and there will be ample time for piloted by the Canadian Genetic Diseases comparison, debate and discussion. Some of the Network and the Biotechnology Human themes will be: efficient methods for very large Resources Council. phylogenies, model-based versus model-free approaches, tree inference with and without Biochemical and Chemical Kinetics ancestor reconstruction, generalizations of trees. September 7-8, 2000 Software packages will be available on-line and Org. : Michael C. Mackey (McGill) there will be facilities for demonstrations and Invited speakers : K. Shoewalter (West Virginia), S. hands-on experimentation. Scott (Leeds) Visitors Preceding the workshop on Molecular, Metabolic, and Gene Control Networks, this Support is available for short and long-term course will introduce the basic concepts and visits. Preference will be given to Junior techniques for the modeling of biochemical investigators. processes. Those wishing to participate in the above activities are invited to write to: Techniques in Brain Mapping Louis Pelletier December 5-8, 2000 Org. : Keith Worsley (McGill), Bernard Goulard Centre de recherches mathématiques (CRM) (UdeM) E-mail: [email protected] World Wide Web: Invited speakers : R. Adler (TECHNION), H. Benali (CHU Pitié Salpêtrière), N. Lange (Harvard), P. Valdes http://www.CRM.UMontreal.CA/biomath (Cuban Neuroscience Center)

48 Annual Report 1998-1999 CRM C O M I N G E V E N T S

General Program 2000-2001

Asymptotic series, differential National Programme CommitteeÊ: algebra and finiteness problems in Funding Recommendations non-linear dynamical systems June 18 - July 7, 2000 The National Programme Committee Org. : Dana Schlomiuk, (UdeM), Luc Bélair, composed of the three canadian mathematical (UQAM). institutes met in Montreal on November 10, 1999. The following events were approved for While the relationship between asymptotic funding : analysis and differential algebra has a long history in linear differential equations, the • Pauline van den Driessche, UVic merger of tools and the opening of a wider scope Western Canada Linear Algebra Meeting of investigation in both the areas of nonlinear May 2000. dynamics and differential algebraic geometry is University of Manitoba more recent. In particular, model theoretical • Luc Vinet, McGill methods have recently come to the fore in the Special Functions 2000 area. These new developments provide ample May-June 2000 motivation for organizing a mini-programme in Arizona State University this area of research. The aim is to get specialists together from • Duncan Murdoch, UWO these different fields and have them talk. Plenty Statistical Society of Canada of time will be reserved for discussion, and the June 2000 whole event will last three weeks, starting with a Ottawa, Ontario. week of mini-courses, and followed by an • Wieslaw Krawcewicz, Alberta, extended two week workshop-working session. Topological and Variational Methods in 1. There will be four mini-courses for graduate Nonlinear Analysis students and potential researchers: June 2000 • on asymptotic analysis, by A. Bolibruch Warsaw (Steklov); • on differential algebra with applications to • Lynn Batten, Manitoba finiteness problems and differential algebraic First Prairie Industrial Problem Solving geometry, by A. Buium (University of Workshop Mexico); August 2000 • on o-minimality and logarithmic- Brandon, Manitoba exponential series, by L. Van den Dries • George Elliott, Fields (University of Urbana-Champaign); • Canadian Annual Symposium on Operator on finiteness theorems in dynamical Algebras systems, by V.Y. Kaloshin (Princeton). May 2001 2. A workshop built-around four themes : • Algebras of quasi-analytic germs, • Arturo Pianzola, Alberta Weierstrass type preparation theorems and Conference in Honour of Robert Moody finiteness results with applications to global August 2001 problems on analytic vector fields Banff, Alberta • Finiteness theorems in non-linear dynamical systems • Ecalle’s theory and applications • Model theory-finiteness theorems in o-minimality

CRM Annual Report 1998-1999 49 C O M I N G E V E N T S

Theme Year 2001-2002 : Groups and geometry

Org. : Steven Boyer (UQAM), Abram Broer (UdeM), each workshop preceded by a mini-course. Jim Carrell (UBC), William Casselman (UBC), Niky Furthermore, given the rather heavy technical Kamran (McGill), Boris Khesin (Univ. of Toronto), requirements of some of the topics, graduate Dani Wise (McGill). courses will be offered through the ISM covering perverse sheaves and intersection The year 2001-2002 will be devoted to homology, D-modules, and geometry and various aspects of the relationship between representation theory. groups and geometry. It will consist of two A series of workshops, listed below with segments. The first (summer-fall 2001) will their organizers, is planned. concentrate on selected interactions between • transformation groups (I. Hambleton) groups, topology and differential geometry. • groups and 3-manifolds (S. Boyer, D. Wise). Topics to be covered include transformation • infinite dimensional Lie groups (N. groups in geometry and topology, geometric Kamran, B. Khesin). group theory, hyperbolic geometry, and • algebraic transformation groups (A. Broer, infinite-dimensional Lie groups. The second F. Knop, J. Carrell). segment (winter-spring 2002) will focus on the • representation theory of real reductive Lie links between algebraic geometry, group theory groups, algebraic and geometric methods and representation theory. Topics to be (W. Casselman). explored include geometric representation • classical invariant theory (E. Campbell, D. theory and algebraic or unitary representations, Welhau). algebraic transformation groups, invariant • quantum groups (P. Etinghof). theory, quantum groups, and affine algebraic • group actions and affine algebraic geometry. geometry (D. Daigle, P. Russell). There will be a significant component of theprogram devoted to graduate training, with

50 Annual Report 1998-1999 CRM C O M I N G E V E N T S

RESEARCH PROGRAMS

Research reports appear in their original language.

Square-integrable group representations, observation et nous voulons estimer un wavelets and Wigner transforms paramètre de position a déjà été étudié. Ce cas ne correspond pas vraiment à la réalité et il doit Twareque Ali être généralisé au cas où nous avons plusieurs My research during the last couple of years was observations. Il serait aussi intéressant de voir centered around the theory of square-integrable comment cette façon de caractériser les queues group representations and the relationship of d’une densité peut s’appliquer au paramètre square-integrability with the Plancherel d’échelle. Si nous réussissons à généraliser au transform. It has been demonstrated that the paramètre d’échelle, il sera intéressant de Plancherel transform for Type I groups is the s’attaquer au modèle de position-échelle et par la unifying link between square-integrability, the suite au modèle multivarié. wavelet transform and the generalized Wigner function. This connection has far-reaching Numerical methods in fluid dynamics consequences, in the sense that it can be used to and electrodynamics generate large classes of Wigner functions for Type I groups. From the point of view of Paul Arminjon physical applications, Wigner functions are P. Arminjon works in the domain of quasi-probability distributions on classical phase Computational Fluid Dynamics (CFD). With A. spaces (coadjoint orbits of the groups in Dervieux, he constructs and analyzes high question), corresponding to quantum resolution non-oscillatory, positivity preserving mechanical states, and hence they can be used to finite volume/finite element methods for study the physical states of atomic and hyperbolic systems, with applications to quantum-optical systems. They can also be compressible flows. interpreted as characteristic signatures of signals With M.C. Viallon, he has constructed a two- in image analyses. In this way, the use of the dimensional, second-order accurate, Plancherel transform in connection with square- nonoscillatory finite volume method for integrability unifies the theories of signal staggered unstructured triangular grids inspired analysis, wavelet transforms and quantum by the Lax-Friedrichs and Nessyahu-Tadmor tomography. On the computational side, a large one-dimensional difference schemes : they also number of generalized Wigner distributions proved the convergence of the method for a have been computed for a special class of group linear hyperbolic equation. semidirect products admitting open free orbits With D. Stanescu, he extended these schemes to under the coadjoint action. These distributions a finite volume method for Cartesian grids, and have been used extensively in atomic and with A. Madrane he developed and applied the quantum optical calculations. triangular method to many typical flow problems ; comparison with other methods Modélisation avec des densités à queues (discontinuous finite elements, etc.) showed the aplaties high resolution and sharp shock capture capacities of the method, which also requires Jean-François Angers shorter computing times. With A. Madrane, he En théorie de la décision bayésienne, en plus de has constructed a mixed finite volume/finite spécifier un modèle statistique pour les element method for the Navier-Stokes equations, observations, nous devons spécifier un second where the convective terms are treated with the modèle pour les paramètres décrivant celui des Arminjon-Viallon finite volume method and the observations. Lorsqu’un des deux modèles est viscous terms with a finite element method. inadéquat, notre échantillon peut alors contenir With A. St-Cyr and A. Madrane, they have also des valeurs extrêmes. Le comportement des extended the method to the three-dimensional règles de décisions en présence de ces case. Results are excellent both for cartesian observations extrêmes dépend surtout de grids and for unstructured tetrahedric grids. For l’aplatissement des queues de la densité des cartesian grids they have proved positivity and a paramètres et de celui de la densité des maximum principle. observations. Il est donc important d’être capable de bien caractériser les queues d’une History of Bourbaki and 20th Century densité. Le cas où nous avons une seule Mathematics

CRM Annual Report 1998-1999 51 R E S E A R C H P R O G R A M

Liliane Beaulieu Modélisation en imagerie This manifold study reconstitutes the history of neurofonctionnelle the Bourbaki group of mathematicians, from its Habib Benali inception in the 1930s until the late 1960s. Le traitement du signal Imagerie par Résonance Through a meticulous examination of the Magnétique fonctionnelle (IRMf) intégrant ses technical and the biographical evidence, it caractéristiques spatiales et temporelles et la illustrates Bourbaki’s work method by reconstruction précise des signaux de l’activité documenting the frequent shifts between neuronale locale dans le cortex en individual and team work and the interplay of MagnétoEncéphaloGraphie (MEG) et en sometimes conflicting mathematical ideas, ÉletroEncéphaloGraphie (EEG), suscitent de especially in the areas of set theory, algebra, and nombreux travaux de recherche où integration theory. As it probes the group’s d’importantes difficultés de modélisation se intellectual and social milieu, the analysis shows posent. how the Bourbaki group came into being and Notre projet vise, d’une part, au développement eventually left its imprint on both the field of et à la validation de modèles spatio-temporels mathematics and French intellectual life in pour l’étude statistique des données de l’IRM general. The study draws on a large body of fonctionnelle cérébrale et, d’autre part, à la unpublished material; sources include minutes caractérisation de populations de neurones sous- of Bourbaki meetings, drafts written for the jacentes à la localisation de ce signal par l’étude group’s internal discussions, correspondence des relations fonctionnelles avec le signal MEG between members, as well as interviews with et EEG. La reconstruction tomographique en former members or witnesses of Bourbaki’s MEG/EEG sera basée, d’une part, sur le calcul deeds. de distances entropiques et informationnelles et, d’autre part, sur l’emploi des approches Equations non linéaires retardées hiérarchiques de traitement des données. Jacques Bélair Les protocoles expérimentaux sont conçus pour La dynamique non linéaire fournit une étudier la dynamique spatio-temporelle des interprétation de changements complexes du réseaux d’activations sur le plan du traitement rythme physiologique comme bifurcations spatio-temporel des informations, via la mise en lorsque les valeurs des paramètres de contrôle correspondance des différentes images sont modifiées. La théorie mène à des fonctionnelles et des images anatomiques. Sur prédictions pour les comportements possibles un plan clinique plus général, on étudiera les dans un environnement expérimental et permet phénomènes de redistribution compensatrice une explication unifiée des divers régimes. Le des aires fonctionnelles dus à des lésions travail de Bélair est concentré sur les feedback cérébrales et à la chirurgie, via la comparaison non linéaires à retard en contrôle et dans les des informations recalées pré et post-opératoires. systèmes d’oscillations hormonales et neuromusculaires, en insistant sur le rôle du Algorithmes d’apprentissage délai, des boucles multiples de feedback et des Yoshua Bengio délais variables dans la génération de Les algorithmes d’apprentissage automatique comportements périodiques (oscillatoires) ou permettent à l’ordinateur d’apprendre à partir irréguliers. d’exemples. Ce champ de recherche est à En collaboration avec J. Mahaffy et M. Mackey, l’intersection de l’intelligence artificielle, on a développé un modèle d’érythropoiesis qui l’inférence statistique, et l’optimisation inclut un mécanisme de destruction à taux numérique. Les algorithmes d’apprentissage constant. Ce travail est étendu pour représenter sont particulièrement utiles dans les situations la thrombopoièse, et inclure les découvertes où nous n’avons pas assez de connaissances sur récentes sur la thrombopoeitine. un problème pour directement énoncer une Un projet de collaboration avec des chercheurs solution sous la forme d’un programme, mais où en pharmacologie, a mené à une co-supervision nous avons des exemples illustrant la tâche à d’étudiant, afin de construire des modèles qui effectuer. Le problème de l’apprentissage peut incorporent des régimes transients pour la s’exprimer comme le choix d’une fonction parmi représentation de mécanismes d’absorption. un ensemble de fonctions selon l’espérance d’un critère (la qualité de la solution choisie par l’ordinateur pour un exemple particulier). Cependant, comme la véritable distribution des exemples est inconnue, cette espérance ne peut

