Annualreport 2005 2006

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AnnualReport 2005 2006

AnnualReport 2005 2006 Centre de recherches mathématiques Université de Montréal C.P. 6128, succ. Centre-ville Montréal, QC H3C 3J7 Canada

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

c Centre de recherches mathématiques Université de Montréal, 2006 ISBN 2-921120-43-7 CENTRE DE RECHERCHES MATHÉMATIQUES

Presenting the Annual Report 2005 – 2006 5 A Year That Set a New Standard for Canadian Mathematics ...... 6

Thematic Program 9 Thematic Year 2005 – 2006: Analysis in Number Theory ...... 10 Aisenstadt Chairholders in 2005 – 2006: M. Bhargava, K. Soundararajan, and T. Tao . . . . . 10 Activities of the Thematic Year ...... 13 Past Thematic Programs ...... 23

General Program 24 CRM activities ...... 25 CRM – ISM Colloquium Series ...... 34

Multidisciplinary and Industrial Program 37 Activities of the Multidisciplinary and Industrial Program ...... 38

CRM Prizes 45 CRM – Fields – PIMS Prize 2006 Awarded to Nicole Tomczak-Jaegermann ...... 46 André-Aisenstadt Prize 2006 Awarded Jointly to Iosif Polterovich and Tai-Peng Tsai . . . . 47 CAP – CRM Prize 2006 Awarded to John Harnad ...... 47 CRM – SSC Prize 2006 Awarded to Jeffrey Rosenthal ...... 48

CRM Outreach Program 50 Jean-Marie De Koninck ...... 51 Ivar Ekeland ...... 52

CRM Partnerships 54 CRM Partners ...... 55 Joint Initiatives ...... 59

Mathematical Education 62 Institut des sciences mathématiques (ISM) ...... 63 Other Joint Initiatives ...... 65

Research Laboratories 67 Applied Mathematics ...... 68 CICMA...... 71 CIRGET ...... 74 LaCIM ...... 76 Mathematical Analysis ...... 79 Mathematical Physics ...... 82 PhysNum ...... 85 Statistics ...... 88

Publications 92 Recent Titles ...... 93 Previous Titles ...... 93 CRM Preprints ...... 96

Scientiﬁc Personnel 98 CRM Members in 2005 – 2006 ...... 99 Postdoctoral Fellows ...... 101 Long-term Visitors ...... 101 Short-term Visitors ...... 103

Governance and Scientiﬁc Guidance 105 Bureau de direction ...... 106 Scientiﬁc Advisory Committee ...... 106

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CRM Administrative and Support Staff 109 The Director’s Ofﬁce ...... 110 Administration ...... 110 Scientiﬁc Activities ...... 110 Computer Services ...... 110 Publications ...... 110 Communications ...... 110

Statement of Revenue and Expenditures for the Fiscal Year Ending on May 31, 2006 111

Mandate of the CRM 114

4 Presenting the Annual Report 2005 – 2006 CENTRE DE RECHERCHES MATHÉMATIQUES

A Year That Set a New Standard for Canadian Mathematics

The year 2005 – 2006 at TRIQ (INstitut TRansdisciplinaire en Informa- the CRM was one of the tique Quantique), and a second one that will deepest, most exciting take shape soon. We have also worked inten- years in the life of the sively on our new web site, with 80,000 dynamic mathematical institutes. pages updated daily and 7,500 hand-written Under the scientific pages, in both French and English. This website direction of Andrew is the result of years of effort to give a complete Granville (Montréal), and easily accessible view of everything that is Chantal David (Concor- of interest to mathematicians and mathematical dia) and Henri Darmon scientists. It is fed by the “CRM Monster,” one (McGill), the CRM the- of the largest databases in mathematics in the matic programme on world. Go to www.crm.umontreal.ca and select “Analysis in Number Theory” was a splendid the language of your choice (the choice is quite year, a wonderful moment of creativity, collab- limited, but still, you have a choice!). orations and discoveries. The three CRM Aisen- The CRM was the first Canadian institute to seek stadt Chair holders, contacted early in 2004 funds from the NSF, NATO, and the Clay Insti- by the organizers, gave splendid lectures and tute simultaneously, and to receive a generous stayed on site at the CRM for several months: response: all of our applications have been sup- M. Bhargava (Princeton), who was a plenary ported with even more enthusiasm than we ex- speaker at the 2006 ICM, K. Soundararajan pected — it is interesting to note that the only (Stanford), and Terence Tao (UCLA), who was NATO Advanced Study Institute in the world, awarded the Fields medal at the 2006 ICM. in any scientific field, to be funded year after What makes the CRM so innovative and stimu- year, is the CRM’s “Séminaire de mathématiques lating is the involvement at all levels of its sci- supérieures,” jointly sponsored by the Univer- entists, whose work naturally attracts top level sité de Montréal’s Department of Mathematics mathematicians from around the world. While it and Statistics. In 2007, we will innovate in an- is relatively easy for a given institute to invite other way by organizing an event that will be a Fields medalist or a Nobel Prize winner for held at Stanford University in June 2007, the a one-day lecture, it is much more difficult and first international large conference to bring to- interesting to invite them and work with them gether most mathematicians developing various for several months before they get the Fields aspects of the “ultimate theory” of Symplectic Medal, hoping that they will receive the high- Field Theory. At the moment of writing, we have est honours. This happened last year with all just received the confirmation from the NSF that three of the young CRM Aisenstadt Chair hold- it would grant us the full amount requested. ers. During the year, more than forty researchers Other new international agreements have been from around the world and many postdoctoral signed this year by the CRM, notably with IN- fellows stayed for extended periods of time at RIA and INSERM (both in France), and with the CRM. Hundreds of invited speakers came to Latin America and with Central Europe (DI- the CRM for the thematic programme, including MATIA). Negotiations are under way with the Tim Gowers (Cambridge, Fields Medalist), Jean CNRS to create three or four GDRI (Groupe de Bourgain (Institute for Advanced Study, Fields Recherche International) that would launch, for Medalist), and Barry Mazur (Harvard). the first time, a complete array of projects jointly The CRM is unique because it is much more than funded by Europe and North America in most a “conference centre”: it is both a place where fields of mathematics. Finally, the CRM is now fascinating and world-class developments take preparing a scientific mission to establish long place, and an institute where ten large laborato- term links and projects between Canada and ries are based. From Number Theory and Geom- most of the top scientific centres in India. This etry – Topology to Brain Imaging and Quantum mission, prepared with the Québec government Informatics, with strong groups in Statistics and and several research vice-principals, will take Applied Mathematics, the CRM’s vitality relies, place in a few weeks (November 2006). Since ultimately, on these laboratories. mathematics is one of the three main disciplines The CRM is currently setting up two new labo- targeted in this mission, and India will host the ratories, one in Quantum Informatics, called IN- next ICM 2010 (after a very tight competition

6 PRESENTINGTHEANNUALREPORT 2005 – 2006 with Montréal), it is natural to establish links ture in November 2006), are attracting 300 hun- with both pure and applied mathematical cen- dred persons from all walks of life for each lec- tres. ture. This year, in collaboration with its educational The lectures rotate between the large Québec partner, the Institut des sciences mathématiques universities, and could very well take place out- (ISM), the CRM launched the Accromαth project. side the universities in large halls located in The Accromαth texts are produced and revised Montréal, Québec, Sherbrooke or Ottawa. The by the most outstanding Canadian editorial goal of the CRM (already reached to a large ex- team, comprising André Ross (editor-in-chief), tent) is to contribute to the visibility and impact France Caron, Louis Charbonneau, Jocelyn Da- of the universities and its researchers, anywhere genais, Jean-Marie De Koninck, André Des- and at any time. We want to stimulate the in- chênes, Christian Genest, Frédéric Gourdeau, tellectual life of this country, so that it becomes Bernard Hodgson and Christiane Rousseau. The an integral part of our environment; we want to members of the editorial team are involved present to Québeckers and Canadians the scien- in the teaching of mathematics at the high tific and cultural issues of the twenty-first cen- school, college or university level, and several tury, and leave our ivory towers while preserv- of them have gained recognition for their con- ing the peace of mind that researchers need to tributions to the popularization of mathemat- work and make discoveries. ics. For instance, Bernard Hodgson (Université One of the best indicators of the vitality of Laval) is secretary-general of the International mathematical research in Canada is the compe- Commission on Mathematical Instruction, based tition for the André-Aisenstadt Prize, awarded in Geneva; this is one of the highest international each year by the CRM Scientific Advisory Panel positions in the field of mathematical instruc- to a young Canadian mathematician working tion. in Pure Mathematics, Applied Mathematics or Frédéric Gourdeau (Université Laval) has re- Statistics. In 2006, the competition was ex- ceived the 2006 CMS Excellence in Teaching tremely tight, so we had to award the Prize to Award in recognition of his sustained and two mathematicians: Iosif Polterovich (Univer- distinguished contributions to teaching at the sité de Montréal) and Tai-Peng Tsai (University undergraduate level. Jean-Marie De Koninck of British Columbia). The other CRM prizes in (Université Laval) received the same award in 2006 were awarded to Jeffrey Rosenthal (Statis- 2004. Christiane Rousseau (Université de Mont- tics, University of Toronto) in collaboration with réal) was until recently president of the Cana- the Statistical Society of Canada, to John Har- dian Mathematical Society and Christian Genest nad (Mathematical Physics, Concordia Univer- (Université Laval) is president-elect of the Sta- sity and CRM) in collaboration with the Cana- tistical Society of Canada. The Accromαth jour- dian Association of Physicists, and to Nicole nal has aroused so much interest in the math- Tomczak-Jaegermann (Mathematics, University ematical community that it has become a focal of Alberta) in collaboration with the Fields Insti- point for Canadian mathematics. Requests for tute and PIMS. subscriptions are coming not only from Ontario I would like to thank the organizers of the and New Brunswick, but from every corner of 2005 – 2006 thematic programme at the CRM, es- the French-speaking world, for instance France pecially Andrew Granville, Chantal David and and Belgium and (soon) Africa. Henri Darmon (but there are so many other Also this year, the CRM lauched the new pro- names), as well as the CRM staff, for their com- gramme “CRM Public Lectures” in order to mitment and dedication. I would also like to reach out to a general audience, high school and thank the vice-principals (research) of the seven college teachers and their students. Because of large universities involved in the CRM enter- their quality and breadth, these lectures are hav- prise; their support is absolutely essential. And, ing an impact on many groups, even groups above all, I would like to emphasize that the of academics in biology, medicine, philosophy, CRM is here to serve the international commu- physics and computer science. Lecturers such as nity of mathematical scientists in all possible Jean-Marie De Koninck (chosen as “Scientist of ways. The directors of the three Canadian In- the Year” by Radio-Canada), Ivar Ekeland (di- stitutes have been working in close collabora- rector of PIMS and former president of the Uni- tion on many national and international issues, versité de Paris-Dauphine) and Bart de Smit, such as the applications for the ICM and the from the University of Leyden (who gave a lec- ICIAM, the Second Canada – France Conference

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(with Octav Cornea and Nassif Ghoussoub as thanks in great part to the Liaison Committee led scientiﬁc directors), and the support extended to by Richard Kane. the three mathematical and statistical societies, to AARMS and to the NPCDS programme in statistics. This year as always, it has been a plea- François Lalonde sure to exchange views and combine our efforts, Director

8 Thematic Program CENTRE DE RECHERCHES MATHÉMATIQUES

HE core of each year’s scientific program at the CRM is its thematic program. The Scientific Advi- Tsory Committee chose for 2005 – 2006 the theme Analysis in Number Theory, because of the spectacular developments taking place in that field and their impact on the international scientific community. The thematic program included six workshops, several seminars and conferences, three Aisen- stadt Chair lecture series (by Manjul Bhargava, K. Soundararajan, and Terence Tao, respectively), a NATO Advanced Study Institute, a CRM – Clay School, long term visits by fifty researchers and some postdoctoral fellowships. In coordination with Montréal universities, the CRM offered two courses in order to help graduate students participate in the activities. The reports are presented in the language in which they were submitted.

Thematic Year 2005 – 2006: Analysis in Number Theory

Organizers: Henri Darmon (McGill), Chantal David (Concordia), Andrew Granville (Mont- réal) The thematic year on Analysis in Number The- ory consisted of two semesters with different foci, both exploring the fruitful interactions between analysis and number theory. The ﬁrst semester focused on p-adic analysis and arithmetic geometry, and the second semester on classical analysis and analytic number theory. In both semesters, several workshops, schools and focus periods have concentrated on the new and exciting developments of the recent years that have emerged from the interplay between analysis and number theory. Here are some of the leading themes of the year: the emerging theory of p-adic families of modular forms and the p- adic Langlands correspondence in high degrees; the new developments in the classical theory of L-functions (non-vanishing L-functions, subconvexity and applications); the recent spectacular advances in additive combinatorics and harmonic analysis, and their applications to number theory. Some of the activities of the theme year have been organized jointly with the program Rational and Integral Points on Higher-Dimensional Varieties held at MSRI from January to May 2006.

Aisenstadt Chairholders in 2005 – 2006: M. Bhargava, K. Soundararajan, and T. Tao

The André-Aisenstadt chairs for the Thematic André-Aisenstadt chairs to stay in residence at Year Analysis in Number Theory were three excep- the CRM for extended periods, from one week to tional young mathematicians working in differ- several months. The quality of the many lectures ent areas of number theory, that have been inﬂu- given by the three André-Aisenstadt chairs, and enced and developed by their scientiﬁc achieve- the inspiration provided by their presence, were ments: Manjul Bhargava (Princeton University), two of the reasons for the great success of the K. Soundararajan (Stanford University) and Ter- special year. ence Tao (UCLA). The organizers are specially proud that they managed to convince the three

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Manjul Bhargava in Science and Engineering (2004) and the MAA Merten M. Hasse Prize for Exposition (2003). He Manjul Bhargava has made phenomenal con- was also the first Clay Mathematics Institute’s tributions to number theory, most notably by five-year Research Fellow (2000 – 2005). his discovery of higher order composition laws. This is the topic of his Ph.D. thesis, written under the direction of Professor Andrew Wiles of K. Soundararajan Princeton University and published as a series of papers in the Annals of Mathematics. Bhargava K. Soundararajan has made brilliant contribu- introduced entirely new and unexpected ideas tions to several areas in analytic number the- that led to his discovery of composition laws ory, which include multiplicative number the- for forms of degree greater than 2, generalising ory, the Riemann zeta function and Dirichlet L- the construction of Gauss for binary quadratic functions, the analytic theory of automorphic forms. Bhargava then applied these composition forms and the Katz – Sarnak theory of symmetric laws to solve a new case of one of the funda- groups associated with families of L-functions mental questions of number theory, that of the (random matrix theory). As an undergraduate asymptotic enumeration of number fields of a at the University of Michigan, Soundararajan given degree d. The question is trivial for d = 1, already made important contributions: first, in and Gauss himself solved the case d = 2 in 1801. joint work with R. Balasubramanian, he proved Davenport and Heilbronn solved the case d = 3 a famous conjecture of Ron Graham in combi- in 1971. Bhargava has now solved the d = 4 and natorial number theory; secondly, he obtained d = 5 cases, which previously had resisted all some fundamental results on the distribution attempts. of the zeros of the Riemann zeta function. In his Ph.D. thesis, written under the direction of Bhargava also ap- Professor Peter Sarnak of Princeton University, plied his work to K. Soundararajan proved that more than seven- make significant eighths of quadratic Dirichlet L-functions have progress on the prob- 1 no zeros at the critical point s = 2 , thereby lem of finding the providing strong evidence for a conjecture of average size of ideal Chowla. This spectacular result was published class groups and on in the Annals of Mathematics. the related conjectures of Cohen and Lenstra. Bhargava’s contri- The work of butions have created a whole new area of re- Soundararajan is search in a classical topic that has seen very little prolific and char- activity since the time of Gauss. Manjul Bhar- acterized by its in- gava has also made exceptional contributions genuity and re- to the theory of representations of positive inte- markable techni- gers by sums of squares, giving a short and dical strength. Here rect proof of the “15-Theorem” of Conway and are some of his Schneeberger, and proving, in collaboration with many remarkable works: his work with Brian Jonathan Hanke, the “290-Theorem” conjectured Conrey proving that a positive proportion of by Conway. Dirichlet L-functions have no zeros on the real axis within the critical strip; his work with Ken Manjul Bhargava received his Ph.D. from Prince- Ono on Ramanujan’s ternary quadratic form; ton University under the advisorship of An- and his collaboration with Andrew Granville, drew Wiles in 2001. After brief visiting positions resulting in many major works on multiplica- at the Institute for Advanced Study and Har- tive functions, character sums, extreme values vard University, he joined the faculty of Prince- of L-functions, and so on. ton University as Professor of Mathematics in 2003, the youngest of that rank at Princeton. K. Soundararajan became a Professor at Stanford Bhargava has received numerous awards and University in 2006, and was previously Professor honors, including the 2005 SASTRA Ramanu- at the University of Michigan at Ann Arbor. He jan Prize (jointly with K. Soundararajan), the has received numerous awards and honors for AMS Blumenthal Award for the Advancement his remarkable research contributions, including of Pure Mathematics (2005), the 2005 Clay Re- the 2005 SASTRA Ramanujan Prize (awarded for search Award, a Packard Foundation Fellowship the first time) for his outstanding contributions in areas of mathematics influenced by Ramanu-

11 CENTRE DE RECHERCHES MATHÉMATIQUES jan, and the 2003 Salem Prize, awarded every and one cannot apply Szemerédi’s theorem di- year to a young mathematician judged to have rectly to them. All the proofs of Szemerédi’s the- done outstanding work in the field of interest of orem rely on the interplay between structure and Raphaël Salem, primarily the theory of Fourier randomness, which Green and Tao were able to Series. He was also the first recipient of the AIM exploit to obtain their spectacular result. Five-Year Fellowship in 1998. Terence Tao completed his Ph.D. at Princeton University under the direction of Elias Stein in Terence Tao 1996. He then moved to UCLA where he became a Full Professor in 2000. His work, of ex- Terence Tao just received the traordinary breadth and depth, was recognised Fields Medal at the ICM in by many prizes and awards, in addition to the Madrid in August 2006, for consecration of the Fields Medal in 2006. Let his contributions to partial us mention here the Ostrowski Prize (2007), a differential equations, com- MacArthur Fellowship (2007), the SASTRA Ra- binatorics, harmonic anal- manujan Prize (2006), the Levi L. Conant Award ysis and additive number (2004), a Clay Research Award (2003), the Bocher theory. He is a supreme Memorial Prize (2002), and the Salem Prize problem-solver whose spectacular work has had (2000). an impact across several mathematical areas. At 31 years of age, Tao has written over 80 research Aisenstadt Chair papers, with over 30 collaborators, and his interests range over a wide spectrum of mathemat- The Aisenstadt Chair was endowed by Mont- ics. Because of the wide range of his accomplish- réal philanthropist Dr. André Aisenstadt. Under ments, it is difficult to give a brief summary of its auspices, one or more distinguished mathe- Tao’s oeuvre. We concentrate here on the work maticians are invited each year for a period of that was related to the 2005 – 2006 CRM The- at least one week, ideally one or two months. matic Year. During their stay the lecturers present a se- One of the achievements that were recognised ries of lectures on a specialized topic. They by the Fields Medal is his work with Ben Green are also invited to prepare a monograph (see on Long Arithmetic Progressions in the Primes, the chapter on publications in the present re- which was announced in 2004, stunning the port for a list of these monographs). At the re- mathematical community. Finding arithmetic quest of Dr. Aisenstadt, the first lecture given progressions in the primes is an old and classi- by an Aisenstadt chairholder should be accessi- cal problem of additive number theory, together ble to a wide audience. Previous holders of the with the Twin Prime conjecture and Goldbach’s Aisenstadt Chair are: Marc Kac, Eduardo Zaran- conjecture. Van der Corput proved in 1929 that tonello, Robert Hermann, Marcos Moshinsky, the primes contain infinitely many arithmetic Sybren de Groot, Donald Knuth, Jacques-Louis progressions of length 3, and before the work of Lions, R. Tyrrell Rockafellar, Yuval Ne0eman, Green and Tao, there were only partial results to- Gian-Carlo Rota, Laurent Schwartz, Gérard De- wards arithmetic progressions of length 4. The breu, Philip Holmes, Ronald Graham, Robert number theory community was thus stunned Langlands, Yuri Manin, Jerrold Marsden, Dan when news of the theorem of Green and Tao Voiculescu, James Arthur, Eugene B. Dynkin, began to circulate: they had proven that there David P. Ruelle, Robert Bryant, Blaine Law- are infinitely many arithmetic progressions of son, Yves Meyer, Ioannis Karatzas, László Babai, length k in the primes, for any positive integer Efim I. Zelmanov, Peter Hall, David Cox, Frans k (and not just k = 4)! At the heart of the work Oort, Joel S. Feldman, Roman Jackiw, Duong of Green and Tao is Szemerédi’s Theorem (1975), H. Phong, Michael S. Waterman, Arthur T. Win- which says that if a subset of the integers has free, Edward Frenkel, Laurent Lafforgue, George positive density, then it contains infinitely many Lusztig, László Lovász, Endre Szemerédi, Peter arithmetic progressions of length k for any k. Of Sarnak, Shing-Tung Yau, Thomas Yizhao Hou, course, the primes do not have positive density, and Andrew J. Majda.