52 Annual Report 1998-1999 CRM R E S E A R C H P R O G R A M pas être calculée, seulement estimée par sa géométrie algébrique: et chaque progrès donne valeur empirique sur les données observées. La lieu à de multiples questions et applications véritable difficulté de l’apprentissage est donc de dans tous ces domaines. généraliser, ou de pouvoir transférer l’information existante dans les exemples Studies in low-dimensional topology disponibles à de nouveaux exemples. Les recherches de Yoshua Bengio se concentrent sur Steven Boyer certains types d’algorithmes d’apprentissage (en His research efforts over the last few years particulier les réseaux de neurones artificiels et focused on the topology of low-dimensional les modèles de Markov cachés) et leurs manifolds, particularly knot theory, and the applications (en reconnaissance de formes, geometric representation theory of 3-manifold reconnaissance de la parole, vision par groups. His primary interest in the first of these ordinateur, analyse de processus industriels, et research areas is to study exceptional la prédiction et prise de décision à partir de phenomena which arise from the geometric séries chronologiques financières). operation of Dehn surgery on knots. Together with his collaborator Xingru Zhang (SUNY at Décomposition de représentations Buffalo) they were able to prove definitive results in several cases they studied. The François Bergeron methods they employed involved an interplay Mes recherches concernent divers aspects de between the topology of 3-dimensional l’interaction entre la combinatoire et l’algèbre, manifolds and the representation theory of their plus particulièrement autour d’un problème fundamental groups. In particular they made central de la théorie de la représentation important theoretical advances in this latter area consistant à décomposer une représentation which led to our applications in surgery theory. donnée en ses composantes irréductibles. On dit que le nombre d’occurrences d’une The fields of algebraic transformation représentation irréductible au sein d’une groups and invariant theory représentation est sa multiplicité. Il appert que le calcul de ces multiplicités est fondamental dans Abraham Broer plusieurs domaines de la physique et des At the moment he is primarily interested in the mathématiques. Ainsi, pour la physique, cette algebraic varieties that are related to the multiplicité peut correspondre aux niveaux representation theory of semisimple Lie groups. atomiques, pour l’algèbre, elle représente une The relations between representation theory and dimension, et pour la combinatoire, elle répond algebraic geometry are deep and very à un problème d’énumération. Un résultat interesting. classique de Frobenius rend accessibles ces Some typical examples of such algebraic calculs (autrement difficiles) dans le contexte de varieties are varieties of nilpotents in a la théorie des fonctions symétriques, au prix du semisimple Lie algebra, decomposition varieties, développement de formules donnant and the cotangent bundle of a flag variety. For l’expression de certains polynômes en termes the study of these varieties one needs algebraic d’une base fixée. Les fonctions de Schur et les geometry, algebraic topology and invariant fonctions de Hall-Littlewood ont classiquement theory. joué ce rôle de bases fondamentales, mais, au In recent years he studied in particular the cours des dernières années, de nouvelles bases structure of decomposition varieties of ont été introduites pour répondre à de nouvelles semisimple Lie algebras, with applications to problématiques. Ces variantes ont été hyperplane arrangements associated with synthétisées par Macdonald pour donner reflections groups. naissance à une nouvelle famille de fonctions symétriques à deux paramètres contenant toutes Control and nonsmooth analysis les bases précédentes. Francis Clarke En utilisant des techniques de la théorie des représentations, de la combinatoire algébrique et A recent paper [IEEE Transactions on Automatic des calculs dans l’algèbre des fonctions Control 42 (1997) 1394-1407] written in symétriques, je cherche à trouver et démontrer collaboration with Yu. S. Ledyaev, E. Sontag and des identités et des propriétés de ces polynômes A. Subbotin solves a well-known and long- de Macdonald. Ce sujet est particulièrement standing question in control theory: we give a intéressant en ce qu’il fait interagir combinatoire, constructive proof of the fact that any théorie de la représentation, analyse asymptotically controllable system admits a harmonique, théorie des fonctions spéciales et retour d'état which stabilises it. In general, it is

CRM Annual Report 1998-1999 53 R E S E A R C H P R O G R A M necessary that this retour d'état be discontinuous. This area of research is becoming more and more One can then prove its robustness by some new important as the volume of voice and data and apparently very promising techniques, and communications increases and as the industry establish interesting relationships with the develops and offers new products. The objective regularity of eventual Liapunov functions. is to maximize the use of a finite spectrum of channels in the increasingly saturated Courbes elliptiques et formes modulaires environment of large Canadian urban areas while maintaining sufficient flexibility for Henri Darmon changing conditions. These optimization and Mes recherches des dernières années ont visé design problems can involve thousands of tout d'abord à démontrer certaines variantes p- frequencies which have to satisfy intra and inter adiques de la célèbre conjecture de Birch et cellular non-interference conditions. This can Swinnerton-Dyer, projet qui a été mené à bien require enormous volumes of intensive dans une série d'articles conjoints avec Massimo computations. Bertolini. Plus récemment, mes travaux avec Bertolini m'ont amené à découvrir une Description de projets généralisation tout à fait inattendue de la théorie classique de la multiplication complexe; cette Rachida Dssouli généralisation, si elle pouvait être placée sur des Nos projets de recherche s’inscrivent dans le bases mathématiques solides, aurait des cadre de l’ingénierie des logiciels de conséquences importantes pour la théorie des télécommunication. On s’intéresse tout nombres. C'est désormais le développement de particulièrement à la modélisation des systèmes cette théorie qui me préoccupe principalement. complexes réactifs et temps réel. La majorité de nos travaux utilisent des techniques formelles Description of some current research telles que la théorie de contrôle, la théorie des areas automates, la théorie des graphes et algorithmes de minimisation. Nos projets sont: Michel Delfour • Les environnements de création de service : Modeling, computation, control and deux projets sont en cours, l’un Bell (LUB) design of thin structures: sur les applications multimédia, et l’autre The use of distance functions and the tangential avec France Telecom. • differential calculus have led to a completely La génération de séquences de test fondées intrinsic theory of thin structures. Applications sur les modèles. Projets en cours : • are numerous: static design, noise reduction in Les tests fondés sur les automates airplanes and pipes, stabilization of high-speed étendus par les données incluant les rotating machines, shape optimization of machines communicantes (Nortel). • vibrating gyroscopes now used in cars, planes Les tests fondés sur les automates and missiles. The new tools and models tend to d’entrée sortie temporisés. Deux demystify the classical theory of shells and modèles de temps sont pris en provide more intuitive constructions of models considération, le temps dense et le of composite shells including piezzoelectric temps discret (CRSNG). • sensors and actuators. This has also helped in La spécification gestion et négociation des understanding certain aspects of the numerical aspects du temps et de performance dans les locking which arise from missing terms in applications multimédia (projet rcm2). Naghdi's model for instance. The work on asymptotic models has also been helpful in Fractional generalization of the KdV identifying three-dimensional approximations equation which converge to the asymptotic model. The Stéphane Durand potential of these methods is considerable in practice, and for the optimal design, since it Using supersymmetry it is possible to generalize becomes possible to simultaneously deal with in a non-trivial way the Korteweg-de-Vries the approximation of a thin structure by a thin equation (KdV) to an integrable system of two shell and the approximation of the shell in a coupled differential equations (Mathieu). single step (Yang, Fortin) from a set of points Knowing that the supersymmetry can itself be specifying the midsurface of the shell. extended (parasupersymmetry and fractional supersymmetry [Durand, Vinet]), it is natural to Radio frequency assignments and look for generalizations to integrable systems of design of cellular systems several coupled differential equations. The formalism of fractional superspace introduced

54 Annual Report 1998-1999 CRM R E S E A R C H P R O G R A M by Durand allows such a generalization in a natural way. This result is reached using the Change of variables in multiple integrals fractional extension of supersymmetry, the Hamiltonian structure of the fractional pseudo- Isidore Fleischer classical mechanics and the fractional Change of variables in multiple integrals is very generalization of a superextension of 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 Méthodes algorithmiques pour l’analyse differentiability and injectivity of the des séquences génomiques transformation. Recent work has succeeded in lightening these hypotheses e.g. by removing Nadia El-Mabrouk continuity from the derivative. This study aims Mes projets de recherche s’orientent sur deux to push this cleaning up further. aspects différents liés à l’analyse des génomes. Le premier aspect se rattache à la phylogénie. Critical point theory for multivalued L’une des méthodes utilisées pour reconstituer le functionals scénario d’évolution d’une espèce consiste à étudier les régularités à l’intérieur de son Marlène Frigon génome, et en particulier à considérer l’ensemble Here are three main aspects of Marlène Frigon’s des gènes dupliqués. La duplication du génome researches: entier est l’un des mécanismes qui entraîne Critical point theory and set-valued analysis l’apparition de gènes dupliqués. A la suite d’un (with differential inclusions) are two very active tel phénomène, le génome subit une suite de domains of mathematics which have, up to now, mutations qui modifie grandement l’ordre et almost no intersection. Marlène Frigon started l’orientation des gènes. Le problème consiste to link those two domains in developing a alors à retrouver le génome initial et les critical point theory for multivalued functionals. mutations survenues. Une façon d’aborder ce One can expect that this theory will lead to many problème est de considérer le nombre minimum applications in differential inclusions and d’opérations de réarrangement nécessaire pour control theory. transformer un génome en un génome dupliqué In collaboration with D. O’Regan of the National (méthode de parcimonie). Ce projet contient de University of Ireland at Galway, Marlène Frigon nombreux aspects différents, et donne lieu à studies differential equations with impulses, i.e. diverses études algorithmiques et combinatoires differential equations such that solutions must intéressantes. satisfy some impulses at fixed or variable Le deuxième aspect de ma recherche concerne la moments. Their work is a part of an important prédiction de motifs biologiques structurés, et en project on differential equations with impulses particulier de motifs d’ARN. Les motifs sont sponsored by INTAS (an international définis par un certain nombre de contraintes association for the promotion of co-operation liées aux structures primaires et secondaires. with scientists from the new independent states Dans la plupart des cas, les motifs sont connus of the former Soviet Union), of which Prof. par leur fonction plutôt que par leur structure. Rogovchenko of Ukrainian National Academy of Le but est alors de développer une méthode de Sciences is the supervisor. Another part of recherche qui soit suffisamment souple pour Marlène Frigon’s research concerns existence permettre de découvrir des structures encore and uniqueness results of fixed points for inconnues, et, de ce fait, d’améliorer la contractive or nonexpensive, single or set-valued connaissance que l’on a du motif et d’affiner les maps. contraintes. L’idée générale est d’élaborer des méthodes efficaces pour la recherche d’éléments structuraux ayant des caractéristiques bien Image segmentation and characterization déterminées, et d’intégrer les différents sous- using level set-based curve and surface programmes dans un programme global evolution, boundary detection and Lie permettant de les utiliser dans un ordre choisi. groups La recherche de sous-motifs de la structure primaire fait appel à des méthodes de pattern- Langis Gagnon matching. La recherche de sous-motifs de la The objective of the current project is the structure secondaire se base sur des development of algorithms based on snakes to considérations variées liées à des contraintes detect contours in images. Methods to refine the d’énergie, de structure (hélice, pseudo-nœud, analysis further and extract morphological épingle à cheveux, etc.), et de bases conservées. information, in both two dimensions and three

CRM Annual Report 1998-1999 55 R E S E A R C H P R O G R A M dimensions, in an automatic way are also within spécialement ceux décrits par des systèmes the scope of this project. multidimensionnels d’équations aux dérivées partielles (EDP) et qui n’ont pu être résolus par Analyse d’autres méthodes (par exemple la diffusion inverse). Le programme de recherche est Paul Gauthier constitué des 4 projets suivants: Les nombres complexes peuvent être identifiés Symétries conditionnelles pour les systèmes aux points du plan. Une fonction complexe d’EDP non-linéaires. w=f(z) est donc une fonction qui envoie les Une comparaison entre les différentes méthodes points du plan des z sur des points du plan des de groupe de Lie servant à solutionner les EDP. w. Le problème principal des fonctions Solutions invariantes et partiellement complexes est d’estimer la grandeur des disques invariantes des équations de la dynamique des contenus dans l’image de f (constante de Bloch). fluides. Le meilleur estimé à ce jour est celui de Gauthier Les ondes de Riemann multiples pour les et Chen. Encouragés par ce succès avec les systèmes quasilinéaires d’EDP et les relations transformations du plan, Gauthier et ses avec la méthode de réduction par symétries. collaborateurs et étudiants ont amorcé une étude semblable pour les transformations de l’espace. Systèmes intégrables, Déformations Ils continuent aussi leurs recherches en isomonodromiques et fonctions approximation. John Harnad Statistical methods and imagery Au cours de l’année passée, un projet Bernard Goulard collaboratif était complété en collaboration avec J. McKay, portant sur des solutions à une classe Bernard Goulard, in collaboration with J.M. Lina de systèmes différentiels généralisant le système and P. Turcotte, extends to remote sensing some de Halphen, avec les solutions générales statistical methods worked out for remote données en termes de certaines fonctions monitoring and classification of nuclear reactor modulaires uniformisant des surfaces de regimes. In the course of this work, focusing on Riemann de genre zéro. scalar quantities (pressure, temperature…), the Un autre projet, complété durant un séjour au properties of some of the functions worked with MSRI à Berkeley, concerne des déterminants de (" wavelets " in particular) have been explored as certains opérateurs intégraux de Fredholm qui one goes from one to two dimensions. We intend figurent comme fonctions de distributions to adapt statistical methods to include extraction spectrales des matrices aléatoires. On a and anomaly detection in imagery, with an eye démontré que ces déterminants étaient des toward applications in several fields "fonctions tau" des systèmes dynamiques qui (environmental surveillance,…). Since last year, déterminent des déformations isomono- in collaboration with two research units of CHU dromiques de certaines classes d'opérateurs Pitié-Salpêtrière of Paris (Dr. H. Benali), B. différentiels linéaires aux coefficients rationnels. Goulard, J.M. Lina and C. Amblard have applied Dans un troisième projet, on a démontré le the statistical methods they recently developed rapport entre l'approche "bihamiltonienne" aux to functional cerebral imaging systèmes intégrables, la séparation de variables (Magnetoencephalography and functional et l'approche développée auparavant, fondée sur Magnetic Resonance). les "coordonnées de Darboux spectrales" et les matrices-R rotationnelles. Ce dernier travail a Symétries et solutions des systèmes amené de nouveaux contacts et échanges non-linéaires fructueux avec le groupe de l'Université de Michel Grundland Milan (F. Magri, P. Casati) et ses réseaux (G. Au cours des dernières années, les recherches de Falqui, de Trieste, M. Pedroni de Genoa). Michel Grundland portent sur les méthodes de réduction par symétries (MRS) ainsi que sur la Geometry and Physics méthode des invariants de Riemann (MRI) et Jacques Hurtubise leurs applications aux équations de la théorie During the year 1997-98, Jacques Hurtubise des champs non-linéaires, à la physique de la worked on several different topics. The first matière condensée ainsi qu’à la dynamique des concerns stability theorems for moduli spaces of fluides. Le développement de ces méthodes holomorphic curves in complex manifolds, and a nous fournit de nouveaux outils pour aborder long article on this topic was finished at the les phénomènes non-linéaires en physique, beginning of the period, and submitted. In

56 Annual Report 1998-1999 CRM R E S E A R C H P R O G R A M another area, a joint project with E. Markman on Joffe s'intéresse depuis longtemps aux propriétés algebraically integrable Hamiltonian systems of asymptotiques de ces processus sous des Prym varieties was brought to fruition. Also, hypothèses minimales. with a student (M. Kjiri), Dr. Hurtubise Formule exacte de l'espérance du rapport de la generalised a previous construction of somme des carrés par le carré de la somme. Il separating coordinates for generalised Hitchin s'agit d'études très techniques dont l'origine se systems, which produces such coordinates, trouve dans le problème précédent mais qui among others, for the elliptic and trigonometric présente un intérêt per se. En collaboration avec matrix systems. Finally, a joint project with Lisa A. Fuchs, J.L. Teugels, A. Joffe a obtenu des Jeffrey on the links between moduli spaces of résultats définitifs sur le comportement bundles over Riemann surfaces and toric asymptotique de ce rapport. varieties has been pushed through, giving rise to "L'ergodicité forte" dans le domaine des a new class of objects on a Reimann surface, that mathématiques pures ne peut être décrite dans of framed parabolic bundles. un langage simple. A. Joffe et I. Fleischer ont obtenu des résultats dans ce domaine. Supersymmetry L'impact du développement des mathématiques pures est complètement imprévisible... mais Véronique Hussin presque toujours inéluctable (it is a tale told by an During the last twenty years, the theory of Lie idiot, full of sound and fury, signifying nothing - groups and algebras has been extended in many Macbeth.) directions. One of them deals with the supersymmetric theories and the notions of Lie Géométrie des équations aux dérivées supergroups and superalgebras. Since it is partielles/ Groupes de Lie de dimension concerned with a unified description of fermionic and bosonic objects, one has to work infinie/ Équations d’onde en relativité with commuting and anticommuting variables. générale The problem of resolving nonlinear differential Niky Kamran equations with such variables has been studied Le programme de recherches de Niky Kamran by V. Hussin, in collaboration with A. Ayari and comporte trois axes principaux. D’une part, il P. Winternitz. New supersolitonic solutions vise à étudier les rapports géométriques qui have been obtained by generalizing the method existent entre les diverses propriétés of reduction by symmetries for such equations. d’intégrabilité géométrique et l’existence de lois Another aspect of the research of V. Hussin de conservation pour les équations aux dérivées deals with the construction of minimal partielles en dimensions m ≥ 3. D’autre part, il uncertainty states in terms of the so-called porte sur l’étude des structures de groupe de Lie “coherent” or “squeezed” states for de dimension infinie qui sont adaptées à la supersymmetric systems in quantum théorie des pseudogroupes de Lie analytiques de mechanics. We make use of new relations type infini. Enfin, il a pour but d’étudier le between the eigenstates of annihilation operators comportement global des solutions d’équations associated with the harmonic and anharmonic d’onde telles que l’équation de Dirac dans les oscillators and the Jaynes-Cummings model variétés pseudo-riemanniennes correspondant important in quantum optics. aux solutions exactes de type trou noir des Probabilités pures et appliquées équations d’Einstein, un des objectifs étant de Anatole Joffe démontrer la non-existence de fermions en Les processus de branchement décrivent configuration stable au voisinage d’un trou noir l'évolution d'une population d'objets (individus, en rotation. plantes, particules) qui se reproduisent suivant un mécanisme aléatoire. Lorsque ces objets se Amélioration de l’estimation harmonique déplacent, le modèle est "la promenade aléatoire Paul Koosis avec branchement"; ce modèle décrit des choses Jusqu’à récemment l’estimation harmonique aussi différentes que le comportement d'un (c.a.d. l’emploi de la formule généralisée de réacteur nucléaire (une population de neutrons Jensen), a été l’un des procédés les plus se reproduisant par les chocs des neutrons sur puissants pour trouver des bornes pour une les atomes) ou la description de la forme d'une fonction analytique dont le comportement précis forêt (une population de graines dispersées par est inconnu. Il est très important en analyse de le vent et les oiseaux). pouvoir établir ces bornes, car elles nous permettent d’augmenter notre connaissance de la fonction en question. Mais l’estimation

CRM Annual Report 1998-1999 57 R E S E A R C H P R O G R A M harmonique n’est pas un outil universel et ne Robert Langlands, Marc-André Lewis et Yvan s’applique pas dans certaines situations; il serait Saint-Aubin donc intéressant de trouver une méthode qui va In order to describe the critical behavior of the plus loin. two-dimensional Ising model, this group of On peut parfois obtenir les bornes qu’on cherche researchers has introduced a field similar to that intégrales pourvu que les figurant dans of the free boson and whose jump lines delimit l’estimation harmonique puissent être the constant spin clusters. The statistical sommes remplacées par des de forme semblable, distribution of this field has been studied by prises sur un ensemble discret de points, et on a Monte-Carlo simulations. It satisfies the two est vu dernièrement que ce remplacement hypotheses of universality and conformal plus petite majorante parfois possible. Pour cela la invariance. Crossings on clusters of positive surharmonique est employée. Le but de ce projet spins have also been investigated and certain of est de comprendre le rôle, encore mystérieux, their properties are similar to those of crossings joué par cet objet dans ce genre de question; on in percolation models. espère pouvoir de cette façon parvenir à une méthode générale. Méthodes de rééchantillonnage et Topologie symplectique et systèmes sélection de paramètres de lissage hamiltoniens Christian Léger François Lalonde Les travaux de recherche de Christian Léger portent sur l’utilisation des méthodes de Les travaux de recherche publiés dans les rééchantillonnage en statistique. Ces méthodes articles se rapportent à trois domaines différents utilisent la puissance de l’ordinateur afin des mathématiques : d’obtenir une approximation de la distribution La théorie de la complexité des algorithmes, en d’un estimateur en vue de construire, par particulier la NP-complétude de problèmes exemple, un intervalle de confiance pour un algébriques qui apparaissent naturellement en paramètre inconnu. Pour valider ces méthodes, informatique théorique; on utilise la théorie asymptotique de même que La topologie différentielle classique, notamment des simulations. Parmi les problèmes la démonstration de la conjecture de particuliers étudiés par Christian Léger ces J.H.C.Whitehead sur les homologies des dernières années, il y a le choix d’un paramètre simplexes plongés sans singularités et de lissage pour des estimateurs non l’établissement des fondements de l’homologie paramétriques où les méthodes de sectionnelle de W. Shih; rééchantillonnage comme le bootstrap et la La topologie symplectique et les systèmes validation croisée sont souvent utilisées. Un hamiltoniens. Les articles les plus récents se travail récent a démontré que la vitesse de rapportent à ce sujet, qui a fait l’objet d’un convergence de l’estimateur avait un rôle intense développement depuis une quinzaine important à jouer dans le succès de ces méthodes d’années. de sélection du paramètre de lissage. Plus La topologie (ou géométrie) symplectique est particulièrement, ce travail a permis d’expliquer l’étude mathématique des espaces courbes, de pourquoi la validation croisée fonctionne pour le forme dimension paire arbitraire, munis d’une choix d’un paramètre de lissage lorsque le symplectique , analogue anti-symétrique d’une problème est « difficile », alors qu’elle ne métrique riemannienne, qui donne à ces espaces fonctionne pas lorsqu’il est « facile ». la structure qu’il faut pour donner un sens aux lois de la physique aussi bien qu’aux procédés de quantification (passage du classique au Analysis of population genetic models quantique). Ce sujet est le versant mathématique Sabin Lessard de ce que les physiciens appellent la théorie des Sabin Lessard's research interests include a wide super-cordes. Son développement a attiré variety of population genetic models and the l’attention des physiciens (Witten, Vafa, concomitant evolutionary dynamics. His Aspinwall, Greene, …) aussi bien que celle des ultimate goals are: a) to explain the maintenance mathématiciens, dont les méthodes ont suivi une of variability in biological populations, b) to évolution rapide depuis vingt ans. develop mathematical and statistical techniques to analyse population genetic structures, c) to The Ising model in domains with deduce general evolutionary principles, and d) boundary to study populations with complex interactions between individuals.

58 Annual Report 1998-1999 CRM R E S E A R C H P R O G R A M q-fonctions spéciales Jean LeTourneux Invariance conforme et intégrabilité La plupart des fonctions spéciales de la physique Pierre Mathieu mathématique possèdent des q-analogues, c’est- La théorie des champs conformes est une théorie à-dire des déformations faisant intervenir un quantique des champs en deux dimensions (2D) paramètre q. De même que les algèbres de Lie ayant une invariance sous tout le groupe fournissent un cadre unificateur pour l’étude des conforme, qui, en deux dimensions, est infini. fonctions spéciales, les q-déformations de ces Grâce à la profonde analogie structurelle entre la algèbres en fournissent un pour celle des q- théorie quantique des champs et la physique fonctions spéciales. En collaboration avec Luc statistique, elle permet d’obtenir la solution Vinet (CRM) et Roberto Floreanini (Trieste), Jean exacte et la classification des phénomènes LeTourneux étudie systématiquement critiques en deux dimensions. En plus de son l’interprétation algèbrique des q-polynômes importance en physique statistique, la théorie spéciaux contenus dans la hierarchie des des champs conformes est fondamentale en polynômes d’Askey-Wilson. théorie des cordes, qui reste le seul cadre théorique viable pour l’unification de la gravité Ondelettes, statistique et processus aux interactions de jauge qui décrivent les autres complexes forces fondamentales. Les percées remarquables réalisées récemment en théorie des cordes, en Jean-Marc Lina particulier la conjecture reliant les espaces anti- En collaboration avec le groupe de recherche de Sitter aux théories avec invariance conforme, PhysNum qu’il codirige avec B. Goulard, Jean- ont donné une nouvelle dimension à cette Marc Lina consacre principalement ses activités interrelation. Finalement, par sa riche structure scientifiques au traitement du signal. Les mathématique, la théorie des champs conformes différents sujets étudiés ont comme en deux dimensions est un des domaines les dénominateurs communs l’analyse statistique, plus fertiles de la physique mathématique les techniques d’inférence et, depuis six ans, la moderne. théorie des ondelettes, qui a donné lieu à une Etant invariantes sous des transformations recherche active dans le contexte des bases en d’échelle, les théories conformes constituent une ondelettes de Daubechies complexes. Les classe restreinte de théories de champs propriétés de ces fonctions ont conduit à des quantiques en deux dimensions, soit les théories travaux plus appliqués, comme l’estimation de sans masse. Néanmoins elles peuvent devenir le signaux dans le domaine de l’industrie nucléaire point de départ d’une nouvelle approche à et, plus récemment, l’imagerie. Ainsi, la l’étude des théories massives en deux modélisation statistique de la représentation dimensions où ces dernières sont obtenues par multi-échelle complexe des images (par un des perturbations appropriées de théories modèle de Markov caché) et la mise au point conformes. Ceci permet d’appliquer la puissante d’un algorithme d’optimisation pour des technologie conforme à la description de observations complexes ont débouché au cours systèmes au voisinage du point critique. Un fait de la dernière année sur des algorithmes remarquable est que certaines perturbations d’estimation robustes et sur une technique donnent des théories massives complètement originale de classification de textures. La intégrables, i.e. pour lesquelles il existe un statistique des signaux complexes est également nombre infini d’intégrales qui commutent. Le à la base d’une étude d’estimation de phase pour projet concerne l’étude des divers aspects de la l’imagerie d’interférométrie radar en relation entre les théories conformes et les collaboration avec l’industrie. Dans le contexte systèmes intégrables quantiques. de l’imagerie cérébrale fonctionnelle, J.M. Lina collabore actuellement avec deux unités de Moonshine and its Haupt modules and recherche à Paris (INSERM et CHU-Pitié- ADE Salpêtrière) pour appliquer des techniques statistiques à la détection des sources John McKay fonctionnelles à partir de données magnéto- We investigate the consequences of the relation électro-encéphalographiques. Parmi les between the Monster sporadic finite group, and principaux aspects de ce problème, on citera la the Haupt modules which describe its prise en compte des informations a priori de representations. This research was started in l’imagerie de résonance magnétique 1979 by the author and is known as Monstrous fonctionnelle ainsi que la modélisation multi- Moonshine. Designated by John Thompson échelle de la surface corticale. (Fields medalist) as a ‘problem for the next

CRM Annual Report 1998-1999 59 R E S E A R C H P R O G R A M

century’ it has recently been explained by faisant parfois mieux. Dans l’article « On a Richard Borchards for which he was awarded a Conjecture of Krishnamoorthy and Gupta » on Fields medal in 1998 at Berlin. By using démolit la conjecture qui prétend qu’un certain recurrence relations for the Fourier coefficients algorithme améliore plusieurs estimateurs of the Haupt modules, and the devices of minimax. Dans un autre contexte, celui de symmetrization and desymmetrization, we l’estimation d’une moyenne pour une believe we have a complete list. A consequence distribution de loi normale en plusieurs of this is the description of many hundreds of dimensions, on sait que lorsque la dimension integrable systems attached to the Haupt excède deux, on peut améliorer l’estimateur modules, generalizing the work of Halphen in donné par la moyenne échantillonnale. Dans