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Activities of the Thematic Year

SMS – NATO ASI 2005 Summer School extraordinarily positive feedback after the end Equidistribution in Number Theory of the School, in fact far more positive than we July 11 – 22, 2005, Université de Montréal would ever have thought possible. Many stu- Financed by NATO, CRM, ISM, and Department dents enthusiastically worked on the lectures in of Mathematics and Statistics of Université de the evenings and weekend and several lectur- Montréal ers have subsequently been asked whether they were willing to supervise a student or postdoc Organizers: Zeev Rudnick (Tel Aviv), Andrew they had met at the School. Somehow the School Granville (Montréal) gained an atmosphere that the students enjoyed! Speakers: Stephan De Bièvre (Lille), Bill Duke (UCLA), John Friedlander (Toronto), Andrew The School talks came under the general head- Granville (Montréal), Roger Heath-Brown (Ox- ing Equidistribution in Number Theory. With ex- ford), Elon Lindenstrauss (New York), Jens citing developments in the understanding of Marklof (Bristol), Zeev Rudnick (Tel Aviv), zeta functions through random matrix theory, K. Soundararajan (Stanford), Yuri Tschinkel researchers in classical analytic number theory (Göttingen), Emmanuel Ullmo (Paris-Sud) et have begun to think more in terms of distribu- Akshay Venkatesh (MIT) tions than they have for a long time (and in new Number of participants: 12 speakers and 75 ways). Also Ratner’s theorem in ergodic the- students ory has found an astonishing variety of applications. With the unification of techniques and We advertised broadly for the Summer School perspectives in algebraic geometry and in the and the amount of interest generated for it was circle method of analytic number theory, dis- impressive. We received 150 applications, in par- tribution questions are taken more seriously in ticular high numbers of outstanding applica- these subjects than they used to. Recently the tions from well-qualified students and young most exciting breakthroughs derived from ideas researchers from NATO and partner countries. that loosely come together under the heading We selected 75 students and twelve main speak- Equidistribution in Number Theory. We decided ers gave series of lectures. Two one-hour lec- that this would be a wonderful subject for a sum- tures were given by Gergely Harcos (University mer school, and since many of the key results of Texas at Austin) and Andrei Yafaev (Univer- have been proved by younger people, we invited sity College, London), respectively. The speak- them to give series of lectures. ers were encouraged to keep the lectures accessible. This led to an incredible enthusiasm from In the first week, Granville and Rudnick covered the students, most of whom hardly missed a lec- the basics of uniform distribution, De Bièvre the ture during two weeks! big picture of the basic physics that is related to these topics (in particular to quantum unique er- The lectures at the Summer School were care- godicity), and Marklof the basics of ergodic the- fully orchestrated to lead a well educated stu- ory on manifolds. Ullmo lectured on the basic dent from the basics of the subject to the point picture for distribution of algebraic points on va- at which he (or she) could get some idea of the rieties, followed by Rudnick, who proved Lang’s subjects at a very high level. These disparate result for torsion points, and Granville, who topics had never before been brought together proved Bilu’s equidistribution theorem. Heath- under one subject, and it became increasingly Brown gave a stunningly beautiful and accessi- clear during the meeting that this was appropri- ble introduction to the classical circle method, ate. Many central, recent advances in the field in a form that fascinated several students. Duke were discussed here, some for the first time in a highlighted the beauty of his early work on professional meeting. The speakers were accessi- the equidistribution of CM-points in hyperbolic ble and the scientific atmosphere during the two space, which has inspired so much recent work, weeks was stimulating, intense and enjoyable. and gave some pointers to the new directions. As a whole, this School has certainly contributed Venkatesh introduced the students to ergodic to the advancement of the subject by providing theory on certain manifolds and the directions an access to the most important, recent devel- he is pursuing. opments in the field to a group of well moti- The second week involved deeper concepts and vated and prepared students. We were delighted material but the speakers did their best to remain by the high level of participation and received accessible, none more so than Lindenstrauss,

13 CENTRE DE RECHERCHES MATHÉMATIQUES author of some of the most important break- mostly through the interesting ideas and ques- throughs on distribution using ergodic theory tions offered here for the first time, and through (for which he has won several major prizes). Lin- the large number of collaborations that were denstrauss focused on examples to bring clar- started at the workshop. In saying so we are al- ity to his exposition of his work. Tschinkel gave most quoting Barry Mazur whose colloquium the big picture of distribution of points on high- talk summarized and ended the workshop. dimensional surfaces, and in particular the alge- The theory of a p-adic Local Langlands Cor- braic geometry involved; he surprised us by pre- respondence had its beginnings in 2000 with senting many simple examples that still defy un- the work of C. Breuil. Given a prime integer derstanding. Friedlander gave us an overview of p > 0, an integer n > 0 and a finite exten- the very important work applying these equidis- sion L of Qp, his idea was to construct a cor- tribution ideas to cryptography, and Granville respondence satisfying functorial properties be- explained how the recent work of Bourgain and tween n-dimensional p-adic representations of his coauthors implies that the Diffie – Hellman the group Gal(Q /L) and unitary representa- protocol is very secure against statistical attacks. p tions of the group GL (L) on p-adic Banach Soundararajan gave a beautiful exposition of the n spaces. heuristics involved in gaining a fine understanding of the distribution of primes. Most of the results have been obtained for the case L = Qp. In this case and for n = 1, the correspondence was easily achieved. For Workshop n = 2 the correspondence was first estab- p-adic Representations lished by Breuil for crystalline representations. September 12 – 16, 2005, CRM If V is a 2-dimensional crystalline representation Sponsored by NSERC, FQRNT, NATO, NSF, and Q Q of Gal( p/ p), let us denote by W the Weil- CRM cll representation attached to Dcris(V). Then, if W Organizers: Adrian Iovita (Concordia), Henri is the GL2(Qp) representation attached to W by Darmon (McGill) the classical Local Langlands Correspondence Speakers: Fabrizio Andreatta (Padova), Joël and if a ≤ b are the Hodge numbers of V, there Bellaïche (Columbia), Laurent Berger (IHES), is a unique invariant norm on the GL2(Qp)- Christophe Breuil (IHES), Frank Calegari (Har- b−a Q2 cll representation U(V) := Sym ( p) ⊗Qp W . vard), Pierre Colmez (Paris 6), Matthew Emerton Let B(V) denote the completion of U(V) with re- (Northwestern), Elmar Grosse-Klönne (Mün- spect to this norm. Then up to twist by a power ster), Michael Harris (Paris 7), H. Hida (UCLA), of the determinant, B(V) is the Banach-space Mark Kisin (Chicago), Barry Mazur (Harvard), representation attached to V. Abdellah Mokrane (Paris 13), Vytautas Pasku- nas (Bielefeld), Michael Spiess (Bielefeld), Glenn A similar strategy (taking into account the use Stevens (Boston), Matthias Strauch (Münster), of L-invariants) was proposed for semi-stable Q Q Jeremy Teitelbaum (Illinois at Chicago), Eric Ur- representations of Gal( p/ p), a strategy that ban (Columbia), Marie-France Vignéras (Paris works modulo the conjecture that the p-adic Ba- 13), Jean-Pierre Wintenberger (Strasbourg) nach spaces thus obtained are non-trivial. This Number of participants: 76 conjecture was proved by Colmez using (Φ, Γ)- modules. Moreover Colmez announced in his The workshop, which attracted many graduate talk at the workshop results on a general p-adic students (about 20) and postdocs, had two ma- Local Langlands Correspondence for n = 2 and jor themes: a p-adic Langlands Correspondence L = Qp. and p-adic families of motives. Our idea in organizing this workshop was that these two themes The talks of M. Strauch, V. Paskunas, M.-F. Vi- have many common features and they are at gnéras and J. Teitelbaum were connected with Q a stage of development where they could in- generalizations to either n > 2 or [L : p] > 1. fluence each other if only the researchers were M. Emerton’s talk reported on a possible theory given the opportunity to interact. We hoped to of a global p-adic Langlands Correspondence create that opportunity by bringing together re- and M. Kisin announced a proof of certain cases searchers from both fields and we have to say of the Fontaine – Mazur conjecture, his proof us- that our hopes were amply fulfilled. We think ing results on the p-adic Local Langlands Corre- that the workshop marked a decisive step in spondence. the evolution of the two themes through the important results reported at the workshop but

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The second theme of the conference, the theme tations in Montréal in September 2005 marked of p-adic variation of motives, started in the a new way of understanding both the p-adic 70s with articles of J.-P. Serre, N. Katz, and Langlands Correspondence and the p-adic vari- H. Hida and continued in the 90s with the work ation of motives and especially the relationship of B. Mazur, F. Gouvea, and R. Coleman. They between the two. realized, conjectured and finally proved that the various congruences modulo powers of a prime p > 0 between elliptic modular eigenforms are Workshop manifestations of the fact that modular eigen- Gathering on Stark’s conjectures forms of finite slope come to this world in p-adic November 1 – 3, 2005, CRM analytic families parameterized by the weight. In fact these families can be explained by the ex- Organizers: Pierre Charollois (Montréal), Henri istence of a geometric object, “the eigencurve,” Darmon (McGill), Samit Dasgupta (Harvard), which is a locally finite cover of the weight space Eyal Goren (McGill) and whose points should be thought of as over- Speakers: Hugo Chapdelaine (McGill), Pierre convergent eigenforms of finite slope. Charollois (Montréal), Henri Darmon (McGill), Samit Dasgupta (Harvard), David Dummit There were very interesting talks on this theme (Vermont), Caleb Emmons (California at San at the workshop: F. Calegari reported on work Diego), Stefan Erickson (Colorado College), Eyal on a construction of an “eigencurve” for mod- Goren (McGill), Andrew Granville (Montréal), ular forms over an imaginary quadratic field, Jonathan Sands (Vermont), Harold Stark (Cal- and G. Stevens on a new, cohomological con- ifornia at San Diego), Mak Trifkovic (McGill), struction of the p-adic families of elliptic eigen- Daniel Vallières (McGill) curves. E. Urban’s talk referred to trace formu- Number of participants: 25 las for p-adic analytic families of modular forms for very general reductive groups, J. Bellaïche re- Cet atelier a été originellement conçu comme ported on results related to the local geometry of une occasion de faire le point, en profitant des the eigenvarities attached to unitary groups, and forces locales déjà présentes à Montréal à l’occa- A. Mokrane sketched a program to define p-adic sion de l’année spéciale en théorie des nombres, families and “eigenvarieties” for modular eigen- sur les conjectures fondamentales formulées par forms on symplectic groups using crystalline- Harold Stark à la fin des années 1970. Ces cohomological methods. Finally H. Hida talked conjectures prédisent l’algébricité de certaines about his work on Λ-adic Barsotti – Tate groups. valeurs spéciales de fonctions L. Elles sont sans doute intimement reliées au 12ième problème The talk of F. Andreatta on a new theory of de Hilbert (ou rêve de jeunesse de Kronecker), relative (Φ, Γ)-modules, that of M. Spiess on 0 qui consiste, selon le modèle des corps cyclo- Drinfel d – Stuhler varieties and that of J.-P. Win- tomiques, à engendrer explicitement des ex- tenberger on the proof of cases of Serre’s conjec- tensions abéliennes spécifiques d’un corps de ture were quite interesting, although not directly nombres par des moyens analytiques. Cette thé- related to the two main themes of the work- matique de recherche est déjà bien présente dans shop. In order to help the young participants fol- la région de Montréal, et les organisateurs sou- low the talks, we asked Christophe Breuil and haitaient en tirer profit pour faire présenter de Matthew Emerton to give expository talks on the manière informelle les progrès récents. main ideas involved in the two themes. En réalité, il s’est avéré qu’un auditoire plus We organizers think that the workshop was of large participerait à cet atelier. C’est ainsi que an exceptionally high level and that, as men- nous avons eu le plaisir de rassembler dans les tioned at the beginning of this report, it marked locaux du CRM un auditoire de plus de vingt a crucial moment in the development of the two personnes, incluant notamment le professeur themes. In fact, now, almost eight months af- H. Stark lui-même. L’exposé introductif, donné ter the event, we see that many of the ideas par David Dummit, a rappelé le cadre exact de presented at the workshop have been followed la conjecture de Stark classique et de ses mul- up, a number of the conjectures presented there tiples généralisations. Il a ainsi permis de ma- have been proved and new and very exciting re- nière très efficace de situer le contexte des tra- sults in the two fields have been announced. At vaux plus spécialisés exposés par la suite. Stefan the AIM conference on p-adic Representations Erickson et Caleb Emmons ont alors pu exposer (Palo Alto, February 2006), M. Emerton stated in les extensions des conjectures de Stark qu’ils ont his talk that the workshop on p-adic Represen- formulées dans leurs thèses.

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Jonathan Sands a expliqué comment, dans le points. His lectures explained the essential use cas des extensions multiquadratiques, les ou- of Borcherds Theory and Arakelov Theory in ob- tils développés pour résoudre la conjecture de taining the results. Another lecture series was Stark permettent de répondre à des questions given by Brian Conrad, who explained the local analogues en K-théorie. Eyal Goren et son étu- intersection numbers calculations in the work of diant ont détaillé les constructions explicites de Gross and Zagier. His lectures provided a solid nombres algébriques qu’ils obtiennent dans le and conceptual foundation to such calculations cas quartique CM, ainsi que les obstructions à ce and one expects that a similar approach will be que ces nombres soient des unités algébriques. indispensable in higher-dimensional cases that L’atelier a abordé les méthodes modulaires, in- are yet to be studied. troduites par Henri Darmon, qui conduisent à Steve Kudla explained some of his research, une nouvelle approche des conjectures de Stark, spanning almost a decade, focusing on joint les rapprochant de la question de la construction work with Michael Rapoport and Tonghai Yang de points de Heegner sur les courbes elliptiques. that relates a particular generating series of zero Ces méthodes conduisent à une meilleure com- cycles on an arithmetic surface and (derivatives préhension des fonctions analytiques requises e of) an Eisenstein series (this is a sample case par le 12 problème de Hilbert. Une avancée of the “Kudla program”). His lectures stressed spectaculaire a été annoncée par Samit Das- again Arakelov Theory and Borcherds Theory gupta, qui laisse espérer une plus vaste géné- techniques. The fourth lecture series was given ralisation n’utilisant pas la modularité. L’atelier by Shou-Wu Zhang, who discussed two top- s’est conclu par un exposé très vivant donné par ics. The first topic was investigated by Johan de Harold Stark. Jong and himself and concerns sub-Shimura varieties of the moduli space of curves; the second Workshop was a survey, and discussion, of some recent re- Intersection of Arithmetic Cycles and Au- sults connecting period integrals and values of tomorphic Forms (derivatives of) L-functions. December 12 – 16, 2005, CRM The last lecture series was given by José Ignacio Sponsored by NSERC, FQRNT, NATO, NSF and Burgos Gil, Jürg Kramer and Ulf Kühn, who de- CRM scribed their joint project of extending Arakelov Organizers: Eyal Goren (McGill), Henri Dar- Theory (part of this project is in collaboration mon (McGill) with Bruinier). The extension that is proposed is Speakers: Kathrin Bringmann (Wisconsin- such that one can apply it to define sub-Shimura Madison), Jan Bruinier (Köln), José Ignacio varieties of the moduli space of principally po- Burgos Gil (Barcelona), James Cogdell (Ohio larized abelian varieties. One could also use the State), Brian Conrad (Michigan), Katia Consani proposed extension to prove finiteness results (Johns Hopkins), Henri Darmon (McGill), Samit for these varieties. Such an application is in- Dasgupta (Harvard), Jens Funke (New Mex- spired by Faltings’ proof of the Shafarevitch con- ico State), Jayce Getz (Wisconsin), David Helm jecture. In addition to these lecture series that (Harvard), Benjamin Howard (Boston College), comprised 13 lectures, there were 14 additional Paul Jenkins (UCLA), Bruno Klingler (Chicago), talks and a colloquium talk. The additional talks Jürg Kramer (Humboldt), Steve Kudla (Mary- covered a spectrum of topics related to the theme land), Ulf Kühn (Humboldt), Kristin Lauter (Mi- of the workshop. Concluding the workshop was crosoft Research), Ron Livne (Hebrew Univer- a colloquium talk by James Cogdell, who spoke sity), A. Raghuram (Oklahoma State), Jeremy on L-functions, modularity and functoriality. Rouse (Wisconsin-Madison), Shou-Wu Zhang As organizers we felt that the workshop was (Columbia) of an exceptionally high level. Clearly some Number of participants: 65 of the talks indicated the directions where The participants came from Canada, the U.S., intensive and influential research will take Germany, Spain, France, Japan and Australia. place in the coming years. The importance Among the participants were also graduate stu- of Borcherds’ work and Arakelov Theory was dents and postdoctoral fellows. The skeleton of stressed throughout the workshop and provided the workshop consisted of 5 lecture series. One new inspiration. The atmosphere was very lecture series was given by Jan Bruinier, who dis- friendly, cooperative and stimulating; many cussed arithmetic intersection theory on Hilbert people were engaged in discussions during the modular surfaces and values of functions at CM breaks and after the lectures, and certain new

16 THEMATIC PROGRAM collaborations have emerged. Especially valu- Langlands functoriality and approximations to- able was the exchange of ideas between three wards the Ramanujan – Peterson – Selberg con- groups: those of arithmetic geometry, Arakelov jecture, and on tools from ergodic theory, such Theory and automorphic forms, respectively. as Ratner’s theorem on the classification of invariant ergodic measures under the action of a Workshop unipotent subgroup. Finally, the timing of the L-functions and Related Themes lectures allowed Philippe Michel to relate those February 13 – 17, 2006, CRM equidistribution problems to classical problems of analytic number theory, such as subconvexity Organizers: Chantal David (Concordia), Ram of L-functions and non-vanishing of L-functions Murty (Queen’s) at the critical point. Speakers: Valentin Blomer (Toronto), Brian Conrey (AIM), Dorian Goldfeld (Columbia), The lectures of Kumar Murty discussed the gen- Andrew Granville (Montréal), Gergely Har- eral space of L-functions and various ways of cos (Texas at Austin), Henryk Iwaniec (Rut- metrizing this space. They also touched upon gers), Emmanuel Kowalski (Bordeaux), Yu-Ru the new theme of limits of L-functions and the Liu (Waterloo), Stéphane Louboutin (Institut de Chebotarev density theorem for infinite exten- Mathématiques de Luminy), Philippe Michel sions. On the first day, Henryk Iwaniec, who (Montpellier), Djordje Milicevic (Princeton), Ku- has now been for decades one of the leaders in mar Murty (Toronto), Yiannis Petridis (CUNY), the field of L-functions and automorphic forms, Guillaume Ricotta (Montréal), Mike Rubinstein gave a magnificent and inspiring talk on his re- (Waterloo), Nina Snaith (Bristol), K. Soundarara- cent work with John Friedlander, in which they jan (Stanford), Mark Watkins (Bristol) gave a new proof of Linnik’s theorem on the Number of participants: 83 least prime in an arithmetic progression by using sieve methods only. This workshop focused on the recent developments in the study of L-functions, and its main One of the remarkable features of the work- themes were: vanishing of L-functions, zero-free shop was the very impressive talks given by ju- regions, size of L-functions, and moments. Many nior mathematicians working in the field of L- new and exciting results on those topics have functions (some of them still completing their been obtained in the last few years, and there Ph.D.). Valentin Blomer and Gergely Harcos are very tantalizing questions that are just at gave a two-part lecture on their new results on the limit of the current techniques. The skeleton subconvexity bounds for general L-functions of of the workshop was three series of lectures by GL(2); this entailed a massive amount of work K. Soundararajan (one of the André-Aisenstadt and improved the previous results. Guillaume chairs), Philippe Michel and Kumar Murty. The Ricotta presented his work on the non-vanishing lectures of Soundararajan were actually Aisen- of cubic twists of L-functions of elliptic curves, stadt chair lectures (see the preceding section on in a very lively and impressive talk. The work of the Aisenstadt chair holders). All three lectures Djordje Milicevic is concerned with a new and were masterfully delivered and sounded like a recent application of the mollification technique concerto! It was remarkable that Soundararajan to large values of automorphic forms. A similar was able to present the main ideas of those tech- idea was also used by Soundararajan and pre- niques very explicitly in simple cases, and then sented in his series of lectures; it involves opti- to apply them in more complicated cases. His mizing two quadratic forms, making one large lectures were very inspiring for all participants. with respect to the other. Finally, Yu-Ru Liu, who is emerging as one of the new experts on the cir- The leading thread of the lectures of Philippe cle method, presented her recent work on War- Michel was three classical problems of equidis- ing’s problem over function fields. tribution of integral points on spheres solved by Linnik and his school in the 1960s. This choice There was also a series of lectures on the myste- allowed him to present, in a manner suitable for rious connections between L-functions and ran- non-experts in the field, very recent techniques dom matrix theory, which have been an impor- used to tackle new equidistribution problems tant source of inspiration for some recent work about special points on homogeneous varieties on L-functions. This was the topic of the lec- under the action of an algebraic group. The ex- tures of Nina Snaith, Mike Rubinstein and Mark perts in the field were also well served by his Watkins. A crucial notion that has emerged from lectures. The recent techniques rely primarily on random matrix theory over the last decade is powerful tools from harmonic analysis, such as that L-functions should be studied in families,

17 CENTRE DE RECHERCHES MATHÉMATIQUES a notion which is also at the heart of the work jan (Stanford), Cameron L. Stewart (Waterloo), of Katz and Sarnak. This notion appeared very Trevor Wooley (Michigan), Jie Wu (Nancy 1) beautifully in the work presented by Emmanuel Number of participants: 77 Kowalski, who showed that over function fields, The workshop Anatomy of Integers gathered one can get upper bounds going beyond Gold- about 70 participants from many different coun- feld’s conjecture in that context, in agreement tries around the world. There has never really with a conjecture of Conrey, Keating, Rubinstein been a meeting dedicated to these questions be- and Snaith about the vanishing of functions over fore; even though this subject includes some of number fields for this family of functions. the most important questions in analytic num- In his lecture, Dorian Goldfeld presented the ber theory, they have always been seen as part material of his forthcoming book on automor- of other topics. Many of the participants seemed phic forms and L-functions on GL(n, R), giving to really enjoy the focus of the conference. There a rigorous but elementary exposition of the sub- are two major “schools” in this area, one in ject. There is a lot of interest for such an explicit North America, the other centered in France. treatment of the subject. Yiannis Petridis pre- The two schools have rarely come together, and sented some results on the distribution of prim- on this occasion we saw many of the leading itive conjugacy classes of cofinite subgroups of young French researchers in North America and SL(2, R). there were some positive interactions. Finally, the workshop ended on a very entertain- Two of the biggest breakthroughs in this area in ing and slightly controversial talk by Andrew the last few years are described below. 1. The Granville, about work in progress with Mark proof of Goldston, Pintz and Yildirim that there Watkins on the rank of elliptic curves in families are “small” gaps between primes infinitely often of quadratic twists. One of the conjectures pre- (this uses classical sieve theory). Goldston gave sented to the audience was that for any non-CM a three-hour lecture series at the workshop en- elliptic curve defined over the rationals, there titled Small Prime Gaps: From the Riemann Zeta are at most finitely many square-free integers d Function and Pair Correlation to the Circle Method, such that the quadratic twist Ed has rank larger in which he gave a broad perspective on such than 10! This talk inspired a lively discussion questions and indeed his own failed attempts between the participants, a perfect finale for a over the last fifteen years! It was a masterful ac- very successful week. The organizers hope that count of many related ideas and the develop- the participants went back home with new ques- ment of thought in the subject. 2. There are many tions, answers and directions for their research! famous questions on the distribution of divisors of integers, a subject that long intrigued Paul Erd˝os. Workshop The question of how often an integer has a pair Anatomy of Integers of divisors a and b with a < b < 2a has not March 13 – 17, 2006, CRM been well understood until the recent publica- Organizers: Jean-Marie De Koninck (Laval), tion of a highly insightful paper by Kevin Ford. Andrew Granville (Montréal) Professor Ford gave a three lecture series on his Speakers: Antal Balog (Rényi Institute), work, in which he resolves several conjectures William Banks (Missouri), Valentin Blomer of Erd˝os,and indeed his work makes it neces- (Toronto), Régis de la Bretèche (Paris-Sud), Jan sary to rewrite what are the main questions to Cannizzo (Stevens Institute), Ernest S. Croot be studied in this area. Most intriguing perhaps (Georgia Tech), Cécile Dartyge (Nancy 1), Kevin is how Ford converts the problem into ques- Ford (Illinois at Urbana-Champaign), John tions about random walks and answers ques- Friedlander (Toronto), Gagan Garg (Indian Insti- tions very similar to some of those that appear tute of Science), Dan Goldston (San Jose State), in recent developments of percolation theory. Andrew Granville (Montréal), Harald Andres Aisenstadt lecturer Soundararajan gave two lec- Helfgott (Montréal), Rizwan Khan (Michigan), tures on some of his exciting recent results. In Sergei Konyagin (Moscow State), Youness Lam- the first lecture he spoke on his improvement zouri (Montréal), Yu-Ru Liu (Waterloo), Flo- (with Granville) of the Polya – Vinogradov in- rian Luca (UNAM), Greg Martin (UBC), Ariane equality, and in the second, on his work with La- Masuda (Carleton), Elie Mosaki (Lyon 1), Jean- garias on smooth solutions to a + b = c. This Louis Nicolas (Lyon 1), Paul Pollack (Princeton), result was improved (during the meeting) by Carl Pomerance (Dartmouth), K. Soundarara-

18 THEMATIC PROGRAM

Soundararajan, working with Konyagin. Konya- fields,” and Masuda to find “consecutive smooth gin was also inspired to improve a long stand- polynomials over a finite field.” ing result on finding as many solutions as possible to a + b = c in S-units, giving examples √ School S (|S|2− 2) of sets with more than exp solutions CRM – Clay School on Additive Combina- (c|S|) (Evertse’s upper bound is exp ). torics Other principal lecturers included Carl Pomer- March 30 – April 5, 2006, CRM ance, who gave a beautiful historical survey on Sponsored by the Clay Foundation, CRM, the anatomy of Euler’s function and its friends; NSERC, NSF, FQRNT and DIMATIA (Czech Re- Harald Helfgott, who spoke on his spectacular public) recent work on bounding the number of primes p for which f (p) is a kth power; Ernie Croot, Organizers: Jozsef Solymosi (UBC), Andrew who spoke on his joint work with Granville and Granville (Montréal), David Ellwood (Clay) Tetali to give very good bounds on the run- Introductory lecturers: Jozsef Solymosi (UBC), ning time of the “matrix part” of the quadratic Andrew Granville (Montréal) sieve factoring algorithm, and to understand the Key lecturers: Ben Green (Bristol), Bryna Kra anatomy of the integers that make up the square (Northwestern), Terence Tao (UCLA), Van H. Vu in that part of the algorithm. Jean-Louis Nico- (Rutgers) las gave a lovely survey entitled Parity of the val- Guest lecturers: Antal Balog (Rényi Institute), ues of the partition function and anatomy of integers, Gregory Freiman (Tel Aviv), Imre Ruzsa (Rényi and Jie Wu a survey entitled Moyennes de cer- Institute), Endre Szemerédi (Rutgers & Rényi In- taines fonctions arithmétiques sur les entiers friables stitute) (which described mostly joint work with Tenen- Number of participants: 118 baum). Finally, Régis de la Bretèche gave a beau- The school started with two introductory mini- tiful survey on his important work with Tenen- courses to prepare the students for the main baum (A Turan– Kubilius inequality for friable inte- lecture series, given by Andrew Granville and gers, with applications). Jozsef Solymosi. Jozsef Solymosi gave an intro- There were also some outstanding shorter talks duction to Hungarian style combinatorial geom- including a talk on smooth twins by Antal Balog, etry, and in particular the connection with Roth’s a talk on sums of smooth squares by Valentin theorem and related results. Andrew Granville Blomer, and a talk on smooth numbers and the developed a historical view of combinatorial circle method by Trevor Wooley. John Friedlan- number theory, then gave complete proofs of der outlined his work on a polynomial divisor the Freiman – Ruzsa structure theorem, and of problem with Iwaniec. Cam Stewart presented Roth’s theorem in the spirit of Gowers. his surprisingly strong theorems on pure powers The mini-courses were followed by the lecture in short intervals. Cécile Dartyge outlined her re- courses, that occupied the bulk of the week. In search with Tenenbaum in a talk entitled Congru- his lecture series Quadratic Fourier analysis, Ben ences for the sum of digits of polynomial values. Greg Green explained beautifully the essential ideas Martin presented his results and conjectures on that go into the new multi-dimensional Fourier smooth values of polynomials. analysis by expounding on the simplest new Two fantastic new results were discussed: Yu- case, quadratic Fourier analysis. The key idea Ru Liu made quite a stir by proving the Erd˝os– is to break functions up into a part that reflects Pomerance’s conjecture for the Carlitz module, structure and a part that reflects random be- and Sergei Konyagin discussed his breathrough haviour, something that can now be done very on covering congruences in Sieving by large mod- efficiently. Bryna Kra gave the audience insights uli (obtained in collaboration with Filaseta, Ford, into ergodic methods in combinatorial number Pomerance and Gang Yu). There were several theory. Starting with a detailed explanation of talks by graduate students, two of the most excit- Furstenberg’s key ideas for proving Szemerédi’s ing being given by Paul Pollack and Ariane Ma- theorem, she showed how research in ergodic suda. They were both intrigued by Chris Hall’s theory is developing today (as in her work with very simple proof that there are infinitely many Host), and especially how it is affecting the de- pairs of irreducible polynomials { f , f + 1} in velopment of methods in combinatorial enumer- any given finite field. Pollack generalized this to ation and in modern harmonic analysis. prove a “weak prime k-tuples conjecture in finite Terence Tao has been fascinated by the three existing proofs of Szemerédi’s theorem: a proof

19 CENTRE DE RECHERCHES MATHÉMATIQUES by combinatorial graph theory (Szemerédi), one Workshop by ergodic theory (Furstenberg) and one by Additive Combinatorics Fourier analysis (Gowers); and by various new April 6 – 12, 2006, CRM proofs and combinations and developments of Sponsored by the Clay Foundation, CRM, the above. In Combinatorial and ergodic techniques NSERC, NSF and DIMATIA (Czech Republic) for proving Szemerédi-type theorems, Tao pulled Organizers: Jozsef Solymosi (UBC), Andrew together these various strands and explained Granville (Montréal) beautifully the analogies between the different Plenary lecturers: Jean Bourgain (IAS), Mei- approaches. Most lovely was his development Chu Chang (UC Riverside), Timothy Gowers of an analytic analogy to the Ruzsa – Szemerédi (Cambridge), Harald Helfgott (Montréal), Ben triangle removal lemma. Van Vu, in Structure of Green (Bristol), Imre Ruzsa (Rényi Institute), sumsets and applications, gave details of the proof Terence Tao (UCLA), Tamar Ziegler (IAS) of his result with Szemerédi on the existence of Speakers: Daniel Berend (Ben Gurion), Manjul long arithmetic progressions in sumsets; they re- Bhargava (Princeton), Gautami Bhowmik (Lille cently obtained the best possible results, conjec- 1), Javier Cilleruelo (Universidad Autónoma tured by Erd˝os. de Madrid), David Conlon (Cambridge), Ernie The four principal lecturers were absolutely ter- Croot (Georgia Tech), Jean-Marc Deshouillers rific. Each had given tremendous thought to his (Bordeaux), Gy˝orgy Elekes (E˝otv˝os Loránd), or her talks, and all are excellent lecturers. On Christian Elsholtz (Royal Holloway, University Saturday, Antal Balog gave a “special guest lec- of London), Jacob Fox (MIT), Nikos Frantzik- ture” on the Balog – Szemerédi – Gowers theo- inakis (Memphis), Alexey Glibichuk (Moscow rem, providing a complete proof. On several State), Ron Graham (UC san Diego), Lau- afternoons we had a discussion session at the rent Habsieger (Lyon 1), Alex Iosevich (Mis- end of the day, which provided the students souri), Koichi Kawada (Iwate), Sergei Konya- with the opportunity to ask questions about the gin (Moscow State), Bryna Kra (Northwestern), points they had not understood. On Monday Michael Lacey (Georgia Tech), Vsevolod Lev evening Terry Tao gave his Aisenstadt Lecture, (Haifa at Oranim), Akos Magyar (Georgia), Ram Long arithmetic progressions in the primes, to a Murty (Queen’s), Melvyn Nathanson (CUNY packed room. Lehman College), Jaroslav Nešetˇril (Charles, On the final day, the three senior mathematicians Prague), Gyan Prakash (Harish-Chandra In- who did the most to create this field were invited stitute), Vidhu Prasad (UMass Lowell), Maria to give presentations. The students found this a Roginskaya (Chalmers University of Technol- very exciting event to wrap up the school and, ogy), Tom Sanders (Cambridge), Ilya Shkredov indeed, these “celebrities” were given an ova- (Moscow State), Yonutz Stanchescu (The Open tion before and after their lectures! Imre Ruzsa University of Israel), Balázs Szegedy (Toronto), gave a beautiful presentation of consequences Sanju Velani (York, England), Trevor Wooley of Plunnecke’s theorem, as well as his recent (Michigan) thoughts on non-abelian analogues. Endre Sze- Number of participants: 145 merédi gave a proof of Roth’s theorem he first The Workshop on Additive Combinatorics was developed twenty-five years ago but never pub- attended by 145 participants from about 30 lished. Finally, Gregory Freiman gave a lecture countries. The meeting was a high profile event entitled Inverse additive number theory: results and with many of the world’s leading analysts par- problems. The school ended up with a panel dis- ticipating, including Jean Bourgain, Tim Gow- cussion involving all of the speakers, and spec- ers, Terence Tao, Ben Green and Sergei Konya- ulation as to what is the best possible form of gin. This reflected the great interest in the meet- Roth’s theorem. ing, the third ever in the subject. The plenary lec- The overall atmosphere at the meeting was su- turers were Terence Tao, Harald Helfgott, Jean perb, because of the remarkable quality of the Bourgain, Mei-Chu Chang, Tamar Ziegler, Ben lecturing and the lecturers’ desire to be available Green, Timothy Gowers and Imre Ruzsa. Ter- to the students. ence Tao gave a talk entitled An infinitary approach to (hyper)graph regularity and removal, in which he explained how he uses the constructions of ergodic theory to avoid complicated estimates yet obtains explicit results.