1881 on the reduction of self-dual Yang-Mills. l’article « Improving on the MLE of a Bounded The ADE problem, now called the McKay Normal Mean » on montre que le même correspondence, involves the remarkable fact phénomène se produit en dimension 1 et 2 that the fundamental groups of type E8, E7, E6 are lorsque la moyenne est tronquée. De façon related to the Monster, Baby, and F24 as Schur générale, on favorise l’approche bayésienne. On multipliers. y parvient plus facilement avec l’aide de l’ordinateur en effectuant d’intenses calculs Lie Theory, Quasicrystals, and Image numériques. Ceci nous amène à raffiner les Processing méthodes de simulations existantes. Dans

l’article « Beyond Accept-Reject Sampling » on Jiri Patera perfectionne la méthode d’acceptation-rejet. Un Following is a list of the research interests being projet en cours est de la rendre encore plus pursued by Jiri Patera. sophistiquée en y incorporant des chaînes de Application of Lie theory. Exploitation of our Markov. most recent results, namely the classification of the gradings of classical simple Lie algebras over Clones et relations the real number field. Most important among the applications is the grading preserving Ivo Rosenberg deformations of the algebras. Universal algebra. The main topic is the study of Study of properties and applications of the cut clones on a finite universe A which are and project point sets ("quasicrystals"). composition closed sets of operations on A, a Completion of a small monograph where the basic problem for finite algebras. Ideals, properties of the 1-dimensional sets are brought congruence kernels and discriminator algebras together, proven, explained. were also studied. Algebraic duality, an Specific applications of image processing and extension of Stone’s duality for boolean algebras, data fusion motivated mainly by our allows topological representations of algebras. It collaboration with Lockheed Martin, Canada. was shown that dualizability is invariant under Most intensive efforts will be invested in the nilpotent shifts. application of "quasicrystals" in cryptography, The very complex problem of local completeness and in the exploration of the many possibilities, and of locally maximal clones on infinite evaluation of demonstration models, and the universes was reduced to a few more security questions. manageable cases. The completeness problem for uniformly delayed circuits over a finite at- Inférence statistique, simulations MCMC least-four-letter alphabet was advanced. The simplicity of the lattice of clones and the François Perron description of all Mal’tsev clones on a finite at- Les intérêts de recherche de F. Perron sont liés à least-three-element universe was studied. la statistique et portent plus particulièrement sur Hyperalgebras. A hyperalgebra on A is an les sujets suivants : théorie de la décision, algebraic structure with values in the set P of analyse multidimensionnelle, statistique nonvoid subsets of A. I. Rosenberg studied them bayésienne et simulations par MCMC (chaînes as C-isotone algebras on P which allowed a de Markov avec Monte-Carlo). Les problèmes universal algebra approach to hyperalgebras and liés à la théorie de la décision visent à améliorer lead to interesting problems on C-isotone clones les estimateurs existants. L’approche privilégiée on P. In particular, hypergroups on A can be consiste à produire de meilleurs estimateurs studied as C-isotone monoids on P. minimax, l’estimateur minimax étant celui qui performe le mieux dans le pire des cas. Un Étude qualitative et bifurcations dans les estimateur est meilleur qu’un autre s’il fait équations différentielles ordinaires toujours au moins aussi bien que l’autre en

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Christiane Rousseau Graphes eulériens : Études des graphes 4- C. Rousseau poursuit son grand programme de réguliers. Inspiré par l'importance de ces recherche amorcé en 1991 avec F. Dumortier graphes pour la théorie des noeuds et par le fait (Diepenbeek, Belgique) et R. Roussarie (Dijon) que peu est connu sur leurs propriétés sur l’existence d’une borne uniforme pour le combinatoires, nous avons fait une étude nombre de cycles limites d’un champ de approfondie de deux paramètres combinatoires vecteurs quadratiques dans le plan (dans le importants, le nombre chromatique et le nombre cadre du 16e problème de Hilbert). Pour de stabilité, pour plusieurs classes de graphes 4- compléter ce programme il faut montrer la réguliers. Pour les deux paramètres il y a des cyclicité finie de 121 graphiques. Un progrès très valeurs "naturelles", et notre recherche porte sur significatif a été accompli avec la thèse H. Zhu l'existence d'algorithmes efficaces pour décider (décembre 1999) qui montre la cyclicité finie de si un graphe 4-régulier donné (avec ou sans graphiques génériques ayant un point nilpotent contraintes additionnelles) atteint les valeurs de type elliptique ou selle. Des applications de naturelles. Le résultat principal de l'étude est ces théorèmes montrent la cyclicité d’environ 35 que pour les deux paramètres le problème graphiques parmi les 121 du programme ci- s'avère NP-complet. dessus. Automorphisme: Pseudo-similarité/ similarité. Ici D’autre part un grand projet de recherche a été on étudie des questions découlant de la théorie initié sur l’organisation respective des champs de reconstruction de graphes. Si en supprimant de vecteurs normalisables, intégrables et deux arêtes d'un graphe (une à la fois) on obtient linéarisables dans l’espace des champs deux graphes isomorphes (pseudo-similarité), quadratiques (ou polynomiaux) du plan les deux arêtes sont-elles dans la même orbite complexe au voisinage d’un point de selle. Dans sous l'action du groupe d'automorphismes du ce projet C. Rousseau collabore avec C. graphe (similarité)? En général la réponse est Christopher (Plymouth, UK), P. Mardesic et R. négative, mais elle est affirmative si le nombre Roussarie (Dijon). d'orbites du graphe est petit. Jusqu'à quel nombre d'orbites les deux types de similarité Modélisation des séries chronologiques coïncident-ils? Ce qui est important dans ce genre de questions, n'est pas nécessairement une Roch Roy réponse finale mais les méthodes utilisées pour Roch Roy s’intéresse à la modélisation des séries reconnaître la similarité de deux arêtes (ou chronologiques. Bien qu’étant un domaine d'autres éléments) d'un graphe. Plusieurs classique de la statistique, l’analyse et la méthodes puissantes de ce type ont été modélisation des séries chronologiques développées au cours de notre étude. demeurent un domaine de recherche d’actualité à cause du grand potentiel d’application dans Biomathématique et sociolinguistique plusieurs disciplines scientifiques. Ses David Sankoff recherches récentes ont porté principalement sur les projets suivants: David Sankoff’s research involves the développement de tests d’indépendance de deux formulation of mathematical models and the séries chronologiques stationnaires ou non- development of analytical methods in the stationnaires et application en économie et en sciences and humanities. This includes the finance. design of algorithms for problems in étude des propriétés d’une classe de modèles de computational biology, applied probability for type régression linéaire généralisé afin de décrire phylogenetic analysis of evolution, and des séries chronologiques à valeurs entières et statistical methodology for studying application en épidémiologie. grammatical variation and change in speech développement d’un algorithme pour communities. Recent work has focused on the l’estimation à vraisemblance maximale exacte evolution of genomes as the result of des modèles ARMA multivariés sous la forme chromosomal rearrangement processes and échelon ou à racines unitaires. on formal models for bilingual syntax. modélisation des séries chronologiques ARMA faibles et application en finance. Études locales et globales de champs de vecteurs analytiques Graphes eulériens et automorphismes de Dana Schlomiuk graphes Les travaux de Dana Schlomiuk portent sur des Gert Sabidussi problèmes locaux (problème de centre) ainsi que sur la géométrie globale de certaines familles de

CRM Annual Report 1998-1999 61 R E S E A R C H P R O G R A M champs de vecteurs polynomiaux ou analytiques available. Dr. Stern’s present research interests dans le plan. Ces travaux visent en particulier à involve applying the methods of nonsmooth donner une base conceptuelle nouvelle pour les analysis to such feedback design problems, in champs de vecteurs polynomiaux dans le plan, order to obtain solutions in a generalized permettant d’en dégager des traits framework. caractéristiques de la dynamique doublement globale (on s’intéresse aux champs dans toute Description de projets l’étendue du plan et cela pour des familles Carolyne van Vliet dépendant de paramètres) afin d’unifier des résultats épars de la littérature et d’en obtenir Nous nous occupons de plusieurs projets, tous des nouveaux. Un trait caractéristique de ces financés par des contrats avec l’Air Force travaux est l’usage des méthodes Américaine (AF-OSR). multidisciplinaires : analytiques, algébriques, Le bruit électrique dans les dispositifs géométriques (plus particulièrement algébro- submicrons de l’arsenure de gallium, qui géométriques). Un autre volet du projet en cours contiennent un puits quantique, porteur d’un porte sur la partie finitude du 16e problème de gaz d’électrons bidimensionnel. Dans certains Hilbert concernant les cycles limites. cas, on trouve des spectres Lorentziens causés par des fluctuations de génération- Data Fusion recombinaison. J’ai récemment donné une théorie complète pour échantillons avec de Elisa Shahbazian multiples niveaux de piège. Cette théorie, Elisa Shahbazian’s main area of expertise is Data asymptotiquement en accord avec des théories Fusion architectures, and how the data fusion antérieures, sera soumise à Physical Review B capabilities should be integrated within large dans un proche avenir. En d’autres cas, le bruit systems. de génération-recombinaison est absent. Since 1994, she has been responsible for Cependant, on trouve des Lorentziens avec conception, prioritization, and coordination of grandeur proportionnelle au courant. Alors, all R&D activities at Lockheed Martin Canada. nous supposons que ce bruit est un "bruit de These activities involve development of grenaille", modulé par centres d’émission intelligent decision support technologies for C4I aléatoire. J’ai expliqué ces données, en utilisant applications (Data Fusion – levels 1, 2, 3 & 4, et modifiant une théorie développée par moi- Resource Management, Imaging, etc.) and the même et des collègues en 1981, basée sur une engineering infrastructure for the establishments distribution de Poisson avec moyen aléatoire of these technologies on board the Naval and (compound Poisson distribution). Les résultats Airborne platforms of Canada, and ont paru dans le Journal of Applied Physics du 15 diversification of these capabilities into décembre 1999. commercial applications such as Intelligent La théorie de transport quantique. Avec mon Transportation and Remote Sensing. étudiant au doctorat Andres Barrios, je continue les études de transports quantiques dans les gaz Nonsmooth analysis: theory and d’électrons de dimension réduite, voir mon applications article dans le volume "Advances in Mathematics CRM’S 25 year" (CRM Ronald Stern Proceedings : and Lecture Notes, vol. 11, 1997). Dr. R.J. Stern’s general area of interest is On cherche à éviter l’approximation nonsmooth analysis and control theory. A perturbative pour les termes d’écoulement, tant general goal in control problems is to design a dans l’équation Master que dans l’équation de feedback law, which achieves some desired Boltzmann quantique. Loin de l’équilibre, il faut behaviour. Examples include problems of éviter le "lemme de Kubo". Pour certains cas on a stabilizing a dynamical system, steering a déjà réussi. Quand la théorie sera complète, les trajectory to a target set in minimal time, or applications pour les systèmes électroniques et minimizing a cost functional subject to some photoniques seront nombreuses, avec des dynamic constraints. Even in some very simple retombées d’importance pour la technologie models of such problems, however, there is frontière. generally no classical (e.g. continuous or smooth) feedback synthesis. The root cause of Physique quantique et combinatoire this is the fact that in optimal control, the value function is generally nonsmooth, while in Luc Vinet problems of stabilization, one only has a Les objectifs principaux des projets de recherche generalized (nonsmooth) Lyapunov function de Luc Vinet sont: de développer les outils

62 Annual Report 1998-1999 CRM R E S E A R C H P R O G R A M théoriques nécessaires à la résolution des as well as location, so we can estimate the extent modèles importants de la physique des systèmes of the signal (joint work with David Siegmund); quantiques à plusieurs corps; d’étendre la d) knots in the excursion set. théorie des fonctions symétriques. Luc Vinet et son étudiant au doctorat, Luc Projection pursuit exploration Lapointe, ont franchi une étape majeure vers la Yannis G. Yatracos résolution algébrique du modèle de Calogero- Sutherland et, ce faisant, ont démontré des A statistic that appears naturally in simple conjectures de longue date portant sur des regression and in a decomposition of the sample polynômes symétriques parmi les plus variance is used to define a projection pursuit importants de la combinatoire algébrique. Avec index which indicates data clustering, groups of Roberto Floreanini (Trieste) et Jean LeTourneux, remote cases in the factor space in multiple Luc Vinet a poursuivi son étude systématique de regression and different data structures. The l’interprétation des q-fonctions spéciales en index is successfully applied in several termes des groupes quantiques. Il a également examples. A version of the statistic can also be entrepris l’étude des symétries des équations suited to group treatment means. aux différences. Description de projets Group Theoretical Methods in Physics Jean-Paul Zolézio and Nonlinear Phenomena in Physics Modélisation et contrôle des coques élastiques Pavel Winternitz en géométrie intrinsèque. Field of research: Mathematical physics, Contrôle en écoulements visqueux et en fluide symmetries and nonlinear phenomena. non newtonien. Applications of Lie groups to the study of Équations de coques précontraintes. difference equations. Équations différentielles de domaine. Exact solutions of nonlinear differential Solution variationnelle pour les équations equations, especially those coming from incompressibles d'Euler. nonlinear optics. La dérivation par rapport au domaine permet Lie algebra contractions and the separation of d’étudier les variations infinitésimales de la variables. solution d’une équation, par rapport aux Classification of Lie algebras and their variations du domaine. La dérivation des subalgebras. équations elliptiques et paraboliques est connue depuis les années 75, la preuve se base sur le The geometry of random images in théorème des fonctions implicites. Toutefois, cette méthode ne fonctionne pas pour les medicine and astrophysics équations hyperboliques et le problème restait Keith Worsley ouvert. The Euler characteristic of the excursion set of a Le premier volet de mes recherches consiste en random field is a tool that has been used over la démonstration de la dérivabilité par rapport the last decade to analyse positron emission au domaine dans l’équation des ondes pour des tomography (PET) images, functional magnetic seconds membres réguliers. On caractérise la resonance images (fMRI), galaxy density maps dérivée comme solution d’un problème and the cosmic microwave background, thought caractéristique au moyen de la dérivée normale to originate from the creation of the universe. de la solution. On établit une condition These images are modelled as a Gaussian nécessaire d’optimalité d’un domaine en random field, and the excursion set is the set of utilisant la dérivée de forme. Le cas Neumann points where the field exceeds some fixed est également étudié. threshold value. The Euler characteristic, which Les travaux de L. Lasiecka, J-L. Lions et R. counts the number of connected components of Triggiani sur l’équation des ondes (1986) the excursion set minus the number of “holes”, donnent une régularité de la dérivée normale, is the basis of a proposed estimator of the qui ne résulte pas de la régularité de la solution. number of “signals” in the image. I have Cette régularité cachée permet à l’équation extended the theory developed by Adler (1981), caractéristique de « survivre » lorsqu’on baisse la The Geometry of Random Fields, to: a) include a régularité du second membre. On montre que la boundary correction for the expected Euler solution de ce problème est la dérivée par characteristic, which leads to a highly accurate P rapport au domaine, également dans le cas où le -value for the field maximum; b) c2, t and F second membre est peu régulier. fields; c) searching over smoothing kernel width