20 THEMATIC PROGRAM

Harald Helfgott discussed his surprising his new fundamental results on sumsets, partic- breakthrough on growth and generation in ularly in the non-abelian setting, for bounds on SL2(Z/pZ). In Sum-product and expanders, Jean the size of A + B + C. Bourgain discussed his work with Gamburd There were many other exciting talks, which and Sarnak extending Helfgott’s result to other we cannot all mention here. For instance, Sergei groups, and then some stunning consequences Konyagin gave new results on the additive prop- of this work, particularly with reference to cer- erties of product sets in fields of prime order. Af- tain sieve questions. Jean Bourgain gave a sec- ter his lecture, Harald Helfgott made a few ob- ond plenary talk, More applications of the sum- servations that allowed Konyagin to prove the product theorem and the quantum cat map, in which remaining major conjectures in this area! Gy˝orgy he solves a well-known question of Kurlberg Elekes discussed his recent work with Ruzsa (On and Rudnick. Then Mei-Chu Chang gave more the structure of sets with many ‘medium-size’ arith- details of her work with Bourgain in a talk enti- metic progressions). After the lecture, Andrew tled Sum-product theorems, exponential sum bounds Granville pointed out that this should easily lead and applications, describing results that are hav- to a general structure theorem for almost all ing an enormous impact on analytic number the- arithmetic progressions inside a set. One of the ory. most extraordinary talks was by Balázs Szegedy, Tamar Ziegler proved a wonderful old conjec- who, in joint work with László Lovász, has been ture of Erd˝osby ergodic theory methods in Con- developing a theory of “graph limits,” allowing figurations in sets of positive upper density in Rm. them to prove many of the deep theorems of One of the key difficulties in Gowers’ norms is Szemerédi, Ruzsa and others by passing to lim- understanding the structures on which they take its and applying topological techniques to such large values. At this stage of development of the graph sets. This work comes close to some the subject, it seems vital to give a more accessible ideas of Tao. description that can be useful for Fourier ana- There were also several lectures on Ramsey the- lysts, and this was the focus of Bryna Kra in Gow- ory, which is an important and related subject. ers norms in ergodic theory and additive combina- We heard Ron Graham speak on some of his torics. In Linear equations in primes, Ben Green dis- favorite Ramsey theory problems and Jaroslav cussed his latest work with Terence Tao, where Nešetˇrilgive a broad survey on Ramsey classes they try to generalize their methods as much as of finite structure. A graduate student, David possible in the direction of the prime k-tuples Conlon, has made an enormous advance re- conjecture. In particular they outlined plans to ported in New upper bounds for Ramsey num- show that for any admissible set of k linear bers, the biggest increase in the bounds since the forms, no two of which are linearly dependent 1930s! An undergraduate student, Jacob Fox, de- over the integers, there are infinitely many inte- scribed his many beautiful contributions to infi- ger values for the variables such that the forms nite Ramsey theory in Partition regularity of lin- all simultaneously take on prime values. ear equations, in which many answers depend on One key issue in understanding Szemerédi’s which axioms of arithmetic one assumes! theorem completely is to understand circum- stances in which one has significantly fewer Workshop arithmetic progressions of length 4 than ex- Analytic Methods for Diophantine Equa- pected, in spite of the fact that all of the tions Fourier coefficients are small. Timothy Gowers May 13 – 18, 2006, Banff International Research described his new elegant construction in A uni- Station form set with few progressions of length 4. Gowers Organized jointly with MSRI norms have proved very fruitful in the hands of the analysts and they affect the more classi- Organizers: Andrew Granville (Montréal), Yuri cal methods of analytic number theory in very Tschinkel (Göttingen), Michael Bennett (UBC), interesting ways. Trevor Wooley and Antal Ba- Chantal David (Concordia), Bill Duke (UCLA) log have been developing variants of the circle Speakers: Arthur Baragar (Nevada), Valentin method after the work of Gowers (this is the title Blomer (Toronto), Régis de la Bretèche (Paris- of their talk!), and explained how one can now Sud), Tim Browning (Bristol), Jean-Louis do much better in the key Diophantine questions Colliott-Thélène (Paris-Sud), Pietro Corvaja in the circle method. The final plenary talk, by (Udine), Ulrich Derenthal (Göttingen), Noam Imre Ruzsa, entitled 2A and 3A, gave details of Elkies (Harvard), Jordan Ellenberg (Wisconsin- Madison), Andrew Granville (Montréal), Roger

21 CENTRE DE RECHERCHES MATHÉMATIQUES

Heath-Brown (Oxford), Harald Helfgott (Mont- faces we heard an explanation of a basic exam- réal), Noriko Hirata-Kohno (Nihon), Patrick In- ple by Michael Joyce and saw a representation gram (UBC), Michael Joyce (Tulane), Hershy theoretic approach to universal torsors by Alexei Kisilevsky (Concordia), Aaron Levin (Brown), Skorobogatov, and a direct approach to these tor- Preda Mihailescu (Göttingen), Per Salberger sors by Ulrich Derenthal. (Chalmers University of Technology), Alexei Among new results was one announced by Skorobogatov (Imperial College), Ramin Takloo- Régis de la Bretèche who showed that a specific Bighash (Princeton), Jeff Thunder (Northern Illi- height zeta function (for a toric cubic surface) nois), Yuri Tschinkel (Göttingen), Ronald von cannot be analytically continued to the whole Luijk (UC Berkeley), Trevor Wooley (Michigan) complex plane (it has a natural boundary), so Number of participants: 39 that the “Riemann Hypothesis” is not even a Some of the oldest questions in mathematics sensible question in general. To count points on stem from the desire to find integer solutions to higher dimensional varieties one can also pro- equations. From the equation in Pythagoras’ the- ceed by the classical circle method. Roger Heath- orem to Fermat’s last theorem, Waring’s prob- Brown told us about his recent major break- lem, the abc-conjecture and Manin’s conjecture, through for counting points on cubic hypersur- professional and amateur mathematicians alike faces (reducing the number of variables in Dav- are thrilled in trying to prove that there are no enport’s famous result). The extension to quar- solutions, or to determine solutions, or to count tic varieties was discussed by Tim Browning. solutions. With such a venerable topic it is not Trevor Wooley explained his idea to prove that surprising that there are many competing ap- the local-global principle works almost always proaches to such questions, some whose time and discussed what he has shown to date. has already come, some that are very hot meth- Noam Elkies showed how root numbers in ods right now, and some whose time is yet to families of elliptic curves, in combination with come. At this meeting at BIRS there were par- heuristics, could be used to predict surpris- ticipants from many of the different schools of ing behavior regarding uniform boundedness of thought in this fascinating subject; it was an in- ranks of elliptic curves over number fields, and teresting opportunity for them to come together to contradict a well-known conjecture on the and find common ground. topology of rational points. Andrew Granville During the last academic year two of the explained his new conjectures on the distribu- world’s major research institutes, the CRM and tion of rational and integral points on curves the Mathematical Sciences Research Institute and specifically how they have an impact in a (MSRI) in Berkeley, have hosted semester long provocative way on the question of the ranks programs on different aspects of these questions. of elliptic curves. Aaron Levin developed tech- It was decided to get together at the end of the niques of Vojta to bound the number of ratio- academic year for a joint meeting, to discuss is- nal points on curves of genus 1 over fields of sues that arose at the thematic programs of both bounded degree; and Jordan Ellenberg gave im- institutes. Thus the participants were primarily pressive new upper bounds, from his work with people who had attended one special year or Akshay Venkatesh, on the heights of points of the other, though perhaps a third were other re- curves of genus 1, breaking through what had searchers who are expert in Diophantine equa- seemed to be a difficult barrier from the work of tions. Heath-Brown. Perhaps the most consistent theme of this meet- There were also several talks on related ques- ing was the topic of counting points on higher tions. Noriko Hirata-Kohno improved Evertse’s dimensional varieties, particularly Manin’s con- theorem by giving good bounds on the total jecture. We heard a highly motivating survey by number of solutions of certain Fermat-type Dio- Yuri Tschinkel, exciting new research from a ge- phantine equations. Preda Mihailescu showed ometric perspective by Per Salberger, from a per- that techniques in the theory of cyclotomic spective of automorphic forms by Ramin Takloo- fields could be used to bound the solutions Bighash and from a perspective closer to Dio- of certain Ljunggren – Nagell type equations. phantine approximations by Jeff Thunder. There Valentin Blomer improved the error term in the were exciting and controversial new perspec- known approximations for representations by tives on Manin’s conjecture on K3 surfaces from ternary quadratic forms using his recent work Arthur Baragar and Ronald von Luijk. To un- on convexity-breaking. Pietro Corvaja explained derstand Manin’s conjecture on del Pezzo sur- how to show that there are large prime fac-

22 THEMATIC PROGRAM tors of any Markov pair and Patrick Ingram points. Finally Harald Helfgott conjectured that showed that multiples of integral points on ellip- the only extreme examples in the large sieve are tic curves cannot themselves be integral, except the images of points from a ﬁnite set of curves, in certain obvious cases. and indicated how he proved this in two dimen- Jean-Louis Colliott-Thélène presented an extensions (with Akshay Venkatesh). sion of the Brauer – Manin obstruction to in- All participants seemed to have greatly enjoyed tegral points (instead of rational points), and the meeting. It was an interesting “coming to- showed how it explained recent results on inte- gether” of different approaches to important gral quadratic forms. Hershy Kisilevsky showed questions, and most speakers tried to be acces- how points on cubic twists give rise to points on sible, so a lot was learned. Several new collab- certain K3 surfaces; combining this with work orations were formed during the meeting; some of the Dokshitzers one discovers surprising fam- results were even proved while in Banff. ilies of surfaces which must contain rational

Past Thematic Programs

The Centre de recherches mathématiques has 1998 – 1999 Number Theory and Arithmetic Ge- organized thematic activities every year since ometry 1993. From 1987 to 1992, the CRM organized 1997 – 1998 Statistics various types of activities, including special 1996 – 1997 Combinatorics and Group Theory semesters, concentration periods and thematic 1995 – 1996 Applied and Numerical Analysis activities. Here is a list of the main activities or- 1994 – 1995 Geometry and Topology ganized by the CRM since 1987. 1993 – 1994 Dynamical Systems and Applica- Here follows a list of thematic activities orga- tions nized by CRM since 1987: 1992 Probability and Stochastic Control (Special Semester) 2004 – 2005 The Mathematics of Stochastic and 1991 – 1992 Automorphic Forms in Number Multiscale Modeling Theory 2003 – 2004 Geometric and Spectral Analysis 1991 Operator Algebras (Special Semester) 2002 – 2003 Math in Computer Science 1990 Nonlinear PDEs and Applications 2001 – 2002 Groups and Geometry (Focal Period) 2000 – 2001 Mathematical Methods in Biology 1988 Shimura Varieties (Special Semester) and Medicine 1987 Quantum Field Theory (Special Semester) 1999 – 2000 Mathematical Physics 1987 – 1988 Fractals: Theory and application 1987 Structural Rigidity (Special Semester)

23 General Program GENERAL PROGRAM

HE CRM’s general program funds a wide variety of scientiﬁc events, both on the premises of the TCRM and elsewhere in Canada. Whether it be for specialized workshops attended by a small number of researchers or large meetings attended by hundreds of participants, the general program promotes research in the mathematical sciences at all levels. The program is quite ﬂexible, allowing projects to be considered as they arise. The reports are presented in the language in which they were submitted.

CRM activities

Short Program on Random Matrices, Ran- sociated to studies of matrix models are certain dom Processes and Integrable Systems stochastic processes, the “Dyson processes,” and June 20 – July 8, 2005, CRM their continuum limits, which are related to the Organized by CIRGET and the Mathematical spectra of random matrix ensembles, and may Physics Laboratory also be studied by related methods. Organizers: John Harnad (Concordia), Jacques Besides the well-known physical applications Hurtubise (McGill) of random matrix theory, such as the Wigner – Lecture series speakers: Mark Adler (Bran- Dyson statistical approach to the distribution of deis), Pavel Bleher (IUPU Indianapolis), high-lying resonances of large nuclei, and the Bertrand Eynard (CEA, Saclay), Alexander Its more recent applications to string theory and (IUPU Indianapolis), Ken McLaughlin (Ari- two-dimensional quantum gravity, there exist zona), Craig Tracy (UC Davis), Pierre van Moer- further new applications under current study, beke (Louvain & Brandeis), Harold Widom (UC such as the computation of correlation functions Santa Cruz) in supersymmetric Yang – Mills theory, and the Workshop speakers: Marco Bertola (Concor- regularization of the Laplacian growth problem dia), Brian Conrey (American Institute of Math- of two-dimensional fluid dynamics. Correlation ematics), Percy Deift (Courant), Philippe di functions between eigenvalues of random ma- Francesco (CEA, Saclay), Sam Howison (Ox- trices also have close similarities to those in in- ford), Vladimir Kazakov (ENS, Paris), Dmitri tegrable quantum spin systems and many-body Korotkin (Concordia), Arno Kuijlaars (Leu- models. There are further remarkable connec- ven), Andrei Okounkov (Princeton), Alexander tions to a variety of probabilistic problems such Orlov (Oceanology Institute, Moscow), Alexan- as random words, tilings and partitions, as well der Soshnikov (UC Davis), Nina Smith (Bristol), as to the statistical distribution of zeros of L- Anton Zabrodin (ITEP, Moscow), Ofer Zeitouni functions. (Minnesota & Technion), Paul Zinn-Justin (Paris- The program provided an opportunity for pro- Sud), Jean-Bernard Zuber (CEA, Saclay) ductive interactions, bringing together top ex- Number of participants: 71 perts and younger researchers beginning work This program tried to emphasize the remarkable in this area The schedule consisted of two parts. connections between two domains that a pri- There were eight extended lecture series on re- ori seem unrelated: random matrices (together lated topics, each of one week’s duration, having with associated random processes) and inte- a survey and pedagogical character and aimed grable systems. The relations between random primarily at younger researchers entering the matrix models and the theory of classical inte- field. The afternoon sessions were of “work- grable systems have long been studied. These shop” character, with one-hour talks presented appear mainly in the deformation theory, when on current work in the field, and contributed parameters characterizing the measures or the talks on topics closely related to the theme of the domain of localization of the eigenvalues are program. Roughly half the participants were ei- varied. The resulting differential equations de- ther young researchers, postdoctoral fellows or termining the partition function and correlation advanced graduate students, and most of these functions are, remarkably, of the same type as received partial financing to help cover their certain equations appearing in the theory of in- travel and/or accommodation expenses. tegrable systems. They may be analyzed effec- The main topics covered were the following: tively through methods based upon the Rie- spectral theory of random matrices; determinan- mann – Hilbert problem of analytic function the- tal ensembles; integral operators in random ma- ory and by approaches related to the study of trix theory; Dyson processes and Airy, Bessel, nonlinear asymptotics in the large N limit. As- sine and Laguerre processes; matrix Riemann-

25 CENTRE DE RECHERCHES MATHÉMATIQUES

Hilbert methods and applications to large N and covered vast areas of pure and applied asymptotics; differential equations for gap dis- mathematics. The conference opened, on Mon- tributions and transition probabilities; relations day morning, with talks by Barry Simon and his to integrable systems and isomonodromic defor- graduate student M. Stoiciu on closely related mations; growth processes and applications to matters concerning the structure of zeros of or- fluid dynamics and crystal growth; applications thogonal polynomials. In particular, M. Stoiciu to random tilings, random words and random talked about the orthogonal polynomial analog partitions; applications to L-functions; applica- of Molchanov’s celebrated result on Poissonian tions to multivariate statistics. The lecture series statistics of eigenvalues. Two long-term collab- part of this program will be published in the orators of Stas, W. Gärtner and W. König, then Springer CRM Series in Mathematical Physics, and gave talks on the parabolic Anderson model. the workshop proceedings will be published as In the afternoon, A. Klein and F. Germinet re- a refereed Special Issue of the Journal of Physics ported on new and truly spectacular results in A: Mathematical and General (Volume 39, Number the spectral theory of random Schrödinger oper- 14, July 2006). ators, while Y. Last gave a beautiful review of the structural properties of Anderson type Hamilto- Probability and Mathematical Physics — nians. The final talk was by A. Soshnikov, whose A Conference in Honor of Stanislav career began in Moscow under Molchanov’s su- Molchanov’s 65th Birthday pervision. June 27 – July 1, 2005, CRM On the second day, spectral theory, group theory Organized by the Mathematical Analysis Labo- and combinatorics were discussed in the morn- ratory ing (A. Laptev, P. Kuchment, R. Grigorchuk, N. Minami), while the afternoon was devoted to Organizers: Don Dawson (Carleton & McGill), financial (R. Carmona) and applied mathemat- Vojkan Jaksic (McGill), Boris Vainberg (UNC ics (A. Kiselev, M. Freidlin), as well as proba- Charlotte) bilistic interacting particle systems (A. Ramirez). Speakers: Leonid Bogachev (Leeds), Rene Car- The talks of Wednesday morning were focused mona (Princeton), K. Chen (UNC Charlotte), on statistical mechanics (A. Figotin, B. Vainberg, Gregory Derfel (Ben Gurion), Alexander Fig- L. Koralov), and the last talk (G. Derfel) dealt otin (UC Irvine), Mark Freidlin (Maryland), Jür- with the asymptotics of the Poincaré functions. gen Gärtner (Berlin), François Germinet (Cergy- On Thursday morning, I. Goldsheid reported Pontoise), Y. Godin (UNC Charlotte), Ilya Gold- on spectacular new results concerning Liapunov sheid (London), Alexander Gordon (Rochester), exponents, S. Warzel presented a new proof of Rostislav Grigorchuk (Texas A&M), J. Holt the celebrated result of Klein on extended states (UNC Charlotte), Dirk Hundertmark (Illinois for the Anderson model on the Bethe lattice, and at Urbana-Champaign), Kostya Khanin (Heriot- K. Khanin dealt with random walks in a quasi- Watt), Werner Kirsch (Ruhr), Alex Kiselev stationary random potential. The first two talks (Wisconsin-Madison), Abel Klein (UC Irvine), in the afternoon were “random”: Y. Godin dis- Frédéric Klopp (Paris 13), Wolfgang König cussed the random string and L. Bogachev, a (Leipzig), Leonid Koralov (Princeton), Peter former student of Molchanov, the random expo- Kuchment (Texas A&M), Ari Laptev (Royal In- nentials. In the afternoon, P. Müller reported on stitute of Technology, Stockholm), Yoram Last new results concerning spectral asymptotics of (Hebrew), N. Minami (Japan), Peter Müller (Göt- Laplacians on bond-percolation graphs. In the fi- tingen), P. Poulin (McGill), Joan Quinn (Queens nal talk, A. Gordon, another former student of College, North Carolina), Alejandro Ramirez Molchanov, discussed the Cantor spectrum for (Pontificia Universidad Católica de Chile), Barry almost periodic one-dimensional Schrödinger Simon (Caltech), Alexander Soshnikov (UC operators. Davis), Thomas Spencer (IAS), Mihai Stoiciu (Caltech) On the morning of the last day, F. Klopp talked Number of participants: 47 about the exponential sums related to the Kro- nig – Penney model in a constant electric field, This conference was in honor of Stanislav while D. Hundertmark discussed bounds on the Molchanov (North Carolina at Charlotte), a lead- spectral shift functions. W. Kirsch then gave a ing probabilist and mathematical physicist who very intriguing talk entitled The draft constitution turned 65 in 2005. The topics discussed at the of the EU, the Electoral College and spin systems. Fi- conference were closely related to the research nally, J. Quinn, a close collaborator of Stas, dis- interests (past and present) of Stas Molchanov

26 GENERAL PROGRAM cussed random generators and various tests for The Strings 2005 conference was held as the randomness with roots in quantum mechanics. culmination of the activities organized for the The afternoon talks were given by graduate stu- theme year, The Geometry of String Theory, which dents (K. Chen, J. Holt and P. Poulin). The pro- is being hosted jointly by the Fields Institute ceedings of the conference will be published in and the Perimeter Institute (in Waterloo). The the CRM/AMS Proceedings and Lecture Notes. “Strings” conferences are the premiere international conference series in the field of string the- Strings05 ory. Every year, it brings together leading re- July 11 – 16, 2005, University of Toronto searchers from around the world to discuss the Sponsors: Fields Institute, Perimeter Institute, latest developments in string theory. Strings05 Pacific Institute of Theoretical Physics, CRM, brought roughly 440 researchers to the first such Canadian Institute for Advanced Research, conference to be held in Canada. The meeting Canadian Institute for Theoretical Astrophysics, took place in the Medical Sciences building at Institute of Particle Physics, PIMS the University of Toronto from July 11 to 16, Organizers: Alex Buchel (Perimeter & West- 2005. ern Ontario), Jaume Gomis (Perimeter), Kentaro As is traditional with the “Strings” meetings, Hori (Toronto), Robert Myers (Perimeter & Wa- the bulk of the conference was devoted to in- terloo), Amanda Peet (Toronto) vited talks highlighting recent progress in the Speakers: Nima Arkani-Hamed (Harvard), Vi- field and charting out new directions. A sam- jay Balasubramanian (Pennsylania), Melanie pling of topics includes: new developments in Becker (Maryland), Niklas Beisert (Princeton), the microscopic description of black hole en- Iosif Bena (UCLA), Dick Bond (CITA & Toronto), tropy, understanding physics on the string the- Raphael Bousso (UC Berkeley), Freddy Cac- ory landscape, a possible holographic descrip- hazo (Perimeter), Atish Dabholkar (Tata Insti- tion of the quark-gluon plasma, and supersym- tute), Frederik Denef (Rutgers), Robbert Dijk- metry breaking in type IIB flux compactifica- graaf (Amsterdam), Michael Dine (Santa Cruz tions. The range of speakers was very broad, Institute for Particle Physics), Michael Dou- extending from established luminaries, such as glas (IHES and Rutgers), Henriette Elvang Renata Kallosh, Ashoke Sen and Ed Witten, to (UC Santa Barbara), Sergey Frolov (Max- new upcoming postdocs and graduate students Planck-Institut fur Gravitationsphysik & Albert- The latter would include: Henriette Elvang, who Einstein-Institut), Amihay Hanany (MIT), Petr is just finishing her PhD at UCSB; Vyacheslav Horava (UC Berkeley & LBNL), Gary Horowitz Rychkov, in his first postdoc at Amsterdam; and (UC Santa Barbara), Anton Kapustin (Cal- Andrei Starinets, a postdoc at Perimeter. tech), Shamit Kachru (SLAC, Stanford), Renata The organizers experimented with several in- Kallosh (Stanford), Per Kraus (UCLA), Mar- novations, which gave the conference a unique tin Kruczenski (Brandeis), Hong Liu (MIT), Canadian flavour. Four of the morning ses- Oleg Lunin (IAS), Juan Maldacena (IAS), sions began with hour-long review talks, includ- Dario Martelli (CERN), Hirosi Ooguri (Cal- ing: Topological string theory by Hirosi Ooguri tech), Joseph Polchinski (UC Santa Barbara), (Caltech); Constructions and distributions of string Fernando Quevedo (Cambridge), Albert de vacua by Frederik Denef (Rutgers); Applying in- Roeck (CERN), Vyacheslav Rychkov (ITFA, Am- tegrability in AdS and CFT by Niklas Beisert sterdam), Nathan Seiberg (IAS), Ashoke Sen (Princeton); Recent progress in perturbative gauge (Harish-Chandra Institute), Steve Shenker (Stan- theories by Freddy Cachazo (Perimeter). These ford), Eva Silverstein (SLAC, Stanford), An- early morning reviews were skillfully presented, drei Starinets (Perimeter), Andrew Strominger providing a streamlined, incisive summary of (Harvard), Shigeki Sugimoto (Yukawa Insti- the exciting developments achieved in these tute for Theoretical Physics, Kyoto), Lennie subjects over the past couple of years. Susskind (Stanford), Tadashi Takayanagi (Har- vard), Alessandro Tomasiello (ITP, Stanford), Another innovation was to finish three of the Henry Tye (Cornell), Angel Uranga (Universi- days with a talk from one of the “affiliated” ar- dad Autónoma de Madrid), Erik Verlinde (ITFA, eas; that is, other subject areas which are of di- Amsterdam), Bernard de Wit (Institute for The- rect interest to string theory or areas with which oretical Physics and Spinoza Institute, Utrecht), string theory hopes to make contact. Dick Bond Edward Witten (IAS), Shing-Tung Yau (Har- began the week with a review of the status vard), Barton Zwiebach (MIT) of experimental cosmology and the prospects Number of participants: 419 for measuring the fundamental cosmological pa-

27 CENTRE DE RECHERCHES MATHÉMATIQUES rameters that string theory will have to predict. string theory research in Canada. The talks and On Tuesday, Nima Arkani-Hamed gave us his activities of the conference are recorded at the vision of how particle theory will advance in the Strings05 website: www.fields.utoronto.ca/ next decade with the advent of new data from programs/scientific/04-05/string-theory/ the Large Hadron Collider (LHC) at the CERN strings2005. The organizing committee would laboratory in Geneva. Hopefully these experi- like to thank Alison Conway, Fields’ Program ments will reveal Nature’s choice for the physics Director, for her calm guidance and continued at the so-called “electroweak scale.” Finally on efforts over the past year to ensure the great suc- Friday, Albert de Roeck, a CERN experimental- cess of the meeting. ist, gave his perspective on the challenges and opportunities that lie ahead at the LHC. Mini-workshop on Computational Aspects Our conference marked the tenth anniversary of of Dynamical Systems the now famous Strings 1995 conference, held July 15, 2005, Concordia at the University of Southern California, which Organized by the Applied Mathematics Labora- marked the beginning of what is now com- tory monly known as the “Second Superstring Revo- Organizer: Sebius Doedel (Concordia) lution.” This anniversary was an opportunity to Speakers: Michael Henderson (IBM T.J. Wat- reflect back on the unanswered questions from son Research Center), Tony Humphries (McGill), the previous decade, and to discuss the future Bernd Krauskopf (Bristol), Hinke Osinga (Bris- prospects for connections between string theory tol), Randy Paffenroth (Caltech) and the next set of exciting experiments. The fo- Number of participants: 15 rum was a panel discussion entitled The Next Superstring Revolution, masterfully led by Steve A “mini-workshop” on Computational Aspects Shenker. The panel was composed of eight lead- of Dynamical Systems was held on July 15, 2005, ing figures in the field: Raphael Bousso, Shamit in the new Engineering and Visual Arts Build- Kachru, Ashoke Sen, Juan Maldacena, Andrew ing of Concordia University. This workshop was Strominger, Joseph Polchinski, Eva Silverstein attended by members of the Applied Mathemat- and Nathan Seiberg. ics Laboratory of the CRM and by graduate students from the Montréal universities. It was sim- A poster session was introduced to make the ilar in scope and format to the one held in 2004, meeting more inclusive and to allow as many in- and a third workshop is planned for the summer terested participants as possible to present their of 2006. The purpose of the workshop was to ex- research. As a result, over 50 posters were set change ideas on computational problems in the up during the week describing a wide variety of numerical study of dynamical systems that arise topics, from D-term Cosmic Strings from N = 2 in important practical applications. Another fo- Supergravity to Duality between Open Gromov – cus was the development and use of visualiza- Witten Invariants and Beilinson – Drinfeld Chiral tion techniques that help understand the com- Algebra. These were all viewed by a large num- plex data that arise from such advanced numer- ber of participants. The conference ended on a ical computations. high note. First the technical session was closed by Shing-Tung Yau with a seminar on Super- The speakers were: Bernd Krauskopf, who pre- string theory with torsion and an invitation to sented new results on bifurcations of mutually come to Beijing for Strings06. delay-coupled lasers; Tony Humphries, who described computational and analytic challenges The final session consisted of two public lec- in the analysis of travelling waves in lattice tures by international superstars in string the- differential equations near propagation failure; ory, on Saturday afternoon. First, Robbert Dijk- Hinke Osinga, who demonstrated how bound- graaf spoke on Strings, black holes, and the end ary value techniques allow the computation of of space and time. This was followed by Lennie one-dimensional manifolds of Poincaré maps in Susskind with Cosmic landscape: string theory and slow-fast systems (where standard techniques the illusion of intelligent design. These master- fail); Michael Henderson, who presented a novel ful lecturers led the capacity audience of over topological approach to computing multidimen- 500 on two engaging tours of mind-bending sional manifolds in dynamical systems, such as concepts like warped space-time, black holes, hyperbolic closed invariant manifolds, and, po- strings, the big bang and the ultimate fate of tentially, inertial manifolds; and Randy Paffen- the universe. Undoubtedly, Strings05 provided roth, who presented new, high-order methods an immense boost to the international profile of in computational electromagnetism, which have

28 GENERAL PROGRAM been implemented on a large-scale parallel com- de Luca (Naples), Juhani Karhumäki (Turku), puter at Caltech. Jean Néraud (Rouen) et Christophe Reutenauer (UQÀM, président du comité de programme). 5th International Conference on Words Une centaine de personnes ont participé au September 13 – 17, 2005, LaCIM (UQÀM) colloque, dont 83 régulièrement inscrites. Les participants sont venus du Canada, des États- Sponsors: CRM, Ministère de l’Éducation, du Unis, d’Italie, de France, de République tchèque, Loisir et du Sport du Québec, Faculté des Sci- de Lettonie, d’Australie, de Finlande et de Po- ences de l’UQÀM, PIMS, VSIS ConfTool, Chaire logne. Arturo Carpi, Maxime Crochemore, Mi- de recherche du Canada en algègre, combina- chel Mendès France, Antonio Restivo, Jeffrey toire et informatique mathématique, Café Rico Shallit et Denis Thérien (remplaçant Volker Die- (Montréal) kert) étaient les conférenciers invités. Organizers: Srecko Brlek (UQÀM), Cédric Dans sa conférence, Antonio Restivo a expli- Chauve (Simon Fraser & UQÀM), Annie Lacasse cité des liens entre la combinatoire des mots (UQÀM), André Lauzon (UQÀM), Geneviève pure et dure, et des applications à la compres- Paquin (UQÀM) sion de textes. De même, l’exposé de Michel Speakers: Boris Adamczewski (CNRS), Petr Mendès France, portant sur l’utilisation du pro- Ambroz (Czech Technical University), Peter cédé de diagonalisation de Cantor pour la dé- Balazi (Czech Technical University), Aleksan- ﬁnition de certains mots de dimension deux, drs Belovs (Latvia), Valérie Berthé (LIRMM a suscité de nombreuses questions de l’audi- & Montpellier), Jean-Pierre Borel (Limoges), toire. Il faut mentionner aussi le très clair ex- Arturo Carpi (Perugia), Julien Cassaigne posé d’Arturo Carpi, sur un sujet qui touche (CNRS), Maxime Crochemore (Marne-la-Vallée), de près de nombreux conférenciers : les répéti- Sébastien Simon Ferenczi (CNRS), Thomas Fer- tions dans les mots. L’exposé de Boris Adamc- nique (Montpellier 2), Wit Forys (Jagiellonian), zewski (sur des travaux effectués avec Jean-Paul Christiane Frougny (Paris 8), Amy Glen (Ade- Allouche) a montré les nombreuses interactions laide), Vesa Halava (Turku), Stepan Holub entre la combinatoire des mots, la transcendance (Charles, Prague), Lucian Ilie (Western Ontario), en théorie des nombres et l’approximation dio- Damien Jamet (Montpellier), Paolo Massazza phantienne par les fractions continues, reliées (Insubria), Michel Mendès France (Bordeaux à une conjecture de Littlewood. Jacques Saka- 1), Jean-Christophe Novelli (Marne-la-Vallée), rovitch a présenté ses travaux avec Christiane Pascal Ochem (Bordeaux 1), Maddalena Poneti Frougny et Shigeki Akiyama sur la représenta- (Firenze), Antonio Restivo (Palermo), Gwénaël tion des nombres réels en base 3/2 et Petr Am- Richomme (Picardie), Kalle Saari (Turku), Bruce broz a exposé ses travaux sur la représentation Sagan (Michigan State), Alessandra Savelli (Po- tau-adique des nombres réels. litecnico di Milano), Jeffrey Shallitt (Water- loo), Benjamin Steinberg (Carleton), Maurice L’exposé de Benjamin Steinberg avait pour su- H. ter Beek (ISTI-CNR, Italia), Denis Thérien jet le comptage des sous-mots, qui a été rap- (McGill), Vincent Vajnovszki (Bourgogne), Luca porté aux représentations triangulaires du mo- Q. Zamboni (North Texas) noïde libre (en collaboration avec Jorge Almeida, Number of participants: 83 Stuart Margolis et Mikhail Volkov). Les mots de dimension 2 ont été introduits par Valérie Ber- Le sujet du colloque Words’05 fut l’étude des thé (en collaboration avec Pierre Arnoux et Da- mots avec l’accent sur le point de vue théo- mien Jamet) pour l’approximation des surfaces, rique. En particulier les aspects combinatoires ainsi que par Thomas Fernique. Les substitu- algébriques et algorithmiques furent privilégiés. tions symboliques constituent un thème central Les motivations pouvaient provenir d’autres do- en combinatoire des mots, comme en font foi maines tels que l’informatique théorique. Ce col- l’exposé de Thomas Fernique et celui de Sébas- loque est le cinquième d’une série de colloques tien Ferenczi, de même que celui de Bruce Sagan sur les mêmes sujets ; les précédentes éditions (portant sur un travail avec Emeric Deutsch), ont eu lieu à Rouen en 1997 et 1999, à Palerme qui a donné des propriétés arithmétiques de la en 2001 et à Turku en 2003. Le colloque com- suite de Thue-Morse. Les mots sturmiens, leurs porta 6 conférences invitées et 28 communica- variantes et leurs généralisations sont un autre tions dûment arbitrées et sélectionnées par le thème central de la combinatoire des mots et comité de programme. Ce comité était formé sont apparus dans les exposés de Jean-Pierre Bo- de Jean Berstel (Marne-la-Vallée), James Cur- rel, Julien Cassaigne (en collaboration avec Anna rie (Winnipeg), Clelia De Felice (Salerno), Aldo

29 CENTRE DE RECHERCHES MATHÉMATIQUES

Frid), Amy Glen, Peter Balazi et Gwénaël Ri- ture of the theory has proved very useful and chomme. has been exploited by Rasmussen to derive what Une transformation nouvelle sur les mots, avec is perhaps the most elegant proof of the Milnor des application dans les algèbres de Hopf com- unknotting conjecture. It also has close ties to binatoires, a été présentée par Jean-Christophe mathematical physics. The workshop, attended Novelli (en collaboration avec Jean-Yves Thi- by many CIRGET members (professors, post- bon) ; il s’agit de la parkisation, semblable à la doctoral fellows and Ph.D. students), brought to- standardisation des mots. Certains exposés ont gether mathematicians who have had a strong été plus particulièrement consacrés à des thèmes impact on the theory so they could discuss new de combinatoire des mots appliquée à la théorie developments in the field. The schedule left des langages et au parallélisme : le mélange des many free hours for discussion and research suites de symboles, dans l’exposé de Maurice ter work, and a number of new research collabo- Beek et Jetty Kleijn, les machines séquentielles rations were initiated. Moreover, several Ph.D. dans celui d’Aleksandrs Belovs et Janis Buls, les students benefited from this introduction to the automates dans celui de Wit Forys et Tomasz field; Liam Watson, for example, has been work- Krawczyk, la reconnaissance des traces (mo- ing in the area ever since the workshop. A noïdes partiellement commutatifs libres) dans follow-up event was organized by Dror Bar- celui d’Alessandra Savelli, Luca Breveglieri et Natan at the CMS Winter 2005 meeting. Stefano Crespi-Reghizzi. L’ensemble de ces communications, ainsi que les conférences invitées, a Workshop on Survival Analysis constitué de l’aveu des spécialistes un colloque November 4 – 6, 2005, CRM cohérent et de très bonne qualité. Organized by the Statistics Laboratory Des actes comportant les communications sélec- Organizers: Masoud Asgharian (McGill), tionnées ont été édités par les Publications du Thierry Duchesne (Laval), Brenda MacGibbon LaCIM, dont le responsable éditorial est Srecko (UQÀM) Brlek. Un numéro spécial de la revue Theoretical Speakers: Michal Abrahamowicz (McGill), Ma- Computer Science A (TCSA) sera édité par Srecko soud Asgharian (McGill), David Beaudoin Brlek et Christophe Reutenauer et comportera (Laval), Kheira Belhandouz (Montréal), Pierre- un choix d’articles sélectionnés et arbitrés selon Jérôme Bergeron (McGill), Rebecca Betensky les critères habituels de TCSA. Les organisateurs (Harvard), Richard Cook (Waterloo), Thierry tiennent à remercier particulièrement Julie Mar- Duchesne (Laval), Marc Fredette (HEC Mont- tineau (Faculté des Sciences de l’UQÀM), France réal), James Hanley (McGill), Ella Huszti Maltais (UQÀM) et Lise Tourigny. (McGill), Jerry Lawlesss (Waterloo), Martin F. Lysy (McGill), Louis-Paul Rivest (Laval), Mériem Said (INRS-ETE), Arusharka Sen (Con- CIRGET – CRM Workshop on Khovanov cordia), Marie-Pierre Sylvestre (McGill), Alain Homology Vandal (McGill), Mei-Cheng Wang (Johns Hop- September 30 – Oct 2, 2005, UQÀM kins), Alex Whitmore (McGill) Organized by CIRGET Number of participants: 99 Organizer: Olivier Collin (UQÀM) The main purpose of the workshop was to bring Speakers: Dror Bar-Natan (Toronto), Mikhail together faculty members and graduate students Khovanov (Columbia), Leonard Ng (Stan- in Québec universities who are actively involved ford), Ciprian Manolescu (Columbia), Jacob in research in survival analysis. The workshop Rasmussen (Princeton), Lev Rozansky (UNC provided them with a platform to communicate Chapel Hill), Adam Sikora (SUNY at Buffalo) their recent activities and learn about new di- Number of participants: 25 rections of research in this field. The workshop Khovanov homology was first developed as a comprised four one-hour keynote talks deliv- homology theory whose Euler characteristic was ered by Rebecca Betensky, Richard Cook, Jerry the famous and useful Jones polynomial in knot Lawless and Mei-Cheng Wang. Nine Québec re- theory. It has been shown to be intriguingly close searchers in survival analysis each gave a 45 to other knot invariants coming from gauge the- minute talk. There were 6 poster presentations ory and symplectic geometry, through the work on various topics in survival analysis by Québec of Ozvath and Szabo, Seidel and Smith among graduate students. others, as explained brilliantly by Mikhail Kho- Jerry Lawless’s keynote talk gave an overview vanov during his lecture. The combinatorial na- of multivariate failure time analysis, emphasiz-