CRM Annual Report 1998-1999 63 R E S E A R C H P R O G R A M

Dans un second volet, je m’intéresse à la Le problème réside dans l’absence de résultat de vibration d’une coque précontrainte. Une coque régularité et l’absence de régularité cachée. On est contrainte par un grand déplacement et démontre un résultat analogue à la dérivabilité petite déformation. On calcule au moyen d’un cachée de l’équation des ondes par des logiciel calcul formel-calcul numérique les méthodes de type extracteur, la régularité positions d’équilibre statique des coques de type intérieure étant obtenue par la théorie des semi- Adèle et logiciel S3CS. On étudie ensuite la groupes. vibration de la coque autour de cette position Parmi les développements futurs, on envisage le d’équilibre stable. La modélisation est effectuée modèle exact p(d,∞) pour les coques au moyen de la fonction distance orientée. précontraintes. On envisage également de L’équation obtenue est de type hyperbolique, on généraliser les résultats de dérivabilité par souhaite dériver les solutions par rapport au rapport au domaine à une plus grande classe domaine. Pour ce faire, nous utilisons les d’équations hyperboliques en extrayant les méthodes développées pour la dérivabilité par hypothèses minimales. rapport au domaine dans l’équation des ondes.

64 Annual Report 1998-1999 CRM COLLABORATIONS

Within its general mandate of promoting communication between the two centres has mathematical research, the CRM maintains a been excellent. Thus, the directors have always wide network of collaborations. Some of these been in regular contact; also, several members of are national in scope, others more regional; the CRM have served on the FI's Scientific others are international. Advisory Panel (SAP), and conversely. The picture was completed recently by the addition A National Institute of PIms, which brings together mathematical scientists from the five main western The CRM is strongly committed to its universities. The CRM has a long tradition of national mission. NSERC had imposed a collaboration with these institutions and with constraint of spending a significant proportion many of the scientists that are involved in the of its grant outside Quebec; the norm was fixed management of PIms, providing substantial at 25%. The CRM has always spent a more support to their activities; this collaboration has substantial fraction of its funds outside its home been maintained by the allocation of a $50,000 area than the other national institutes, and has start-up fund to PIms, to help in the interim always met this norm quite easily. This has not period before the arrival of their own NSERC only been a question of political will; it has come funding. about quite naturally, in achieving the aim of The most striking example of the better scientific performance. The CRM takes collaboration between the three institutes is the measures to ensure that the largest possible MITACS network, of which more below; we number of scientists across Canada benefit from report now on other examples of this its activities and become involved in their collaboration. The CRM-FI prize awarded in planning. For instance, it appoints to its recognition of outstanding accomplishments in Advisory Committee eminent Canadian the mathematical sciences in Canada was scientists from various parts of the country; it is created in 1994. This year's winner is R. V. present at all important forums where the future Moody of the University of Alberta. The directions of the Canadian mathematical administrative responsibility in this matter sciences are discussed; it urges its organisers to alternates each year between the CRM and the make efforts to ensure the participation of the FI. Nominations for the 1999 prize are currently Canadian specialists in their activities; it being received. Scientific collaboration continues organises and supports scientific events across between the FI and the CRM. This year, they co- the country; and it collaborates with Canadian sponsored a large conference on combinatorics institutes, societies and associations. A new and power series,as well as two conferences on initiative this past year has been to set aside and operator theory. The program for 1999 includes advertise a specific budget for the participation a summer workshop on “particles, fields and of Canadian graduate students in our strings.” One new initiative is a joint thematic programmes. The CRM is the only national period in symplectic geometry and topology, institute which operates in the two official during the spring of 2001. languages of Canada and it is highly visible on The allocation to PIms of course also funded the international scene. In keeping with its a large number of scientific activities, a list of national role, it coordinates its activities with the which can be found in the PIms annual report. Fields Institute, PIms, CMS, CAMS, SSC, CAP, Several pan-Canadian initiatives were launched AARMS, CCARMS, and collaborates with in the course of the last few years, jointly piloted technology transfer centres as well as with other by the three institutes: one can mention, apart institutes abroad. from MITACS, the initiative to create a national program to fund off-site activities at the The Fields Institute (FI) and the institutes, and a re-launching of the Canada- Pacific Institute for the Mathematical China mathematics initiative. This has resulted Sciences (PIms) in a Canada-China Mathematics congress at the The importance of coordinating the scientific end of August 1999, which will be reported on at activities of the CRM and the Fields Institute (FI) length in next year’s report. was stressed when the FI was created at the beginning of the 1990's. Since the beginning, Canadian Associations and Professional Societies

CRM Annual Report 1998-1999 65 C O L L A B O R A T I O N S

There are now two regional university the principal partners in the mathematics associations for the promotion of mathematics in component of the project, and is in some sense a Canada: the Atlantic Association for Research in precursor, having signed an agreement with the the Mathematical Sciences (AARMS) and the Institute of Mathematical Sciences at Nankai Central Canada Association for Research in the University. The CRM is continuing its Mathematical Sciences (CCARMS). The CRM is collaboration with the American Mathematical already involved with these organisations and Society, in particular with its two series of looks forward to developing closer ties. This past publications with the AMS, the CRM year, the CRM sponsored a CCARMS Monograph series and the CRM Proceedings conference. The CRM is also much involved with and Lecture Notes. The CRM has also signed a number of professional societies related to the exchange protocols with Osaka University and mathematical sciences: the Canadian with Seoul's Asia-Pacific Center for Theoretical Mathematical Society (CMS), the Canadian Physics. Further agreements are expected in the Applied Mathematics Society (CAMS), the framework of the Canada-China initiative. Statistical Society of Canada (SSC) and the Canadian Association of Physicists (CAP). Over A Solid Regional Base the years and particularly recently, the CRM has All this activity rests on a solid base of funded many meetings that were held under cooperation with universities in the region, in their ægis. An important segment of the particular the Montreal universities, and most Canadian mathematical community gathers at particularly the Université de Montréal, whose the winter and summer meetings of the CMS. support for the CRM has been unceasing. The This year the CRM subsidised a special session Université de Montréal releases each year six of in Operator Theory and one in Relativity and its faculty members to work at the CRM, and the Geometry at the 1998 Saint John Summer support of these faculty members is an essential Meeting as well as a special session in Number asset for the CRM's scientific activities. There is Theory at the Kingston winter meeting. Also, the in addition a regular program of teaching release president of the CMS is an ex-officio member of with the other Montréal universities, bringing the CRM Advisory Committee and is thus able the equivalent of another two positions to the to make the case directly for activities that the CRM each year. On an ad-hoc basis linked to the CMS would wish the CRM to support. The CRM theme program, the CRM has also been and the Canadian Association of Physicists arranging release of research personnel from (CAP) jointly sponsor the CAP-CRM Prize Laval and Queen’s; it is hoped that these recognising outstanding work in theoretical and arrangements can be formalised and put on a mathematical physics. This collaboration will more permanent footing, as well as being undoubtedly be reinforced by the 1999-2000 extended to other universities in the region. The thematic year in mathematical physics. Each partnerships of the CRM with the other research year CAMS holds a general meeting. This year, it institutes in the Montreal area have been very takes place at Laval University, in parallel with profitable. More will be said about these in the the Finite Element Days. The CRM is supporting next section. this conference. The 1997-1998 theme year in statistics gave the CRM the opportunity to The Institut des Sciences collaborate with the Statistical Society of Canada Mathématiques (SSC) In addition to supporting the SSC annual congress in 1998, the CRM has sponsored a One important vehicle for collaboration with CRM-SSC prize to recognise important work by the Quebec universities is the Institut des a young Canadian statistician. Sciences Mathématiques. This institute, which encompasses most of Quebec’s universities, is International Collaboration principally concerned with coordinating graduate training. The links with research are The Université de Montréal is part of the 3x3 obvious, and indeed, the CRM and the ISM have Canada-China Consortium with UBC, Toronto a long standing partnership, in particular in and McGill in Canada; Beijing, Nankai and Tsing offering postdoctoral fellowships, in organising Hua Universities in China. The CRM is one of the CRM-ISM colloquium, and in organising special courses for the CRM’s thematic programmes.

66 Annual Report 1998-1999 CRM C O L L A B O R A T I O N S

INDUSTRIAL PARTNERSHIPS

CRM'S industrial program has experienced (physiological and cellular systems, neural remarkable growth in the past year. Several networks). The latter directed by Leon Glass major initiatives were completed and others (McGill University) is a project to model cardiac were launched. arryhtmia. Its goal in to control these arrythmia which is of great interest to companies working MITACS in this field. In the Commercial/Industrial field the The network entitled "Mathematics of various projects all seek to improve operations Information Technology and Complex Systems" research algorithms which, using tools of (MITACS) is a network of centres of excellence modeling and optimization, permit the manage- in mathematics financed by the Canadian ment of, for example, resources, schedules, government and supported by the three inventories, client demand, or planning. The Canadian mathematical institutes (CRM, Fields, team of Brigitte Jaumard (Polytechnique) is PIms). The initial instalment of the financing is working on combinatorial problems in the field $14, 000,000 for four year. The MITACS project of wireless communication problems in the field was one of three accepted from among 77 of wireless communication (cellular telephones) proposals. such as planning the usage of frequency bands. The MITACS network currently has 21 This project also touches on the problem of research projects divided among five themes: artificial intelligence: decision making in the Biomedical, Commercial/Industrial, Information presence of uncertainty. The project directed by Technology, Trading and Finance, an François Soumis (Polytechniqe) concentrates on Manufactuting. The project teams, which often the extension to larger problems of an already have components in several universities, are successful mathematical programming tool made up university professors, research (GENCOL), based on the generation fo columns. associates, postdoctoral research fellows, and In the field of quantitative finance, the scientists working in industry. majority of projects are concentred on the The project teams, which often contain modeling of risk, and on prediction and decision components from several universities, consist of systems. All of these projects are of interest to university professors, research associates, banks and other financial institutions who must postdoctoral fellows, master’s and Ph.D. face the ever-increasing sophistication of their students, and scientists working in industry. At international competitors. The project of Jean- the moment 188 university professors are Marie Dufour (Université de Montréal) applies research membres or the MITACS network. This networking is essential for the activities of progress in research in econometrics (in MITACS: networking among researchers particular continuous time models, models of derivatives) and statistics to high-dimensional associated with a project, networking among parametric and non-parametric models. projects related to the same theme, and This problem of inference for high- networking with industry, The research and dimensionnal data is central for the last of technology transfer of the MITACS network are CRM'S five projects, that of Yoshua Bengio supported by an administrative centre whose (Université de Montréal), wich falls in the head office is located at the host institution, the framework of the Information Technology University of Toronto, with branches in the three theme. The MITACS projects of this theme are institutes. varied: symbolic calculation, modeling The MITACS projects managed by the CRM components of communication networks, cover 4 of the 5 research themes: Biomedical prediction and follow-up of aircraft and other (Project Head: Leon Glass), Commercial/Indus- military targets. Bengio's project is concentrated trial (Project Heads: François Soumis and on automatic learning algorithms and Brigitte Jaumard), Finance (Project Head: Jean- computational statistics applied to the extraction Marie Dufour), and Information Technology of useful information from large data bases. (Project Head: Yoshua Bengio). It is important to note that most of the In the biomedical field, the MITACS projects MITACS centres in Québec, in fact, have a have an orientation toward either statistics majority of their researchers in the rest of (human population, epidemics) or modeling

CRM Annual Report 1998-1999 67 I N D U S T R I A L P A R T N E R S H I P S

Canada, and that these projects are linked to request was successful, and new computer other projects in the MITACS network. The equipment is now being installed. management of the network is organized around The scientific projects of the network are the three research centres, each of which directs progressing well and the ncm2 has submitted a a certain number of projects. In addition each first progress report to NSERC in January 1999 centre has a university-industry liaison agent with the results of work carried out within the who is responsable for developing industrial three major themes of the network: (1) risk contacts for existing projects, as well as new management, (2) information processing, projects for the network. imaging and parallel computing, and (3) transport and telecommunications. Overall, the Network for Computing and projects have involved the participation of about Mathematical Modeling (ncm ) 50 researchers in the network centres, and about 2 90 postdoctoral fellows and graduate students. The CRM is one of the five Montreal-based The total value (cash and in-kind) of industry centres which together have created the contributions in 1998-1999 was $1174K. Network for Computing and Mathematical Finally, the ncm has pursued its networking m 2 Modeling, nc 2 (in French: Réseau de calcul et activities, encouraging integration. In particular, de modélisation mathématique, rcm2), a unique it has organized during the year two events for collaboration which allows the network to its series of Distinguished Lectures: On April 20, respond to the needs of industry in a large 1999, the network was host to Dr. Habib Benali, number of fields related to a common theme of Institut national de la santé et de la recherche computing and mathematical modeling. In médicale (Paris), who spoke on "L'imagerie March 1997, the ncm2 received a 5-year NSERC neurofonctionnelle: méthodes et applications". grant with an average of $600K per year. Dr. Benali has undertaken joint research work The other centres of the network at the time with the Physnum group at CRM, and he is now of creation were the Centre for Research on an associate member of CRM. On May 6, 1999, Computation and its Applications (CERCA), the Dr. Darrell Duffie, from the Graduate School of Center for Interuniversity Research and Analysis Business, Stanford University, spoke on "Default on Organizations (CIRANO), the Centre for Timing and Valuation", a topic in mathematical Research on Transportation (CRT), and the finance. Group for Research in Decision Analysis (GERAD). Establishment of the Bell University The year 1998-1999 has been rather active for Laboratory the ncm2. The major undertaking was the setting- up of the Bell University Laboratory (BUL). For The CRM was actively involved in the establishment of the Bell University Laboratory. the ncm2 proper, this has required an important modification. Since the network was not a legal As early as 1998, Luc Vinet, director of the CRM entity, and as a preliminary requirement for the and president of the ncm2, began to negotiate with Bell Canada’s executive office to develop BUL agreement with Bell, the ncm2 was incorporated with letters patent received on university/industry partnerships capable of September 16, 1998. The first meeting of the answering the needs of partners in the areas of Board of Directors was held on March 9, 1999. training, research, and economic development. In addition, two new members joined the An agreement between Bell Canada and the network: the Centre de Recherche Informatique ncm2 for the set-up and management of the Bell de Montréal (CRIM) and the Institut National de University Laboratory was signed on December la Recherche Scientifique-Télécommunications 16, 1998. (INRS-Télécommunications). These two The Bell University Laboratory aims at newcomers make a significant contribution to creating innovations in the field of multimedia research and applications (mainly interactive reinforce the presence of the ncm2, precisely in areas of interest to the BUL. applications aimed at the general public, electronic commerce applications and new The ncm2 has also played a leadership role in the creation of the Réseau Québécois de Calcul generations of evolved networks) as well as at de Haute Performance (RQCHP). This promoting the training of a highly qualified, infrastructure was the object of a grant international calibre workforce in these areas. application submitted on February 4, 1999 to the The guiding principles of the Bell University Canada Foundation for Innovation, for a total of Laboratory are: a deep integration with the approximately $16M including federal, university environment; a balance between provincial and private contributions. This exploratory research, applied research and

68 Annual Report 1998-1999 CRM I N D U S T R I A L P A R T N E R S H I P S applications development; and a multidiscipli- Upon the departure of Luc Vinet, who had nary approach. been the General Director of the Laboratory These objectives and guiding principles are since its creation, Michel Gendreau, Director of made possible thanks to a $12M over 3 years the CRT, was appointed to that position. investment which will be used to finance The Bell University Laboratory is funded by research projects, to create an endowment fund Bell Canada. Governmental agencies such as the in order to recruit elite researchers, and to Canadian Foundation for Innovation, the establish an infrastructure. Quebec Ministry of Education, the Natural

In May of 1998, the ncm2 had requested an Sciences and Engineering Research Council infrastructure grant of close to $4 million from (NSERC), the Consortium for Software the Canadian Foundation for Innovation (CFI) in Engineering Research (CSER) as well as order to set-up a Multimedia Applications equipment suppliers also financially contribute Research Institute (MARI) to which a planned, to the Laboratory’s success. Bell sponsored research laboratory could have Fifteen research projects had been accepted been added. The CFI approved the project, by the Bell University Laboratory as of June 30th, which finished 5th among 54 requests, in January 1999. Of these, 5 are affiliated with the CRM. of 1999. They are Yoshua Bengio’s "Datamining", A Management Committee comprising 3 Bell Rachida Dssouli’s "Service Creation Environ- representatives (including the President of this ment : A Quality Driven Service Engineering Committee), the directors of the member-centres Methodology", Bernard Goulard’s "M3Int: Multi- of the ncm2, and the Laboratory’s Administrative Media Mathematical Imaging on the Net", and Director manages the Bell University Jiri Patera’s "Development of the Aperiodic Laboratory. An Executive Board comprising a Encryption Method" and "Evaluation and Bell representative, the Laboratory’s General Demonstration of a New Family of Director and the Laboratory’s Administrative Cryptographic Systems". Director reports to the Management Committee and ensures the smooth functioning of the Laboratory on a regular basis. Myriam Bouroche was hired in May of 1999 as the Bell University Laboratory’s Administrative Director and Secre- tary-Treasurer, replacing Beatrice Kowaliczko.

CRM Annual Report 1998-1999 69 PUBLICATIONS

The CRM publishes monographs, lecture notes, proceedings, software, videos and research reports (for the latter see below). 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. Two collections, edited by CRM, have been published and distributed by the AMS for the past eight years. 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. These series were newly created. During the year 1998-1999, the first three volumes of the series in Physics appeared and the first volume of the Lecture Notes in Statistics was delivered to the publisher. Of particular note was the publication by the CRM of three volumes containing the complete works of the renowned number theorist Sarvadaman Chowla. The following list of “Recent Titles” contains books that have appeared during the year 1998-1999 or that will be published soon. Recent Titles

AMSÊ: CRM Monograph Series • Alan Coley, Decio Levi, Robert Milson, • James D. Lewis, A Survey of the Hodge Colin Rogers and Pavel Winternitz (eds.), Conjecture, 2e Edition (with an annexe by B. Bäcklund and Darboux Transformations: the Geometry of Soliton Theory, (to appear). Brent Gordon), vol. 10, 1999. • • Spencer J. Bloch, Higher Regulators, Algebraic Israel M. Sigal et Catherine Sulem, Nonlinear K-Theory, and Zeta Functions of Elliptic Curves, Dynamics and Renormalization Group, (to vol. 11, (to appear). appear). • Masayoshi Miyanishi, Open Algebraic Surfaces, vol. 12, (to appear). Springer-VerlagÊ: CRM Series in Mathematical Physics AMSÊ: CRM Proceedings & Lecture Notes • Robert Conte (eds.), The Painlevé Property: • Serge Dubuc et Gilles Deslauriers (eds.), One Century Later, 1999 • Spline Functions and the Theory of Wavelets, Richard MacKenzie, Manu B. Paranjape and vol. 18, 1999 Wojciech J. M. Zakrzewski (eds.), Soliton: • Rajiv Gupta et Kenneth S. Williams (eds.), Properties, Dynamics, Interactions, Number Theory, vol. 19, 1999 Applications, 1999 • • Katie Coughlin (ed.), Semi-Analytic Methods Jan Felipe van Diejen and Luc Vinet (eds.), for the Navier-Stokes equations, vol. 20, 1999 Calogero-Moser-Sutherland Models, (to • appear). Michel Fortin (ed.), Plates and Shells, vol. 21, • 1999 Yvan Saint-Aubin and Luc Vinet (eds.), • Jan Felipe van Diejen et Luc Vinet (eds.), Algebraic Methods in Physics - A Symposium Algebraic Methods and q-Special Functions, vol. for the 60th Birthday of Jíri Patera and Pavel Winternitz, (to appear). 22, 1999 • • Pierre Hansen et Odile Marcotte (eds.), Yvan Saint-Aubin and Luc Vinet (eds.), Graph Colouring and Applications, vol. 23, (to Theoretical Physics at the End of the XXth appear). Century. Proceedings of the CRM Summer • B. Brent Gordon, James D. Lewis, Stefan School, June 27-July 10, 1999, Banff, Alberta, Müller-Stach, Shuji Saito et Noriko Yui Canada, (to appear). (eds.), The Arithmetic and Geometry of Algebraic Cycles, vol. 24, (to appear). Les Publications CRM • Decio Levi et Orlando Ragnisco (eds.), SIDE • Michael Barr and Charles Wells, Category III - Symmetry and Integrability of Difference Theory for Computing Science, 1999 Equations, vol. 25, (to appear). • James G. Huard and Kenneth S. Williams • Michael Barr and Robert V. Moody (eds.), (ed.), The Collected Papers of Sarvadaman Directions in Mathematical Quasicrystals, (to Chowla, appear). I, II, III, (to appear). • John Harnad, Pavel Winternitz (eds.), Integrable Systems : from Classical to Quantum, (to appear).

70 Annual Report 1998-1999 CRM P U B L I C A T I O N S

Previous Titles

AMS : CRM Proceedings & Lecture Notes • Joel S. Feldman, Richard Froese, and Lon M. • Michel Delfour (eds.), Boundaries, Interfaces Rosen (eds.), Mathematical Quantum Theory I: and Transitions (Banff, 1995), CRM Proc. Many-Body Theory and Group Theory Lecture Notes, vol.13, Amer. Math. Soc., (Vancouver, 1993), CRM Proc. Lecture Providence, RI, 1998. Notes, vol. 7, Amer. Math. Soc., Providence, • RI, 1994. Alain Vincent (eds.), Numerical Methods in • Fluid Mechanics (Montréal, 1995), CRM Proc. Donald A. Dawson (ed.), Measure-valued Lecture Notes, vol.16, Amer. Math. Soc., Processes, Stochastic Partial Differential Providence, RI, 1998. Equations and Interacting Systems (Montréal, • John Harnad and Alex Kasman (eds.), The 1992), CRM Proc. Lecture Notes, vol. 5, Bispectral Problem (Montréal, 1997), CRM Amer. Math. Soc., Providence, RI, 1994. • Theta Functions. From Proc. Lecture Notes, vol.14, Amer. Math. M. Ram Murty (ed.), the Classical to the Modern Soc., Providence, RI, 1998. , CRM Proc. • François Lalonde (eds.), Geometry, Topology Lecture Notes, vol. 1, Amer. Math. Soc., and Dynamics, (Montréal, 1995), CRM Proc. Providence, RI, 1993. • Optimal Control via Lecture Notes, vol. 15, Amer. Math. Soc., Philip D. Loewen, Nonsmooth Analysis Providence, RI, 1998. , CRM Proc. Lecture • Olga Karlampovich (eds.), Summer School in Notes, vol. 2, Amer. Math. Soc., Providence, Group Theory (Banff, 1996), CRM Proc. RI, 1993. • Lecture Notes, vol.17, Amer. Math. Soc., Andrei L. Smirnov and Rémi Vaillancourt Asymptotic Methods in Mechanics Providence, RI, 1998. (eds.), , CRM • Luc Vinet (ed.), Advances in Mathematical Proc. Lecture Notes, vol. 3, Amer. Math. Sciences: CRM’s 25 Years (Montréal, 1994), Soc., Providence, RI, 1993. CRM Proc. Lecture Notes, vol. 11, Amer. Math. Soc., Providence, RI, 1997. AMS : CRM Monograph Series • Peter G. Greiner, Victor Ivrii, Luis A. Seco • Yves Meyer, Wavelets, Vibrations and Scaling, and Catherine Sulem (eds.), Partial CRM Monograph Series, vol. 9, Amer. Math. Differential Equations and their Applications Soc., Providence, RI, 1997. (Toronto, 1995), CRM Proc. Lecture Notes, • John Milton, Dynamics of Small Neural vol. 12, Amer. Math. Soc., Providence, RI, Populations, CRM Monogr. Ser., vol. 7, Amer. 1997. Math. Soc., Providence, RI, 1996. • Donald E. Knuth, Stable Marriage and its • Ioannis Karatzas, Lectures on Mathematics of Relation to Other Combinatorial Problems. An Finance, CRM Monogr. Ser., vol. 8, Amer. Introduction to the Mathematical Analysis of Math. Soc., Providence, RI, 1996. Algorithms, CRM Proc. Lecture Notes, vol. • David Ruelle, Dynamical Zeta Functions for 10, Amer. Math. Soc., Providence, RI, 1996. Piecewise Monotone Maps of the Interval, CRM • Joel S. Feldman, Richard Froese, and Lon M. Monogr. Ser., vol. 4, Amer. Math. Soc., Rosen (eds.), Mathematical Quantum Theory Providence, RI, 1994. II : Schrödinger Operator (Vancouver, 1993), • Andrew M. Bruckner, Differentiation of Real CRM Proc. Lecture Notes, vol. 8, Amer. Functions, CRM Monogr. Ser., vol. 5, Amer. Math. Soc., Providence, RI, 1995. Math. Soc., Providence, RI, 1994. • Decio Levi, Luc Vinet, and Pavel Winternitz • Eugene B. Dynkin, An Introduction to (eds.), Symmetries and Integrability of Branching Measure-Valued Processes, CRM Difference Equations (Estérel, 1994), CRM Monogr. Ser., vol. 6, Amer. Math. Soc., Proc. Lecture Notes, vol. 9, Amer. Math. Providence, RI, 1994. Soc., Providence, RI, 1995. • Maximilian Ya. Antimirov, Andrei A. • Hershy Kisilevsky and M. Ram Murty (eds.), Kolyshkin, and Rémi Vaillancourt, Applied Elliptic Curves and Related Topics (Sainte- Integral Transforms, CRM Monogr. Ser., vol. Adèle, 1992), CRM Proc. Lecture Notes, vol. 2, Amer. Math. Soc., Providence, RI, 1993. 4, Amer. Math. Soc., Providence, RI, 1994. • V. Kumar Murty, Introduction to Abelian • Guido Mislin (ed.), The Hilton Symposium Varieties, CRM Monogr. Ser., vol. 3, Amer. 1993 : Topics in Topology and Group Theory Math. Soc., Providence, RI, 1993. (Montréal, 1993), CRM Proc. Lecture Notes, vol. 6, Amer. Math. Soc., Providence, RI, 1994.