30 GENERAL PROGRAM ing the difference between marginal models and The workshop ended with a panel discussion those specified by conditional random effects. moderated by Brenda MacGibbon. The panel Multivariate versions of the Cox model and the discussants were Richard Cook and Rebecca accelerated failure time model were also pre- Betensky. Beforehand the moderator had given sented. Richard Cook talked about recent devel- the discussants a list of questions concerning opments in the analysis of recurrent event data. present and future directions for research in sur- He proposed a method that could account for vival analysis. Richard Cook, with the help of heterogeneity and offer protection against adap- Brenda MacGibbon and Rebecca Betensky, high- tive (or is it “informative”?) censoring, proper- lighted how the research interests of the work- ties that are desirable in the analysis of clinical shop speakers could be used to solve impor- trial data. Rebecca Betensky’s talk was mainly tant problems related to survival analysis. These focused on goodness of fit tests for truncation interests included: multivariate models; copula distributions using prevalent cohort survival models; frailty models; nonparametric estimates data. Mei-Cheng Wang presented an overview of bivariate distributions; independent and de- of the prevalent cohort survival analysis and re- pendent right censoring and interval censoring; cent advances in the field. They both addressed marginal versus conditional methods; selection some aspects of recent advances in the field of effects (length-biased sampling, left, right or in- survival analysis with informative censoring. terval truncation, truncation with multivariate Michal Abrahamowicz presented her work with failure time data, uncertain time origins); time- Todd MacKenzie on joint estimation of time scales; robust methods; goodness of fit; predic- dependent and nonlinear effects of continuous tion of future outcomes. covariates in survival analysis. Thierry Duch- The important problems he emphasized in- esne summarized the recent literature on life- cluded: research on interval-censored data with time regression models based on time transfor- covariates; marker processes (boundary crossing mations and outlined ideas for further research models, Markov models); prediction of failure in that area. Alex Whitmore presented joint work times with censoring; receiver operating charac- with Mei-Ling Lee that involved modeling time teristic curves (fixed and time dependent covari- to event data using hitting time distributions. ates); recurrent events; Bayesian methods; ge- Louis-Paul Rivest presented a new method that netic applications (including dimension reduc- uses a generalization of the copula-graphic es- tion and multiplicity issues); joint modelling of timator to estimate marginal survivor functions longitudinal and failure time data; incorporation for truncated data when the times of truncation of classification and regression trees in survival and the times of death are correlated. Marc Fre- analysis. dette discussed calibrating prediction intervals In conclusion, many of the participants in the for recurrent events where they can be modelled workshop felt that their interest in survival anal- using non-homogeneous Poisson processes. ysis research had increased and were impressed Masoud Asgharian presented his collaborative by the wide array of open problems in the work on survival data, which involved theoret- area. They were also happy to be exposed to ical results for estimation of the survival func- the research done by their colleagues at vari- tion based on prevalent cohort survival data ous Québec universities; hopefully this work- (with applications to the analysis of survival shop will be the beginning of more collaborative with dementia in Canada). Alain Vandal pre- research. sented joint work with R. Gentleman and X. Liu on the bivariate NPMLE with censored data using a graph theoretical approach; he highlighted Homotopy Theory Conference in Honor of the challenges in nonparametric estimation with Joe Neisendorfer’s 60th Birthday survival data. Arusharka Sen presented efficient November 18 – 20, 2005, CRM estimators of linear functionals of a bivariate dis- Organized by CIRGET tribution function when each variable is subject to random censoring. James Hanley gave an en- Organizer: Octav Cornea (Montréal) tertaining lecture on the survival analysis of the Speakers: Martin Bendersky (CUNY, Hunter Titanic survivors, which he used to illustrate the College), Frederick Cohen (Rochester), Bray- difference between current lifetables and cohort ton Gray (Illinois, Chicago), Steven Halperin lifetables. (Maryland), Richard Kane (Western Ontario), Ran Levi (Aberdeen), Chuck McGibbon (Wayne State), Haynes Miller (MIT), Douglas C. Ravenel

31 CENTRE DE RECHERCHES MATHÉMATIQUES

(Rochester), Daniel Tanré (Lille), Laurence Tay- them with some numerical examples. He con- lor (Notre Dame) cluded with the problem of computing mean Number of participants: 45 exit times from a region for a stochastic differ- A conference celebrating Joe Neisendorfer’s 60th ential equation. This is an important problem birthday gathered 45 participants for two days in finance that needs to be solved in order to at the CRM in a pleasant and friendly atmo- price some of the more exotic stock options be- sphere. A number of young mathematicians and ing developed. At present there is no consen- graduate students were among the participants. sus on the best way to estimate mean exit times, Chuck McGibbon presented a talk entitled Joe but Higham’s lecture brought the audience up to Neisendorfer and his work, an appreciation. The date on the best methods available. talks of the other speakers covered the develop- The second short course was given by Howard ment of some central themes in homotopy the- Elman during the afternoons. He described in ory as well as some interactions with dynamical detail an approach to an important and dif- systems and singularity theory (in Bendersky’s ficult problem in scientific computing: solv- talk), with group theory (in Levi’s talk), as well ing the equations of incompressible fluid dy- as with geometric topology in the talks by Lau- namics. He considered all computational as- rence Taylor. pects of the problem from the discretization to the linear algebra necessary for an efficient solution. This is a formidable task; so on Sat- The Third Montréal Scientific Computing urday Elman started with the simpler linear Days convection-diffusion equation. An important as- February 25 – 26, 2006, CRM pect of this problem is the presence of boundary Organized by the Applied Mathematics Labora- layers when the diffusion coefficient is small. He tory showed how stabilization is used to overcome Organizers: Paul Tupper (McGill), Anne the limits of standard finite element schemes Bourlioux (Montréal), Thomas Wihler (McGill) and described an effective preconditioner for Speakers: Howard Elman (Maryland), Des this setting. On Sunday he tackled the incom- Higham (Strathclyde) pressible Navier-Stokes equations in full. His Number of participants: 70 approach through the linearized equations re- sulted in subsidiary problems, one of which was This was the third successive year of the Mont- the convection-diffusion equation presented the réal Scientifc Computing Days. The two-day day before. Elman concluded by demonstrating program consisted of two short courses given by a Matlab software package for two-dimensional guest lecturers, a sequence of short contributed incompressible flow problems in which he had talks, and a poster session. The purpose of the implemented the techniques described in his lec- event was to bring together people from the tures. nearby scientific computing community to learn about the latest techniques and exchange ideas. Interspersed with the short-course lectures were An important audience for the Days is graduate contributed lectures of 15 minutes each. These students. The short course lectures are given at were mostly given by students from nearby uni- the level of an advanced graduate student and versities in Ontario and Québec. Other students the contributed lectures and poster session were presented posters on their work during the Sat- conceived with students particularly in mind. urday night pizza and poster session. The first short course was given by Des Higam on Saturday and Sunday mornings. His topic Mini-Course on the Interval in Graph The- was the theory and numerics of stochastic dif- ory & Informal Workshop on Graph Theory ferential equations. On the first day he intro- April 25 – May 25, 2006, CRM duced the audience to the basics of random vari- Organizer: Gena Hahn (Montréal) ables, Brownian motion, and stochastic differen- Speakers: Pierre Ille (Institut de Mathématiques tial equations. He assumed only a little under- de Luminy, CNRS), Kathie Cameron (Wilfrid graduate probability, thus making his presen- Laurier), François Genest (Concordia), Mateja tation accessible to a wide audience. The next day he presented the Euler – Maruyama method Šajna (Ottawa) for computing trajectories of stochastic differ- Number of participants: 9 ential equations. He introduced the concepts of Pierre Ille a donné un cours sur les intervalles strong and weak convergence and illustrated dans les graphes pendant quatre semaines, à rai-

32 GENERAL PROGRAM son de quatre heures par semaine. Le cours a été batros. Les autres conférences ont été données suivi d’activités libres et d’échanges. Un atelier par Bill Kendall, Carl Schwarz, Roger Pradel, informel sur la théorie des graphes a eu lieu du Rémi Choquet, Gilles Gauthier et Louis-Paul Ri- 19 au 24 mai. Pierre Ille y a présenté la preuve vest. Ils ont traité de différents aspects, tant pra- d’une conjecture de Sabidussi et une caractéri- tiques que théoriques, de l’utilisation des don- sation des graphes infinis indécomposables. Ka- nées de capture-recapture pour estimer des ca- thie Cameron a donné une conférence intitulée ractéristiques démographiques de populations Finding an easily recognizable strong stable set et animales. Une cinquantaine de personnes ont as- Mateja Šajna une conférence intitulée On the exis- sisté à ces présentations. tence of regular self-complementary uniform hyper- Un atelier de formation à l’utilisation du logiciel graphs. Le sujet de la conférence de François Ge- M-Surge développé par le CEFE s’est déroulé du nest était le nombre de stabilité des puissances mardi 2 mai au vendredi 5 mai 2006. Une ving- de la 5-roue. taine de personnes, provenant de 6 pays diffé- rents, ont participé à cet atelier. Les formateurs Analysis Day 2006 étaient Jean-Dominique Lebreton, Roger Pradel, May 1st, 2006, CRM Rémi Choquet et Gilles Gauthier. Le logiciel M- Organized by the Mathematical Analysis Labo- Surge permet d’ajuster des modèles statistiques ratory multi-états à des données de capture-recapture. De tels modèles permettent de faire varier les pa- Organizer: Dmitry Jakobson (McGill) ramètres démographiques, tels le taux de survie, Speakers: Octav Cornea (Montréal), Emmanuel selon l’état de l’animal. Cet état peut être associé Fricain (Lyon 1), Leonid Parnovski (University à l’âge de l’animal (jeune ou adulte), à sa loca- College, London) lisation géographique (le lieu de sa capture) ou Number of participants: 24 au fait d’avoir été capturé ou non à l’occasion This activity is the second edition of the Analysis précédente. Ils permettent également de calculer Day organized since 2004 – 2005 by the Mathe- des taux de transition d’un état à l’autre. Cet ate- matical Analysis Laboratory (which is only three lier s’est terminé par des présentations des parti- years old). Emmanuel Fricain talked on repro- cipants, le vendredi 5 mai, illustrant l’utilisation ducing kernel bases in the de Branges spaces, de M-Surge sur des données de différentes es- Octav Cornea on measuring Lagrangian man- pèces animales. ifolds and Leonid Parnovski on the distribution of lattice points in Euclidean and hyperbolic Workshop on Probabilistic Symmetries and spaces. Their Applications May 15 – 17, 2006, University of Ottawa Capture 2006: A Scientific Meeting and a Sponsored by the Fields Institute, the University Workshop on Capture – Recapture Models of Ottawa and CRM May 1 – 5, 2006, Université Laval Organizers: Gail Ivanoff (Ottawa), Raluca Organizers: Gilles Gauthier (Laval), Louis-Paul Balan (Ottawa) Rivest (Laval) Speakers: Federico Bassetti (Pavia), Kameswar- Speakers: Rémi Choquet (CEFE, Montpellier), rao Casukhela (Ohio State), André Dabrowski Gilles Gauthier (Laval), Bill Kendall (Patuxent (Ottawa), Gail Ivanoff (Ottawa), Olav Kallen- Wildlife Research Center, Washington), Jean- berg (Auburn), Rafal Kulik (Carleton & Sydney), Dominique Lebreton (CEFE, Montpellier), Roger Fabrizio Leisen (Modena e Reggio Emilia), Ser- Pradel (CEFE, Montpellier), Louis-Paul Rivest guei Novak (Middlesex), Fabio Spizzichino (La (Laval), Carl Schwarz (Simon Fraser) Sapienza), Neville Weber (Sydney) Number of participants: 50 Number of participants: 35 L’atelier a débuté par une journée de confé- The workshop was particularly timely in that rences le lundi 1er mai. L’allocution d’ouver- 2006 marks the centenary of the birth of Bruno ture a été prononcée par M. Jean-Dominique de Finetti, the Italian mathematician whose fa- Lebreton, membre de l’Académie des sciences mous theorem on the structure of infinite ex- de France et directeur du Centre d’Écologie changeable sequences initiated the study of Fonctionnelle et Évolutive (CEFE) de Montpel- probabilistic symmetries. The invited speak- lier. Elle portait sur la combinaison de données ers were Olav Kallenberg, Fabio Spizzichino, de capture-recapture et d’information démogra- Neville Weber and André Dabrowski. Profes- phique pour prédire la survie d’une espèce d’al- sor Olav Kallenberg, currently the foremost re-

33 CENTRE DE RECHERCHES MATHÉMATIQUES searcher in the field, gave the three keynote lec- Colloquium on Potential Theory — 74e tures, which gave an outstanding overview of congrès de l’Acfas the general theory of the major symmetries (con- May 15 – 19, 2006, McGill University tractability, exchangeability, and rotatability). Sponsors: Consulat général de France à Mont- Professor Fabio Spizzichino gave a fascinating réal, CRM, Mathematical Analysis Laboratory, account of de Finetti’s unique philosophy of FQRNT, Office of the Vice-Principal (Research & statistical inference, as well as a lecture on an International Relations, McGill) application of exchangeability in reliability the- Organizer: Kohur Gowrisankaran (McGill) ory. Professor Neville Weber’s first lecture intro- Speakers: Hiroaki Aikawa (Hokkaido), Do- duced the use of martingale techniques in the minique Bakry (Toulouse), Lucian Beznea (Ro- study of U-statistics, while his second focused manian Academy), Jürgen Bliedtner (Frank- on a more advanced analysis of the asymptotic furt), Khalifa El Mabrouk (Monastir), Stephen behaviour of exchangeable arrays. Professor An- Gardiner (University College, Dublin), Ivan dré Dabrowski discussed the relationship be- Gentil (Paris-Dauphine), Joe Glover (Florida), tween positive dependence and exchangeabil- Wolfhard Hansen (Bielefeld), Farida Hmissi (Tu- ity for sequences. The subject of Gail Ivanoff’s nis), Klaus Janssen (Düsseldorf), Paul Koosis talks was conditional symmetries on arrays, and (McGill), Jaroslav Lukes (Charles, Prague), the associated martingale structures and sam- Nikolai Makarov (Caltech), Javad Mashreghi pling properties. Contributed talks were given (Laval), Yoshihiro Mizuta (Hiroshima), Ivan by Rafal Kulik, Federico Bassetti, Fabrizio Leisen Netuka (Charles, Prague), Eugen Popa (Iasi), and Kamesh Casukhela. Philippe Poulin (McGill), Nicolas Privault (La The participants came from Canada, the USA, Rochelle), Josie Ryan (Milligan College, Ten- Italy and Australia. Approximately half of the nessee) attendees were graduate students or postdoc- Number of participants: 23 toral fellows. All participants commented on the The colloquium consisted of twenty-one talks, benefits of a broad exposure to an important each of them lasting 45 minutes. Each talk was subject, in an intimate environment that pro- attended by more or less all the participants. The vided ample opportunity for interaction and dis- talks generated a lot of interest in the most cur- cussion. It is hoped that some of the young re- rent research topics of the three principal areas searchers will be inspired to tackle some of the of the theory. These areas are the classical poten- challenging open problems proposed by Profes- tial theory from a modern perspective, the prob- sor Kallenberg. The organizers are pleased to ac- abilistic aspects of the theory and the abstract knowledge the co-sponsorship of the Institute of cone settings with applications. An overwhelm- Mathematical Statistics. They wish to thank At- ing number of talks were delivered in French las Mathematical Conference Abstracts for pub- and there were three Canadian participants (in- lishing the workshop abstracts free of charge. cluding a graduate student from McGill).

CRM – ISM Colloquium Series

The CRM, together with the Institut des sciences mathématiques du Québec (ISM), the Québec universities graduate mathematics consortium, runs two Montréal colloquium series, one in mathematics and the other in statistics (the latter jointly with GERAD, an operations research centre located in the André-Aisenstadt building). During the academic year, these series offer survey talks on topics of current interest by distinguished mathematicians and statisticians.