CRM Annual Report 1998-1999 71 P U B L I C A T I O N S

• Dan V. Voiculescu, Kenneth J. Dykema, and • Robert Bédard, Groupes linéaires algébriques, Alexandru Nica, Free Random Variables, CRM Les Publications CRM, Montréal, 1991. Monogr. Ser., vol. 1, Amer. Math. Soc., • Rudolf Beran and Gilles R. Ducharme, Providence, RI, 1992. Asymptotic Theory for Bootstrap Methods in Statistics, Les Publications CRM, Montréal, Springer-Verlag : 1991. • CRM Series in Mathematical Physics James D. Lewis, A Survey of the Hodge Conjecture, Les Publications CRM, Montréal, • Luc Vinet and Gordon Semenoff (eds.), 1991. Particles and Fields (Banff, 1994), CRM Series • David W. Rand and Tatiana Patera, in Mathematical Physics, Springer, New Concorder: Concordance Software for the York, 1998. Macintosh, Les Publications CRM, Montréal, 1991 (guide de l’utilisateur et logiciel). Les Publications CRM • David W. Rand and Tatiana Patera, Le • Maximilian Ya. Antimirov, Andrei A. Concordeur: un logiciel de concordances pour le Kolyshkin and Rémi Vaillancourt, Macintosh, Les Publications CRM, Montréal, Mathematical Models for Eddy Current Testing, 1991 (guide de l’utilisateur et logiciel). Les Publications CRM, Montréal, 1998. • Véronique Hussin (ed.), Lie Theory, • Xavier Fernique, Fonctions aléatoires Differential Equations and Representation gaussiennes, vecteurs aléatoires gaussiens, Les Theory (Montréal, 1989), Les Publications Publications CRM, Montréal, 1997. CRM, Montréal, 1990. • Faqir Khanna and Luc Vinet (eds.), Field • John Harnad and Jerrold E. Marsden (eds.), Theory, Integrable Systems and Symmetries, Les Hamiltonian Systems, Transformation Groups Publications CRM, Montréal, 1997. and Spectral Transform Methods (Montréal, • Paul Koosis, Leçons sur le théorème de Beurling 1989), Les Publications CRM, Montréal, at Malliavin, Les Publications CRM, 1990. Montréal, 1996. • M. Ram Murty (ed.) Automorphic Forms and • David W. Rand, Concorder Version Three: Analytic Number Theory (Montréal, 1989), Les Concordance Software for the Macintosh, Les Publications CRM, Montréal, 1990. Publications CRM, Montréal, 1996 (guide de • Wendy G. McKay, Jiﬁí Patera and David W. l’utilisateur et logiciel). Rand, Tables of Representations of Simple Lie • Decio Levi, Curtis R. Menyuk, and Pavel Algebras. I. Exceptional Simple Lie Algebras, Winternitz, Self-Similarity in Stimulated Les Publications CRM, Montréal, 1990. Raman Scattering (Montréal, 1993), Les • Anthony W. Knapp, Representations of Real Publications CRM, Montréal, 1994. Reduc-tive Groups, Les Publications CRM, • Jacques Gauvin, Theory of Nonconvex Montréal, 1990. Programming, Les Publications CRM, • Wendy G. McKay, Jiﬁí Patera and David W. Montréal, 1994. Rand, SimpLie User’s Manual—Macintosh • Rémi Vaillancourt, Compléments de Software for Representations of Simple Lie mathématiques pour ingénieurs, Les Algebras, Les Publications CRM, Montréal, Publications CRM, Montréal, 1993. 1990 (guide de l’utilisateur et logiciel). • Robert P. Langlands and Dinakar • Francis H. Clarke, Optimization and Ramakrishnan (eds.), The Zeta Functions of Nonsmooth Analysis, Les Publications CRM, Picard Modular Surfaces (Montréal, 1988), Les Montréal, 1989. Publications CRM, Montréal, 1992. • Hedy Attouch, Jean-Pierre Aubin, Francis • Florin N. Diacu, Singularities of the N-Body Clarke and Ivar Ekeland (eds.), Analyse non Problem, Les Publications CRM, Montréal, linéaire (Perpignan, 1987), Les Publications 1992. CRM, Montréal and Gauthiers-Villars, Paris, • Jacques Gauvin, Théorie de la programmation 1989. mathématique non convexe, Les Publications • Samuel Zaidman, Une introduction à la théorie CRM, Montréal, 1992. des équations aux dérivées partielles, Les • Pierre Ferland, Claude Tricot, and Axel van Publications CRM, Montréal, 1989. de Walle, Analyse fractale: Application • Lucien Le Cam, Notes on Asymptotic Methods Windows ™ 3.x d’initiation aux ensembles in Statistical Decision Theory, Les Publications fractals, Les Publications CRM, Montréal, CRM, Montréal, 1974. 1992 (guide de l’utilisateur et logiciel). • AMS/International Press Stéphane Baldo, Introduction à la topologie des • ensembles fractals, Les Publications CRM, Duong H. Phong, Luc Vinet and Shing-Tung Montréal, 1991. Yau (eds.), Mirror Manifolds and Geometry,

72 Annual Report 1998-1999 CRM P U B L I C A T I O N S

AMS/IP Studies in Advanced Mathematics, • Donald E. Knuth, Mariage stables et leurs Amer. Math. Soc., Providence, RI, Internat. relations avec d’autres problèmes combinatoires, Press, Cambridge, MA, and CRM, Montréal, Presses de l’Université de Montréal, 1976. 1998 (vol.10). • Robert Hermann, Physical Aspects of Lie Group Theory, Presses de l’Université de Collection de la Chaire Aisenstadt Montréal, 1974. • Quelques problèmes mathématiques • Yuri I. Manin, Quantum Groups and Mark Kac, en physique statistique Noncommutative Geometry, Les Publications , Presses de l’Université CRM, 1988. de Montréal, 1974. • La transformation de Weyl • Laurent Schwartz, Semimartingales and Their Sybreen de Groot, et la fonction de Wigner: une forme alternative Stochastic Calculus on Manifolds, Presses de de la mécanique quantique l’Université de Montréal, 1984. , Presses de • Yuval Ne’eman, Symétries, jauges et variétés l’Université de Montréal, 1974. de groupe, Presses de l’Université de Montréal, 1979. Divers • R. Tyrrell Rockafellar, La théorie des sous- • Pierre Ferland, Claude Tricot, and Axel van gradients et ses applications à l’optimisation, de Walle, Fractal analysis user’s guide. fonctions convexes et non convexes, Presses de Introduction to fractal sets using Windows ™ l’Université de Montréal, 1979. 3.x., Amer. Math. Soc., Providence, RI and • Jacques-Louis Lions, Sur quelques questions Centre de recherches mathématiques, Mon- d’analyse, de mécanique et de contrôle optimal, tréal, 1994. Presses de l’Université de Montréal, 1976.

CRM Annual Report 1998-1999 73 P U B L I C A T I O N S

Research Reports

[CRM-2547] Emil Horozov and Alex Kasman, geometric properties of one-dimensional Darboux transformations of bispectral quantum quasicrystals, September 1998. integrable systems, June 1998. [CRM-2567] D. Gomez Ullate, Stéphane [CRM-2548] Robert Konik, Frédéric Lesage, Lafortune and Pavel Winternitz, Symmetries of Andreas W. W. Ludwig and Hubert Saleur, Two- discrete dynamical systems involving two species, leg ladders and carbon nanotubes: Exact properties at September 1998. finite, 1998. [CRM-2568] Rafael Hernandez Heredero, Decio [CRM-2549] Lubomir T. Dechevsky and Serge Levi and Pavel Winternitz, Symmetries of the Dubuc, Multidimensional dyadic iterative discrete Burgers equation, September 1998. interpolation and Fourier multipliers on Lebesgue [CRM-2569] Pavel Winternitz, Lie groups and spaces, June 1998. difference equations, September 1998. [CRM-2550] Stéphane Durand, EPR-type [CRM-2570] Lubomir Dechevsky, Brenda behaviors modeled by wormhole-based time travel, MacGibbon and James Ramsay, On smooth July 1998. bijections between subsets of Rn, September 1998. [CRM-2551] Igor Loutsenko and Vyacheslav [CRM-2571] Miloslav Havlicek, M. Posta and Spiridonov, Spectral self-similarity, one- Pavel Winternitz, Nonlinear superposition formulas dimensional Ising chains, and random matrices, July based on imprimitive group action, October 1998. 1998. [CRM-2572] Yanick Dupuis and Dana [CRM-2552] M. Ali Ayari, M. Iadh Ayari and Schlomiuk, Géométrie des champs de vecteurs Véronique Hussin, Computation of Lie hamiltoniens à point de selle, October 1998. supersymmetries for the supersymmetric two bosons equations, July 1998. [CRM-2573] Robert Roussarie and Dana Schlomiuk, On the geometric structure of the class [CRM-2553] Marlène Frigon, On a new notion of of planar quadratic differential systems, October linking and application to elliptic problems at 1998. resonance, July 1998. [CRM-2574] Pavel Winternitz, Lie groups and [CRM-2554] David J. Fernández C., Véronique difference equations, October 1998. Hussin and B. Mielnik, A simple generation of exactly solvable anharmonic oscillators, July 1998. [CRM-2575] Paul Arminjon and Aziz Madrane, A staggered Lax-Friedrichs-type mixed finite [CRM-2555] Richard Fournier, Extensions of the volume/finite element method for the simulation of geometric-arithmetic means inequality to a disc of the viscous compressible flows on unstructured complex plane, July 1998. triangular grids, October 1998. [CRM-2556] M. Ali Ayari, Véronique Hussin and [CRM-2577] Paul Bracken, Classical Yang-Mills Pavel Winternitz, Group invariant solutions for the coupled to a scalar triplet invariant under subgroups N=2 super Korteweg-de Vries equation, July 1998. of the conformal group, October 1998. [CRM-2557] Stéphane Lafortune, Basile [CRM-2578] Frédéric Lesage and Hubert Saleur, Grammaticos and Afred Ramani, Constructing Strong coupling resistivity in the Kondo model, integrable third order systems: the Gambier approach, October 1998. July 1998. [CRM-2579] David Bryant, The complexity of the [CRM-2559] Michèle Grenier and Christian breakpoint median problem, November 1998. Léger, Bootstrapping regression models with BLUS residuals, August 1998. [CRM-2580] David Bryant, Rapid evaluation of least squares and minimum evolution criteria on [CRM-2560] Denis Choquet, Pierre L'Écuyer and phylogenetic trees, November 1998. Christian Léger, Bootstrap confidence intervals for ratios of expectations, August 1998. [CRM-2581] Frédéric Lesage and Hubert Saleur, Perturbation of infra-red fixed points and duality in [CRM-2561] Christian Léger and Brenda quantum impurity problems, November 1998. MacGibbon, On the bootstrap in cube root asymptotics, August 1998. [CRM-2582] Alexei Zhedanov, A method of constructing Krall's polynomials, December 1998. [CRM-2564] Jean-Marc Lina, Paul Turcotte and Bernard Goulard, Complex dyadic multiresolution [CRM-2583] Luc Vinet and Alexei Zhedanov, analyses, August 1998. Generalized little q-Jacobi polynomials as eigensolutions of higher-order q-differential operators, [CRM-2565] Zuzana Maskov, Jíri Patera and December 1998. Edita Pelantov, Quadratic irrationalities and

CRM Annual Report 1998-1999 74 P U B L I C A T I O N S

[CRM-2584] Paul Bracken and A. Michel [CRM-2599] David J. Fernández C. and Grundland, On certain classes of solutions of the Véronique Hussin, Higher order SUSY, linearized Weierstrass-Enneper systems inducing constant non-linear Heisenberg algebras and coherent states, mean curvature surfaces, December 1998. February 1999. [CRM-2585] François Gingras, Yoshua Bengio [CRM-2600] Igor Nikolaev and Evgeny and Claude Nadeau, Generalized little q-Jacobi Zhuzhoma, Flows on 2-dimensional manifolds: an polynomials as eigensolutions of higher-order q- overview, February 1999. differential operators, January 1999. [CRM-2601] Louis-Sébastien Guimond and [CRM-2586] M. K. Atakishiyeva and Natig M. Christiane Rousseau, Finite cyclicity of finite Atakishiyev, Fourier-Gauss transforms of bilinear codimension nondegenerate homoclinic loops with generating functions for the continuous q-Hermite real eigenvalues in R3, March 1999. polynomials, January 1999. [CRM-2602] Lubomir T. Dechevsky and James [CRM-2587] A. A. Izmest'sev, G. S. Pogosyan, O. Ramsay, Penalized wavelet estimation with Besov Aleksey N. Sissakian and Pavel Winternitz, Lie regularity constraints, April 1999. algebra contractions for overlap functions, January [CRM-2603] A. Odzijewicz and A. Michel 1999. Grundland, The superposition principle for the Lie [CRM-2588] Francis H. Clarke, Yuri S. Ledyaev, type first order PDEs, April 1999. L. Rifford and Ronald J. Stern, Feedback [CRM-2604] Robert P. Langlands, Marc-André stabilization and Lyapunov functions, January 1999. Lewis and Yvan Saint-Aubin, Universality and [CRM-2589] D. Gomez-Ullate, Stéphane conformal invariance for the Ising model in domains Lafortune and Pavel Winternitz, Symmetry with boundary, April 1999. classification of systems of differential-difference [CRM-2605] Francis H. Clarke, S. N. Nobakhtian equations, January 1999. and Ronald J. Stern, Universal near-optimal [CRM-2590] Basile Grammaticos, Alfred Ramani feedbacks, April 1999. and Stéphane Lafortune, The Gambier mapping, [CRM-2606] Alexander Turbiner and Pavel revisited, January 1999. Winternitz, Solutions of nonlinear differential and [CRM-2591] Basile Grammaticos, Alfred Ramani, difference equations with superposition formulas, K. M. Tamizhmani and Stéphane Lafortune, April 1999. Again, linearisable mappings, January 1999. [CRM-2607] V. Dorodnitsyn and Pavel [CRM-2592] Paul Bracken, Classical Yang-Mills Winternitz, Lie point symmetry preserving equations invariant under subgroups of the conformal discretizations for variable coefficient Korteweg-de group without coupling to matter, January 1999. Vries equations, April 1999. [CRM-2593] Basile Grammaticos, Alfred Ramani [CRM-2608] M. Mintchev, E. Ragoucy, Paul and Stéphane Lafortune, Schlesinger Sorba and Philippe Zaugg, Yangian symmetry in transformations for linearisable equations, January the nonlinear Schrödinger hierarchy, May 1999. 1999. [CRM-2609] Joseph M. Mahaffy, Age-structured [CRM-2594] M. Iadh Ayari, Lien entre les variétés modeling of hematopoiesis, May 1999. singulières des Équations aux dérivées partielles et les [CRM-2610] Richard Fournier, Inequalities pseudopotentiels représentant les algèbres de Lie de involving weighted means in a disc of the complex dimension finie, January 1999. plane, May 1999. [CRM-2595] Alexeï V. Penskoï, Lagrangian time- [CRM-2611] Richard Fournier, On boundary zeros discretization of the Korteweg-de Vries equation, of solutions of a class of functional equations, May January 1999. 1999. [CRM-2596] John Harnad, Picard-Fuchs [CRM-2612] E. V. Ferapontov, Transformations of equations, Hauptmoduls and integrable systems, quasilinear systems originating from the projective December 1998. theory of congruences, May 1999. [CRM-2597] John Harnad and John McKay, [CRM-2613] John Harnad, On the bilinear Modular invariants and generalized Halphen system, equations for Fredholm determinants appearing in December 1998. random matrices, May 1999. [CRM-2598] Joseph M. Mahaffy, Samuel W. Polk [CRM-2614] E. V. Ferapontov and A. Michel and Roland K. W. Roeder, An age-structured Grundland, On the bilinear equations for Fredholm model for erythropoiesis following a phlebotomy, determinants appearing in random matrices, May February 1999. 1999.