CRM – ISM Mathematics Colloquium September 23, 2005 Maciej Zworski (Berkeley) Counting quantum states in chaotic scattering Coordinators: Pengfei Guan (McGill), Alexan- der Shnirelman (Concordia) September 30, 2005 Louis Nirenberg (New September 9, 2005 Tom Graber (Caltech) York University) Towards a quantum McKay correspondence A geometric problem and the Hopf lemma September 16, 2005 Barry Mazur (Harvard) October 7, 2005 Richard Schoen (Stanford) Families of modular forms and their representations The Yamabe problem revisited

34 GENERAL PROGRAM

October 14, 2005 Yum-Tong Siu (Harvard) March 3, 2006 Fedor Bogomolov (Courant) Multiplier ideals] A new technique linking analysis Geometry of algebraic varieties over small fields and algebraic geometry (Fp, Q) October 21, 2005 Fadil Santosa (Minnesota) March 10, 2006 Peter Zograf (Steklov, St. Peters- Seeing better with mathematics: A mathematical burg) problem arising in design of ophthalmic lenses Witten-Kontsevich theory and Weil-Petersson vol- umes of moduli spaces of algebraic curves October 28, 2005 Emmanuel Letellier (Paris 6) From Kazhdan – Springer to the topological proper- March 17, 2006 Vladimir Retakh (Rutgers) ties of the Riemann – Hilbert monodromy map Algebras associated to directed graphs and related to factorizations of noncommutative polynomials November 4, 2005 Alexander Shnirelman (Con- cordia) March 24, 2006 John Mather (Princeton) The mystery of 2-dimensional fluid Arnold Diffusion November 11, 2005 Walter Craig (McMaster) April 7, 2006 Helmut Hofer (Courant) On the Boltzmann equation: Global solutions in one Quantitative Symplectic Geometry spatial dimension April 21, 2006 Alice Chang (Princeton) November 18, 2005 Gregory Margulis (Yale) Conformal invariants associated with a smooth mea- Quantitative Oppenheim conjecture sure November 25, 2005 Edward Nelson (Princeton) The mystery of stochastic mechanics CRM – ISM – GERAD Statistics Collo- December 2, 2005 Alexey Kokotov (Concordia) quium Extremal properties of some functionals on the mod- Coordinators: Christian Léger (Montréal), uli space of genus two Riemann surfaces Pierre Duchesne (Montréal), Brenda MacGibbon December 9, 2005 Tamás Erdélyi (Texas A&M) (UQÀM), Arush Sen (Concordia), Russell Steele Excursions in unimodular polynomials (McGill) December 16, 2005 James W. Cogdell (Ohio September 19, 2005 Rob Kass (Carnegie Mel- State) lon) L-functions, modularity, and functoriality Bayesian curve fitting and neuron firing patterns January 6, 2005 Vašek Chvátal (Concordia) September 23, 2005 Bradley Efron (Stanford) Recent advances in solving the Travelling Salesman Fifty years of empirical Bayes Problem September 30, 2005 Reg Kulperger (Western January 13, 2006 Michael Goldstein (Toronto) Ontario) Anderson localization for shifted and skew-shifted po- A stochastic competing species model and ergodicity tentials: Some recent developments October 7, 2005 Giles Hooker (McGill) January 20, 2006 Vitaly Bergelson (Ohio State) Diagnostics and extrapolation in machine learning: Ergodic theory and the properties of large sets Extending the functional ANOVA January 27, 2006 Adrian Iovita (Concordia) October 14, 2005 Richard Lockhart (Simon On the arithmetic of elliptic curves Fraser) Bayes-assisted goodness-of-fit tests February 3, 2006 G. M. Zaslavsky (Courant) Nonergodic and nonmixing chaos and pseudochaos October 21, 2005 Alejandro Murua (Montréal) Analysis of health outcomes at the turn of the century February 10, 2006 Yousef Saad (Minnesota) Solution of sparse matrix problems by domain October 28, 2005 Jonathan Taylor (Stanford) decomposition-type methods Deformation based morphometry, Roy’s maximum root and recent advances in random fields February 17, 2006 Roman Schubert (Bristol) Universality in wave propagation for large times November 4, 2005 Jerry Lawless (Waterloo) Multivariate failure time analysis February 24, 2006 Des Higham (Strathclyde) A new model for protein-protein interaction networks November 11, 2005 Bernd Sturmfels (Berkeley) Algebraic factor analysis: Tetrads, pentads and beyond

35 CENTRE DE RECHERCHES MATHÉMATIQUES

November 18, 2005 David Binder (president of February 10, 2006 Scott L. Zeger (Johns Hop- the SSC) kins) Why take a design-based approach to modeling data Micronutrient supplementation, birth weight and in- from complex surveys? fant mortality: On estimation of percentile-specific, mediated intervention effects November 25, 2005 Josée Dupuis (Boston) Genetic linkage analysis of quantitative traits in the February 17, 2006 Shojaeddin Chenouri (Water- Framingham heart study: Open problems and statis- loo) tical challenges Data depth: Theory, computations and applications November 25, 2005 Eric Kolaczyk (Boston Uni- February 24, 2006 Shelley Bull (Mount Sinai versity) Hospital & University of Toronto) Network Kriging Bias reduction of locus-specific effect estimates via the bootstrap in linkage scans for quantitative trait Loci December 2, 2005 Derek Bingham (Simon Fraser) March 3, 2006 Vanja Dukic (Chicago) Sequential experiment design for contour estimation A Bayesian SEIR approach to modeling smallpox epi- from computer simulators demics December 9, 2005 James M. Curran (Auckland) March 10, 2006 Xiao-Li Meng (Harvard) A MCMC method for resolving two-person DNA How “crude” is Harvard President’s calculation? mixtures March 31, 2006 Yongzhao Shao (NYU School of January 20, 2006 Keith Knight (Toronto) Medicine) Boundaries, Poisson processes, and linear programs Some recent developments in testing for finite mix- ture models January 27, 2006 Yulia R. Gel (Waterloo) On strong consistency of the regularized least- April 7, 2006 Fateh Chebana (INRS-ETE) squares estimates of infinite autoregressive models Locally asymptotically optimal tests for nonlinear time-series models February 3, 2006 Jamie Stafford (Toronto) Iterated conditional expectations

36 Multidisciplinary and Industrial Program CENTRE DE RECHERCHES MATHÉMATIQUES

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

Activities of the Multidisciplinary and Industrial Program

Fifth Summer School in Quantum Comput- Workshop High-Dimensional Partial Differ- ing ential Equations in Sciences and Engineer- August 1 – 5, 2005, Université de Montréal ing Sponsored by CIAR, MITACS and CRM August 7 – 12, 2005, CRM Organizers: Alain Tapp (Montréal), André Sponsored by CRM, CERMICS (École Nationale Méthot (Montréal) des Ponts et Chaussées, France), IBM Canada Speakers: Gilles Brassard (Montréal), Richard Higher Education and Research Sector, Min- Cleve (Waterloo), Claude Crépeau (McGill), istère délégué à la recherche et aux nouvelles Daniel Gottesman (Perimeter), Patrick Hayden technologies (France, ACI Nouvelles interfaces (McGill), Peter Høyer (Calgary), Michele Mosca des mathématiques), Regroupement québécois (Waterloo), Barry Sanders (Calgary), Alain Tapp sur les matériaux de pointe (RQMP), Vice- (Montréal), John Watrous (Calgary), Ronald de Rectorat à la recherche de l’Université de Mont- Wolf (Amsterdam) réal Number of participants: 75 Organizers: André Bandrauk (Sherbrooke), For the second time the Summer School in Quan- Michel Delfour (Montréal), Claude Le Bris tum Computing, a tradition that is well estab- (École Nationale des Ponts et Chaussées) lished by now, took place in Montréal. In pre- Speakers: André Bandrauk (Sherbrooke), vious years it took place also in Toronto, Wa- Thomas Brabec (Center for Research in Photon- terloo and Calgary. The School was targeted ics, Ottawa), Eric Cancès (ENPC), Goong Chen towards graduate students from the fields of (Texas A&M), Michel Côté (Montréal), Pierre computer science, physics and mathematics. No Degond (CNRS, Toulouse), Michel Delfour prior knowledge of quantum computing was as- (Montréal), Matthias Ernzerhof (Montréal), sumed. It attracted around sixty students. Many Maria J. Esteban (Paris-Dauphine), André Fortin of them were starting graduate studies in one of (Laval), Michael Griebel (IAM, Bonn), Wagdi the Canadian research groups in quantum com- Habashi (McGill), Tom R. Hurd (McMaster), puting. Many others, who work in related ar- Raymond E. Kapral (Lash Miller Chemical Labs, eas, attended the school in order to get a ba- Toronto), Bernard Lapeyre (ENPC), Yvon Maday sic knowledge of that field. Quantum computing (Paris 6), David A. Mazziotti (Chicago), Robert is a recent research field at the frontier of com- G. Owens (Montréal), Anthony T. Patera (MIT), puter science and physics. It is concerned with Gilles H. Peslherbe (Concordia), Andreas Savin the use of the laws of quantum mechanics to (Paris 6), Luis A. Seco (Toronto), Robert E Wyatt process information. If a quantum computer is (Texas at Austin) ever built, it will have significant impact on com- Contributing students and postdocs: Gérard puter science in general, but most importantly Lagmago-Kamta (Sherbrooke), Emmanuel Lorin on cryptology. The talks covered the following de la Grandmaison (Sherbrooke), Roy Mahapa- topics: introduction to the computation model tra (Wilfrid Laurier), Julien Salomon (Paris 6), of quantum information, quantum cryptogra- Evgueni Sinelnikov (Laval) phy, Grover’s search type algorithms, Shor’s fac- Number of participants: 63 (including 19 stu- toring algorithm, quantum information theory, dents) proofs in the quantum world, error correction High-dimensional spatio-temporal partial dif- and fault tolerant computation, implementation ferential equations are a major challenge for the of the quantum computer, non locality, pseu- scientific computing of the future. Up to now dotelepathy and communication complexity. deemed prohibitive, they have recently become manageable by combining recent developments in numerical techniques, appropriate computer implementations, and the use of computers with parallel and even massively parallel architec-

38 MULTIDISCIPLINARY AND INDUSTRIAL PROGRAM tures. This opens new perspectives in many ticiens ont pris connaissance des applications fields of applications. The kinetic plasma physics les plus novatrices et les plus récentes. Les or- equations, many-body Schrödinger equation, ganisateurs avaient identifié et invité une dou- Dirac and Maxwell equations for molecular elec- zaine de conférenciers qui avaient collaboré avec tronic structure and nuclear dynamic computa- Philip Holmes à divers stades de sa carrière : tions, options pricing equations in mathemati- leurs exposés ont permis d’illustrer les nom- cal finance, and Fokker-Planck and fluid dynam- breux domaines où la théorie des systèmes dy- ics equations for complex fluids, are examples of namiques joue un rôle important dans l’inter- equations that can now be handled. This work- prétation d’observations expérimentales ou sous shop brought together experts of international contôle. stature in that broad spectrum of areas to com- Les sujets suivants ont été abordés : machine- pare their approaches and bring out common rie aéronautique (Campbell et Stone), outillage problem formulations and research directions automobile (Shaw) et optimisation de la pro- in the numerical solutions of high-dimensional duction de semi-conducteurs (Ambruster). Les partial differential equations. These equations présentations théoriques (en particulier celles are to be found in various fields of science and de Guckenheimer, Chillingworth et Ghrist) ont engineering but the emphasis was on chemistry eu une place importante dans cet atelier, ainsi and physics. The proceedings of the workshop que les applications à la biologie : dynamique will be published in the AMS Series CRM Pro- de populations (Damokos), rythmes cellulaires ceedings and Lecture Notes. (D. Rand et B. Rand) et interactions entre neu- rones (Shea-Brown). Daniel Koditschek rem- International Workshop on Applied Dy- plaça brillamment Robert Full, présentant avec namical Systems — Mechanics, Turbu- un enthousiasme contagieux ses travaux sur les lence, Knots, Cockroaches, and Chaos robots cherchant à reproduire le très robuste October 15 – 16, 2005, CRM comportement des cafards. Une douzaine de Sponsored by the Applied Mathematics Labora- participants présentèrent également des affiches. tory Un segment inédit de cette conférence fut un Organizers: Jacques Bélair (Montréal), Sue Ann échange d’une heure environ sur l’état actuel Campbell (Waterloo), Jeff Moehlis (UC Santa de la dynamique nonlinéaire, en particulier les Barbara), N. Sri Namachchivaya (Illinois at liens entre la théorie mathématique et les besoins Urbana-Champaign), Steve Shaw (Michigan de l’ingénierie et les stratégies à employer pour State) rapprocher les communautés de mathématiciens Speakers: Dieter Armbruster (Arizona State), et d’ingénieurs. La conférence se déroula dans Sue Ann Campbell (Waterloo), David Chilling- une atmosphère festive, eu égard à la célébra- worth (Southampton), Gabor Damokos (Bu- tion concomitante des remarquables réalisations dapest University of Technology and Eco- de Philip Holmes durant les soixante premières nomics), Daniel Koditschek (Pennsylvania), années de sa vie. Robert Ghrist (Illinois at Urbana-Champaign), John Guckenheimer (Cornell), David Rand (Warwick), Richard Rand (Cornell), Steven Shaw Workshop on Mathematics in Brain Imag- (Michigan State), Eric Shea-Brown (Courant), ing and its Applications to Cognitive and Emily Stone (Montana) Clinical Neurosciences Number of participants: 47 October 17 – 18, 2005, Institut universitaire de gériatrie de Montréal Cette conférence internationale visait à conso- Organized by the PhysNum Laboratory lider les ponts entre les théoriciens et les utilisateurs des systèmes dynamiques, en réunis- Organizers: Habib Benali (CHU Pitié- sant des spécialistes d’expertises variées et ve- Salpêtrière), Julien Doyon (Montréal), Jean-Marc nant d’horizons divers (génie, sciences, mathé- Lina (École de Technologie Supérieure) matiques) et en cherchant à identifier les direc- Speakers: Guillaume Marrelec (INSERM), tions émergentes de recherche de la discipline. Pierre Bellec (INSERM), Jean Daunizeau (Mont- Les utilisateurs des domaines du génie et des réal), Julien Doyon (Montréal), Hugues Duffau sciences appliquées y ont trouvé une occasion (CHU Pitié-Salpêtrière), Saad Jbabdi (INSERM unique de s’approprier les plus récents déve- & Oxford), Odile Jolivet (Faculté de Médecine loppements de la théorie et les résultats ma- Pierre et Marie Curie), Jean-Marc Lina (École de thématiques connexes, alors que les mathéma- Technologie Supérieure), Mélanie Pélégrini (Fac-

39 CENTRE DE RECHERCHES MATHÉMATIQUES ulté de Médecine Pierre et Marie Curie), Vincent tive les aspects bayésiens et entropiques de la re- Perlbarg (INSERM) construction des sources d’activation cérébrale. Number of participants: 30 V. Perlbarg fit état de ses travaux à propos du La capacité de visualiser in vivo les structures bruit structuré présent en IRM. Finalement, H. cérébrales mises en jeu par des tâches cog- Benali et M. Pélégrini ont présenté la recherche nitives chez l’homme modifie en profondeur menée au sein de l’équipe de Paris (IMPARABL) le domaine des sciences cognitives humaines. ainsi que les outils logiciels qui y sont dévelop- Pendant des décennies, l’étude de la cogni- pés. tion humaine se basait uniquement sur la pré- sence de lésions et des symptômes neuropsycho- MITACS – MSRI – AFMnet – CRM Work- logiques associés. Avec l’avènement des tech- shop on Therapeutic Efficacy in Population niques d’imagerie fonctionnelle de résolution Veterinary Medicine spatio-temporelle toujours croissante, une nou- October 19 – 22, 2005, Banff International Re- velle discipline apparaît : les neurosciences cog- search Station nitives où l’image est le principal outil. Cette dis- Sponsored by MITACS, AFMnet, MSRI, CRM, cipline jette un nouveau regard sur les relations Pfizer Animal Health, Scheringer-Plough Ani- fonctionnelles au sein du cerveau, telles que dé- mal Health, Aventis finies en psychologie ou en neuropsychologie. Organizers: Fahima Nekka (Montréal), Jacques L’imagerie neurofonctionnelle est un domaine Bélair (Montréal), Renée Bergeron (Laval), de recherche pluridisciplinaire où l’analyse, la Jérôme del Castillo (Montréal), Jun Li (Mont- modélisation et le traitement du signal sont réal), Jeff Lucas (MITACS), Daniel Pettigrew indispensables pour reconstruire et interpréter (Fédération des Producteurs de Porcs du les données recueillies par les instruments. La Québec), Don Schaffner (Rutgers) mise en place de méthodes d’analyse fiables List of participants: Jacques Bélair (Montréal), et robustes est un atout majeur pour tous les Madonna Benjamin (Elanco Animal Health), utilisateurs d’imagerie cérébrale. Ainsi, les as- Renée Bergeron (Laval), Dave Bernier (Mont- pects méthodologiques plus ancrés dans le sec- réal), Jérôme del Castillo (Montréal), Hermann teur des mathématiques appliquées sont-ils de- Eberl (AFMnet & Guelph), James France (AFM- venus au fil des dernières années un thème net and University of Guelph), Harold G. important en imagerie médicale. En réunissant Gonyou (Prairie Swine Centre), Bruce Groves les principaux acteurs du regroupement CRM- (Pfizer Animal Health Canada), Tony Hayes CRIUGM (Centre de recherche de l’Institut uni- (Guelph), Judith Lafrance (Laval), Ann Letel- versitaire de gériatrie de Montréal), cet atelier vi- lier (Montréal), Jeff Lucas (MITACS), Murray sait d’abord à consolider la collaboration entre McLaughlin (AFMnet), Claude Miville (Fédéra- les centres montréalais (CRM et CRIUGM) et tion des Producteurs de Porcs du Québec), l’unité 678 de l’INSERM (CHU Pitié-Salpêtrière). Fahima Nekka (Montréal), Alan Paulson (AFM- En invitant les membres de ces institutions à pré- net and Dalhousie), Caroline-Emmanuelle Petit- senter leurs travaux, l’atelier donnait ainsi l’oc- Jetté (Montréal), Candido Pomar (Agriculture casion d’illustrer ce regroupement international and Agri-Food Canada), Richard Reid-Smith auprès de la communauté des neurosciences. (Public Health Agency of Canada), Steven L’exposé de G. Marrelec, aujourd’hui chercheur Sanches (Montréal), Heidi Schraft (Lakehead), à l’INSERM, mit en perspective les difficultés Alan Theede (Pfizer Animal Health Canada), méthodologiques de traitement de la connecti- Lisbeth Truelstrup (AFMnet & Dalhousie), Lau- vité fonctionnelle en neuroimagerie. Ce thème rence T. Yang (St. Francis Xavier) fut repris par P. Bellec qui mit l’accent sur les This workshop has been organized by the MI- aspects temporels de l’apprentissage via les ré- TACS BIO5 team around the general theme seaux. Le point de vue plus neuroscientifique de of therapeutic efficacy in population veterinary ce problème fut décrit par J. Doyon. La présen- medicine. It has brought together researchers tation de S. Jbabdi portait sur l’étude des fibres working in applied mathematics, veterinary sci- et des chemins géodésiques dans le cerveau. Ce ences, behavioural sciences as well as in mi- thème, assez récent, fut évoqué dans la présen- crobiology and nutrition. The workshop was tation du Docteur H. Duffau (neurochirurgien) attended by academic researchers as well as comme un des outils pertinents pour la prépa- speakers and participants from other public sec- ration d’une chirurgie du cerveau. Les exposés tors (Agriculture and Agri-Food Canada and de J. Daunizeau et J.-M. Lina ont mis en perspec- the Public Health Agency of Canada). Repre-