CRM Annual Report 1998-1999 75 P U B L I C A T I O N S

[CRM-2619] Richard Fournier and Stephan [CRM-2663] J. Courteau and Sabin Lessard, Ruscheweyh, On extreme points of a class of Optimal sex ratios in structured populations, May functions related to a convolution conjecture, May 1999. 1999. [CRM-2664] John McKay, The semi-affine Coxeter- [CRM-2657] Nantel Bergeron and F. Sottile, A Dynkin diagram and G < SU2, 1999. Pieri-type formula for isotropic flag manifolds, 1998. [CRM-2665] François Perron, Beyond accept-reject [CRM-2658] Niky Kamran, R. Milson and P. J. sampling, 1999. Olver, Invariant modules and the reduction of non- [CRM-2666] M. Deza and Ivo G. Rosenberg, n linear partial equations to dynamical systems, 1999. semimetrics, 1999. [CRM-2659] F. Finster, Niky Kamran, J. Smoller [CRM-2667] Langis Gagnon, A. Jouan, Elisa and S.-T. Yau, Non-existence of time periodic Shahbazian and Pierre Valin, Fusion of imagery solutions of the Dirac equations in axisymmetric attributes with non-imaging sensor reports by black hole geometries, 1999. truncated Dempster-Shafer evidential Reasoning, [CRM-2660] F. Lalonde, D. McDuff and L. July 1998. Polterovich, Hamiltonian fibrations, 1999. [CRM-2668] J. R. Duquet, Elisa Shahbazian and [CRM-2661] D. Gatien and F. Lalonde, Pierre Valin, A blackboard architecture for Holomorphic cylinders with Lagrangian boundaries incremental implementation of data fusion and periodic orbits of Hamiltonians systems, 1999. applications, July 1998. [CRM-2662] Tao Yi and Sabin Lessard, [CRM-2669] J. R. Duquet, M. Macieszczak, Elisa Fundamental theorem of natural selection and Shahbazian and Pierre Valin, A generic expert frequency-dependent selection: Analysis of the diploid system infrastructure for fusion and imaging decision matrix game model, March 1999. aids, October 1998.

76 Annual Report 1998-1999 CRM FINANCIAL REPORT

The CRM’s fiscal year begins June 1 and ends $170,000 for fiscal 1999-2000 reserved for the May 31. The financial statement presents, on a network activities managed by the CRM within cash-flow basis, the major expenses and income the Mathematics of Information Technology and of the CRM during 1998-1999, as well as its Complex Systems Network of Centres of financial position at the beginning and the end Excellence. CFI-QC: $278,020 in matching grants of the period. The overall results have been from the Canadian Foundation for Innovation broken down into seven principal columns and the Government of Québec for the purchase representing the following sources of financing: of computer network equipment. In addition, the National Science and Engineering Research Sun Microsystems and Anixter Canada Inc. Council (NSERC Centre and NSERC- ncm2 ), the donated extra equipment valued at more than Fonds pour la formation de chercheurs et l’aide $68,500. The Université de Montréal: a à la recherche du Québec (FCAR Centre), the substantial grant of $722,000 has been received National Centres of Excellence program (NCE- from the Comité d’étude et d’administration de MITACS), the Canadian Foundation for la recherche (CEDAR) of the Vice-rectorat à la Innovation (CFI) with matching funds from the recherche of the Université de Montréal (a Government of Québec, the Université de decrease of 5% on the $760,000 received in 1996- Montréal (CEDAR), and other sources. 1997). Other important sources of income include the Canadian Institute for Advanced MAJOR SOURCES OF REVENUS FOR 1998-1999 Research (CIAR), the McConnell Foundation NSERC-Centre ...... $880,000 and Dr. André Aisenstadt who is the CRM’s

NSERC-ncm2 ($648,894 – $479,891) ...... $169,003 major benefactor; finally the CRM earns FCAR-Centre...... $203,750 revenues from books in the CRM series NCE-MITACS...... $95,000 published by the American Mathematical CFI-QC...... $278,020 Society (AMS), from Springer-Verlag, and from Université de Montréal* ...... $722,000 its own in-house publication program, as well as Other sources...... $360,461 from registration fees charged for attending scientific activities. We also consider as revenues In addition, the Université de Montréal furnishes the sums turned over to us by our university space and some services. partners and by the Institut des sciences mathématiques (ISM) for joint postdoctoral Revenues fellowships; these sums are managed by the During 1998-1999, the CRM received income CRM. The contribution of industrial partners of (presented at the bottom of the Statement) from the CRM’s ncm2 projects is similarly accounted the following sources. NSERC-Centre: an for; those sums paid directly to CRM researchers operating grant of $880,000 to pursue its national are not. mandate. NSERC- ncm2: the second instalment of $648,894 of a five-year grant of $3.2 for the Expenses The expenses of the CRM are presented ncm2. The financing of the ncm2 funds activities in four other research centres in addition to the under three major categories: Scientific CRM: CERCA (Centre de recherche en calcul Activities, Publications and Administration. appliqué), CIRANO (Centre universitaire de Major items under Scientific Activities include: recherche en analyse des organisations), CRT (1) scientific personnel: the remuneration of (Centre de recherche sur les transports), and professors at the Université de Montréal who GERAD (Groupe d’études et de recherche en undertake research as full-time members of the analyse des décisions). The management of the CRM; expenses associated with the detachment of Montreal-area professors so they can work at ncm2 is largely decentralized and $479,891 of the $648,894 instalment is allotted to these four the CRM; as well as remuneration of centres; of the remaining $169,003, $86,003 postdoctoral researchers and summer students; constitutes the CRM’s portion and $83,000 is (2) scientific programs: the thematic program in reserved for centralized activities managed by number theory and arithmetic geometry, the Banff summer school of 1998 related to the the CRM in the name of the ncm2. FCAR-Centre: theme year and the advanced payment on the the third annual instalment of $203,750 of a 1999 summer school; the general scientific three-year operating grant from its Research program, constituted mainly of contributions of Centres Program. NCE-MITACS: A first the CRM to off-site scientific activities, the instalment of $95,000 from a first-year grant of colloquia and seminar series organized jointly

CRM Annual Report 1998-1999 77 F I N A N C I A L R E P O R T with the Montreal-based ISM, expenses the Summer School in Banff, numerous off-site associated with the four prizes for excellence in scientific events sponsored by the CRM (often in the mathematical sciences (the André-Aisenstadt collaboration with the Fields Institute or the Prize, the Canadian Association of Physicists Pacific Institute for the Mathematical Sciences), (CAP)-CRM Prize in Theoretical and and the expenses related to non-Québec Mathematical Physics, the CRM-Fields Institute Canadians visiting the CRM in order to Prize, and the CRM-Statistical Society of Canada participate in its scientific programs. The ratio of (SSC) Prize in Statistics), the conference and such Canadian expenses to the overall NSERC- workshop programs of the ncm2, and finally Centre funded expenses is 49% for the scientific expenses related to invited researchers; (3) the programs only (51% last year), and 32% (39% personnel involved directly in the management last year) for the total expenses funded by of scientific programs; and (4) the research- NSERC. This ratio of 32% is more than the support personnel involved directly in the threshold of 25% suggested by the CRM-Fields delivery of computer services for the UNIX Institute Coordinating Committee in its last system and support to researchers for report. manuscripts. The rubric Publications includes remuneration to personnel assigned to the Financial Statement publications program as well as expenses The statement for the year thus indicates a directly related to this program. Finally, the surplus of $235,933 for operations, contributing administrative part of the financial statement to an accumulated surplus of $576,894. Two includes: the remuneration of the director’s accounts in particular are responsible for the office personnel, payments for administration greater part of the financial year’s surplus: the and services to researchers and for first corresponds to the MITACS project which administrative computing systems, expenses started only in April 1999 and has therefore not a related to meetings of the Advisory Committee great amount of incurred expenses; the second and other committees of the CRM, current corresponds to ncm2, for which the NSERC operating expenses, and expenses related to contribution was abnormally high this year. computer equipment. Finally, a more prudent management of the grants was adopted for the year, since the CRM’s Mandate NSERC grant was up for renewal. In general, the The national mandate of the CRM is reflected accumulated surplus corresponds to deferred in the NSERC column of the statement labelled revenues for activities that will take place in as Canada outside Québec. Under this heading financial years following their accounting as are singled out those NSERC-Centre funded revenue. expenditures of the CRM that occur in Canada but outside of Québec. Such expenses include

78 Annual Report 1998-1999 CRM F I N A N C I A L R E P O R T

Financial Statement

NSERC-Centre Canada outside NSERC- FCAR- NCE- UdeM Other Overall Total Québec ncm 2 Centre MITACS CFI-QC CEDAR Sources Total Scientific Activities Scientific Personnel Salaries 10,000 10,000 25,083 521,992 26,360 583,435 Partnerships 27,845 1,157 29,002 Release Time 37,711 37,711 Postdoctoral Researchers: • CRM 44,917 4,426 27,041 76,383 • CRM/ISM 30,668 45,000 75,668 • CERCA/CRM 10,806 12,833 23,639 Students and Others 25,650 16,650 7,500 9,000 42,150 Subtotal: Scientific Personnel 149,886 26,650 37,008 1,157 559,703 120,233 867,987 Scientific Programs Statistics 23,033 843 - 8,950 5,671 19,754 Number Theory & Arithmetic Geometry 81,010 24,205 7,710 88,720 Transfert to PIms 50,000 50,000 50,000 Mathematical Physics 19,237 600 3,493 22,730 Summer School 44,905 44,905 44,905 General Scientific Program 86,218 45,437 7,611 93,829 Colloquia and Seminar Series 12,153 2,242 19,770 14,420 46,343 Prizes 5,449 3,177 10,018 15,467 Guest Researchers and Other Expenses 70,239 19,887 - 46 13,767 83,959 Subtotal: Scientific Programs 392,244 191,297 19,723 - 8,950 62,690 465,707 Canada-outside-Québec Ratio: 49% Personnel - Scientific Programs 116,665 50,750 116,665 Personnel - Direct Research Support 69,583 28,906 98,489 Total: Scientific Activities 728,377 268,697 56,732 30,062 550,753 182,924 1,548,848 Canada-outside-Québec Ratio: 37% Publications Personnel 73,864 73,864 Direct Publication Expenses 6,980 10,452 17,432 Total: Publications 6,980 73,864 10,452 91,297

Administration Personnel Executive 43,217 3,788 18,817 63,433 4,467 129,934 Aministration and Research 38,006 26,731 76,788 6,031 56,207 3,446 207,209 Programmer Analysts 57,434 57,434 Subtotal: Personnel 81,223 3,788 45,548 76,788 6,031 119,640 65,347 394,577 Advisory Committee 7,354 3,207 181 7,534 Operating Expenses 53,075 2,398 3,146 422 5,648 42,528 104,819 Computer Equipment 2,373 13,987 5,113 278,235 7,653 17,865 325,226 Total: Administration 144,024 9,394 48,694 90,775 11,566 278,235 132,942 125,921 832,156

Total: Expenses 879,382 278,091 105,425 194,701 11,566 278,235 683,695 319,296 2,472,301 Canada-outside-Québec Ratio: 32% Revenues Operating Grants 880,000 203,750 722,000 142,645 1,948,395 Research Network, Equipment & Other Grants 648,894 95,000 278,020 1,021,914 Contributions from Universities & Partners - 479,891 122,364 - 357,527 Industrial Contributions 35,000 35,000 Sales and Registrations 60,452 60,452 Total: Revenues 880,000 169,003 203,750 95,000 278,020 722,000 360,461 2,708,234

Surplus (Deficit) 618 63,578 9,049 83,434 - 215 38,305 41,165 235,933

Cash at the beginning of the period 154,164 - 17,483 7,501 0 0 1,206 195,573 340,961 Cash at the end of the period 154,782 46,094 16,550 83,434 - 215 39,512 236,737 576,894

CRM Annual Report 1998-1999 79

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