40 MULTIDISCIPLINARY AND INDUSTRIAL PROGRAM sentatives of Pfizer Animal Health and Elanco The feedback from the participants was ex- Animal Health were present. The conferences tremely positive. They found the workshop use- covered different aspects relating to animal col- ful and were thankful for an opportunity to lective therapy, especially in swine and poul- gain insight into MITACS and AFMnet. They try, in terms of determinants and outcomes. A were encouraged to see genuine collaboration complete portrait of animal behaviour in the between mathematicians, pharmacologists and context of therapeutic efficacy was drawn. A animal behaviourists. They deemed the work- whole overview of the Canadian Integrated Pro- shop to be a very useful brainstorming meeting. gram for Antimicrobial Resistance Surveillance (CIPARS) has been given to explain the national Workshop program of antimicrobial use in food animals Current Issues in Functional Imaging with and surveillance system for antimicrobial resis- Optical Devices tance arising from food animal production. May 11 – 12, 2006, CRM Organized by the PhysNum Laboratory A general idea of mathematical approaches used to handle biological complexity has been given Organizers: Habib Benali (CHU Pitié- with emphasis on the need for collaborative ef- Salpêtrière), Frédéric Lesage (École Polytech- forts between mathematical sciences and exper- nique de Montréal), Jean-Marc Lina (École de imental research. For instance, the researchers Technologie Supérieure) involved in the MITACS seed project used Speakers: Simon R. Arridge (University Col- dynamical systems (represented by the multi- lege, London), David Boas (Massachusetts Gen- compartmental approach defined by systems of eral Hospital & Harvard Medical School), ODE) with stochastic input. They analyzed the Claude Boccara (École supérieure de physique statistical properties of these systems in terms et de chimie industrielles de Paris), Emmanuel of stability and conservation of the dynamical Candes (Caltech) system. This approach is new in pharmacoki- Number of participants: 80 netics and should be used in other areas of biology. The researchers also introduced competi- Cet atelier a réuni près de 70 chercheurs et tion mechanisms in collective behaviour that ac- étudiants autour des méthodes optiques pour count for dynamical interactions between indi- l’imagerie fonctionnelle dans le domaine biomé- viduals, and this approach has to be put within dical. En effet, l’imagerie optique connaît des the framework of hierarchical nonlinear models développements rapides, en particulier dans le used for repeated measurement data. domaine de l’optique proche infrarouge. Par exemple, la mesure in vivo des signaux optiques During the workshop very interesting discus- à très haute résolution temporelle permet l’étude sions took place, always balanced between the anatomo-fonctionnelle du cortex cérébral. D’une different areas of research. The presence of in- façon générale, ces imageurs de nouvelle géné- dustrial researchers from Pfizer Animal Health ration utilisent l’absorption de certaines molé- in particular, allowed the researchers to gain a cules, qu’elles soient endogènes, comme l’hémo- clear idea of the pharmaceutical industry expec- globine, ou exogènes, comme les marqueurs mo- tations and practices. The workshop concluded léculaires spécifiques de certaines pathologies with a discussion about collaborations and per- (la maladie d’Alzheimer, par exemple). L’atelier spectives, that took place on October 22. From a porté sur tous les aspects du domaine : la phy- this discussion it emerged that the following siologie sous-jacente, les acquisitions, le traite- questions were important and should be ad- ment des données, la modélisation et les mé- dressed. Is the veterinary use of antibiotics ap- thodes numériques de reconstruction d’images. propriate? How can we improve antibiotics use to make it safer and more efficient? How does Expert reconnu au niveau international pour the risk of using the labelled dose compare with l’avancement de ces travaux en imagerie diffuse the risk of using an unapproved one? Three infra-rouge, D. Boas a ouvert l’atelier avec un ex- main areas of research have been identified for posé couvrant l’ensemble de la problématique the full MITACS project: impact of feeding be- de l’imagerie NIRS. Ce cours fut certainement haviour on dosage efficacy, alternatives to an- une excellente entrée en matière pour appréhen- tibiotics and their assessment, and risk analysis. der l’ensemble du domaine, aussi bien les ori- The involvement of pharmaceutical companies gines physiologiques que les aspects de modé- in the MITACS project was also discussed. lisation. Son exposé sur ces questions méthodo- logiques était une transition vers le cours de S. Arridge, qui a présenté les équations de trans-

41 CENTRE DE RECHERCHES MATHÉMATIQUES port décrivant la propagation de la lumière dans l’inobservance thérapeutique afin de la contrô- le milieu biologique. Son exposé, riche en in- ler, et à cerner les pratiques et approches utili- formations sur les aspects techniques de la mo- sées dans les outils de mesure de l’observance délisation numérique du problème direct, a su et dans son analyse. L’accent fut mis sur le rôle mettre en perspective les difficultés de modélisa- à attribuer aux différentes sources de variabilité, tion. Dans sa seconde moitié, ce cours aborda la des sources induites par les formes pharmaceu- résolution du problème inverse et les techniques tiques elles-mêmes aux différents facteurs impli- de reconstruction d’images. qués dans leur action pharmacologique, en pas- Ce sujet fut repris et développé par E. Candes, sant par la façon dont les médicaments sont ad- qui fit un cours des plus complets sur la syn- ministrés. thèse tomographique par curvelets. Domaine re- L’atelier a réuni de grands spécialistes de lativement récent de l’analyse numérique, ce l’inobservance, dont John Urquhart, qui est le secteur des mathématiques appliquées n’en est fondateur de la discipline de la “pharmionique” pas moins un des plus dynamiques à l’heure et l’inventeur du système électronique MEMS actuelle. Incidemment, au moment où l’atelier pour la mesure de l’inobservance. L’importance avait lieu, E. Candes venait de recevoir le prix de l’inobservance comme source majeure de Waterman pour l’ensemble de son travail en la variabilité thérapeutique ainsi que son im- analyse harmonique. Le dernier cours fut donné pact économique sur le système de santé ont par C. Boccara, dont l’expertise en imagerie op- été démontrés en faisant référence à plusieurs tique, sous toutes ses formes, est notoire. Son études pour des pathologies différentes dans des exposé a mis en persective l’ensemble des tech- contextes différents. niques optiques dans le cadre applicatif. Ce re- tour sur les aspects pratiques terminait de facon brillante l’ensemble des cours. Workshop Between Specialists of Brain and Spine Imaging and Mathematicians Inter- En s’adressant aux chercheurs et aux étudiants ested in the Questions Arising from Imag- en neuroimagerie, ces quatre spécialistes ont ing réussi à couvrir tous les aspects de l’imagerie op- May 23, 2006, CRM tique : la physique des acquisitions, la méthodo- logie du traitement et les applications cognitives Organizers: Habib Benali (CHU Pitié-Salpê- et cliniques. trière), François Lalonde (Montréal) List of participants: Jean-François Angers (Montréal), Habib Benali (CHU Pitié-Salpê- Workshop trière), Yves Bourgault (Ottawa), Michel Delfour Drug Intake Behavior and Pharmaceutical (Montréal), Julien Doyon (Centre de recherche Practice: Data Acquisition and Modeling de l’Institut universitaire de gériatrie de Mont- May 15, 2006, CRM réal), Bernard Goulard (Montréal), Rick Hogue Organizer: Fahima Nekka (Montréal) (Centre de recherche de l’Institut universitaire Speakers Els Goetghebeur (Harvard & Ghent), de gériatrie de Montréal), Tony Humphries Jun Li (Montréal), Fahima Nekka (Montréal), (McGill), Frédéric Lesage (École Polytechnique), Jacques Turgeon (Montréal), John Urquhart (UC Jean-Marc Lina (École de Technologie Supé- San Francisco & Maastricht), Bernard Vrijens rieure), Serge Rossignol (Montréal), Olivier (AARDEX Ltd., Switzerland & Liège) Rousseau (Ottawa), Thomas P. Wihler (McGill) Number of participants: 20 Ces dernières années, plusieurs collaborations L’inobservance thérapeutique est un problème bilatérales ont pris forme, impliquant d’abord mondialement reconnu, avec des conséquences l’équipe PhysNum du CRM (B. Goulard, J.- directes sur l’efficacité du traitement. Ce pro- M. Lina, F. Lesage) à Montréal et l’équipe blème est particulièrement important dans le cas IMPARABL-U678-INSERM (H. Benali) à Paris. des maladies chroniques, avec un rôle jugé do- Ces collaborations se sont étendues à plusieurs minant dans la variabilité thérapeutique. De par équipes du Regroupement Neuroimagerie Qué- la nature de ses caractéristiques variables, l’ob- bec (les équipes de J. Doyon et S. Rossignol, en servance se prête bien aux méthodes stochas- particulier). Le but de la rencontre avec d’autres tiques et statistiques, qui ont pour objectif de chercheurs du CRM était d’étendre ces collabo- quantifier son effet dans une perspective d’op- rations en persuadant des mathématiciens du timisation de la stratégie d’administration mé- CRM de se joindre au projet des mathématiques dicamenteuse. Cet atelier visait à comprendre en imagerie cérébrale. L’atelier a comporté plu-

42 MULTIDISCIPLINARY AND INDUSTRIAL PROGRAM sieurs conférences (courtes) suivies de tables NPCDS/MITACS Spring School on Statis- rondes. tical and Machine Learning: Topics at the Interface Serge Rossignol expliqua que la compréhension des processus fonctionnels de la moelle épi- May 23 – 27, 2006, CRM nière chez l’homme et chez l’animal constitue Sponsored by MITACS un enjeu majeur de santé publique. Il décri- Organizers: Yoshua Bengio (Montréal), Hugh vit le travail de son équipe, c’est-à-dire l’étude A. Chipman (Acadia), Russell Steele (McGill) des mécanismes de récupération fonctionnelle Speakers: Yoshua Bengio (Montréal), Hugh A. de la marche après lésion spinale chez le chat. Chipman (Acadia), Antonio Ciampi (McGill), Il dit qu’il est important de développer des ou- Helmut Kröger (Laval), Doina Precup (McGill), tils mathématiques permettant d’établir des cor- Russell Steele (McGill), Ji Zhu (Michigan) rélations claires (dans un contexte physiologique Number of participants: 41 cohérent) entre les changements électrophysio- Research in Learning has a long history of cross- logiques des réflexes et les images en IRM ou fertilization of ideas between Statistics and Com- en optique de la moelle. Rick Hogue décrivit les puter Science, and the goal of this school was to principes physiques qui sous-tendent l’imagerie continue this rich and mutually beneficial tradi- par résonance magnétique. tion. This event was taught by and directed at Habib Benali expliqua que l’équipe IMPARABL Statistical and Machine Learners. The week be- développe des modèles mathématiques des pro- gan with a one-day introduction to key concepts cessus physiologiques cérébraux. Elle propose in statistical and machine learning. This intro- un modèle des processus hémodynamiques et duction was an opportunity to stress (and con- métaboliques mis en jeu lors de l’activation trast) the underlying philosophies of both dis- neuronale ; ce modèle comporte une trentaire ciplines. Several specific topics, originating in d’EDO. Frédéric Lesage ajouta qu’on voit émer- one of the two disciplines but containing sig- ger l’imagerie optique (IO) diffuse comme une nificant contributions from each area, were then nouvelle modalité, qui permet de mesurer les discussed in detail. Neural networks were cov- changements du volume sanguin dans les ré- ered during the second day, model-based clus- gions corticales du cerveau grâce à la transmis- tering during the third, support vector machines sion de la lumière dans les tissus biologiques. during the fourth, and manifold learning and L’utilisation du spectre infrarouge est promet- self-organizing maps during the fifth. Increas- teuse, mais elle pose le problème de la modé- ingly popular amongst machine learners, man- lisation de la propagation de la lumière et de ifold methods attempt to identify a nonlinear la reconstruction tomographique des images. La subspace (surface) in a high-dimensional space, modélisation de la propagation de la lumière est such that the data are all close to this sur- difficile car l’information sur la distribution spa- face. Connections of manifold methods to kernel tiale des tissus n’est pas souvent disponible. methods, which form the basis of support vector Après les présentations, les chercheurs ont eu machines, were also discussed. des échanges sur la complexité des problèmes The School was a tremendous success. The at- physiologiques du cerveau et de la moelle tendance remained mostly constant throughout épinière. Certains modèles comme ceux de the course of the workshop and initial feedback FitzHugh-Nagumo-Rinzel, évoqués par H. Be- from the participants was overwhelmingly pos- nali, sont utilisés aussi dans des applications itive. The computational labs were extremely cardiaques (tel que mentionné par Yves Bour- well received and were probably the most useful gault). Il serait très intéressant que l’équipe innovation with respect to the standard work- PhysNum et celle d’Yves Bourgault aient des in- shop model. The participants very much en- teractions. Les organisateurs de l’atelier pensent joyed applying what they learned during the lec- que l’objectif de sensibiliser les chercheurs du tures and the labs worked very well for learn- CRM a été atteint. D’autres échanges pourront ing and breaking up the day. Most of the par- avoir lieu afin de susciter l’intérêt des chercheurs ticipants knew some of the material presented, du CRM pour la problématique cérébrale et celle but very few (even among the speakers!) had de la moelle épinière. been exposed to all of the material; as a result many participants learned a great deal and began applying some new techniques to their own research at the end of the lab periods. The or-

43 CENTRE DE RECHERCHES MATHÉMATIQUES ganizers are very grateful to the Department cilities, which enhanced their ability to provide of Computer Science and Operations Research nice computing labs. (DIRO) for letting them use their computing fa-

44 CRM Prizes CENTRE DE RECHERCHES MATHÉMATIQUES

HE CRM created and administers, either alone or jointly, four of the eight major national prizes Tin the mathematical sciences, namely: the CRM – Fields – PIMS Prize, the Prize for Theoretical Physics awarded in collaboration with the Canadian Association of Physicists (CAP), the Prize for young researchers in Statistics awarded jointly with the Statistical Society of Canada (SSC), and the CRM Aisenstadt Prize awarded to rising young Canadian stars, selected by CRM’s Scientiﬁc Advi- sory Panel. The CRM has invested enormously in time, effort and in its own resources, to propel leading Canadian scientists into the spotlight, giving them international recognition when they most need it.

CRM – Fields – PIMS Prize 2006 Awarded to Nicole Tomczak-Jaegermann

Nicole Tomczak- NSERC and CMS committees, the Canada Coun- Jaegermann, this cil Killam Research Fellowship Committee, the year’s recipient, is Canada Research Chairs College of Reviewers, one of the world’s as well as the Scientiﬁc Board of BIRS. She has leading mathe- also served as the University of Alberta Site Di- maticians work- rector of PIMS and as Associate Editor of the ing in functional Canadian Journal of Mathematics and the Cana- analysis. She has dian Mathematical Bulletin. made outstanding contributions to inﬁnite- A detailed description of the achievements dimensional Banach space theory, asymptotic of Nicole Tomczak-Jaegermann may be found geometric analysis, and the interaction between in Le Bulletin du CRM (Spring 2006), at these two streams of modern functional analysis. the address www.crm.umontreal.ca/rapports/ She is one of the few mathematicians who have bulletin/bulletin12-1.pdf. contributed important results to both areas. In particular, her work constitutes an essential in- The CRM – Fields – PIMS Prize gredient in a solution by the 1998 Fields Medalist W.T. Gowers of the homogeneous space problem This prize was established in 1994 as the CRM – posed by Banach in 1932. Fields prize to recognize exceptional research Professor Tomczak-Jaegermann received her in the mathematical sciences in Canada. This is Master’s (1968) and Ph.D. (1974) degrees from one of the two most prestigious prizes in math- Warsaw University in Poland. She held a po- ematical sciences in Canada, in recognition of sition at Warsaw University from 1975 to 1983 exceptional research achievements over a whole and was visiting professor at Texas A&M Uni- career. In 2005, PIMS became an equal part- versity during 1981 – 1983. In 1983 she moved ner in the awarding of the prize and its name to the University of Alberta where she holds a was changed to the CRM – Fields – PIMS prize. Canada Research Chair in Geometric Analysis. A committee appointed by the three institutes She gave an invited lecture at the International chooses the recipient. The previous recipients of Congress of Mathematicians in 1998, is a Fel- the prize are H. S. M. (Donald) Coxeter (1995), low of the Royal Society of Canada, and received George A. Elliott (1996), James Arthur (1997), a Killam Research Fellowship and the Krieger- Robert V. Moody (1998), Stephen A. Cook (1999), Nelson Prize Lectureship of the Canadian Math- Israel Michael Sigal (2000), William T. Tutte ematical Society. She has served the Canadian (2001), John B. Friedlander (2002), John McKay research community, in particular by sitting on (2003), Edwin Perkins (2003), Donald A. Dawson (2004), and David Boyd (2005).

46 CRMPRIZES

André-Aisenstadt Prize 2006 Awarded Jointly to Iosif Polterovich and Tai-Peng Tsai

After obtaining his optimal partial regularity result for the incom- Master’s degree pressible Navier – Stokes equation. He proved from Moscow State an even more remarkable result, i.e., the non- University in 1995, existence of self-similar blow-up solutions (as Dr. Polterovich ob- proposed by Leray in 1934) with finite local tained his doctor- energy in three dimensions. Tsai has also em- ate from the Weiz- barked on a deep and detailed study of long- mann Institute in time asymptotics in nonlinear Schrödinger equa- 2000. Following postdoctoral experiences at tions with several coauthors. These papers re- the CRM, MSRI and the Max Planck Institute, veal a variety and subtlety of behaviours, and Dr. Polterovich accepted a tenure-track position are becoming quite influential. at the Université de Montréal, in 2002. A detailed description of the work of Iosif Dr. Polterovich works in geometric spectral the- Polterovich and Tai-Peng Tsai may be found ory, his broad variety of results being notable in Le Bulletin du CRM (Spring 2006), at for both their importance and novelty. Perhaps the address www.crm.umontreal.ca/rapports/ most exciting was Polterovich’s announcement bulletin/bulletin12-1.pdf. in 2000 of an “explicit” formula for the heat invariants of a Riemannian manifold; these ge- The André-Aisenstadt Prize ometric invariants had been studied for more than fifty years, yet Polterovich presented them Created in 1991, the André-Aisenstadt Mathe- in a striking and useful way, which will un- matics Prize is intended to recognize and re- doubtedly be central to much forthcoming re- ward research achievements in pure and ap- search by him and others. plied mathematics by talented young Canadian After completing his mathematicians. This prize consists of a $3,000 B.Sc. at the National award and a medal. The recipient is chosen by Taiwan University the CRM’s advisory committee. At the time of in 1991, Dr. Tsai ob- consideration, candidates must be Canadian cit- tained his Ph.D. from izens or permanent residents of Canada, and no the University of more than seven years from their Ph.D. Minnesota in 1998 The previous recipients of the André-Aisenstadt under the supervi- Prize are Niky Kamran (1992), Ian Putnam sion of Vladimir Sverak. Following a three-year (1993), Michael Ward (1995), Nigel Higson postdoc at the Courant Institute, and a further (1995), Adrian S. Lewis (1996), Lisa Jeffrey year at the Institute for Advanced Study, Dr. Tsai (1997), Henri Darmon (1997), Boris Khesin became an assistant professor at UBC in 2002. (1998), John Toth (1999), Changfeng Gui (2000), Dr. Tsai is an outstanding researcher in nonlin- Eckhard Meinrenken (2001), Jinyi Chen (2002), ear partial differential equations. In recent work Alexander Brudnyi (2003), Vinayak Vatsal with Kang and Gustafson, Tsai obtained the (2004), and Ravi Vakil (2005).

CAP – CRM Prize 2006 Awarded to John Harnad

The 2006 CAP – CRM Prize tems with a sound mastery of the geometrical as- was awarded to John Har- pects of the theory, his work has had, in the last nad (Concordia University), thirty years, a deep and lasting impact on our for his outstanding contribu- understanding of these subjects. tions to the theory of inte- After obtaining a B.Sc. from McGill University grable systems with connec- in 1967 and a M.Sc. from the University of Illi- tions to gauge theory, inverse nois in 1968, John Harnad did a D.Phil. in theo- scattering and random matri- retical physics at the University of Oxford un- ces. Combining a vivid intuition of physical sys- der the direction of Professor J.C. Taylor. Af-

47 CENTRE DE RECHERCHES MATHÉMATIQUES ter postdoctoral years at the E˝otv˝os Institute John Harnad’s most recent work is devoted to in Budapest and Carleton University in Ottawa the theory of random matrices. He and his col- (1972 – 1975), he became a research associate at laborators have established a relationship be- the CRM (1975 – 1984), and an associate profes- tween isomonodromic deformations and the sor at the Stevens Institute of Technology (1985 – spectral theory of random matrices. This en- 1986) and the École Polytechnique de Montréal abled them to establish connections between (1986 – 1989). He became a faculty member at isomonodromic tau functions, orthogonal and Concordia University in 1989 and is now the di- biorthogonal systems of polynomials associated rector of the Mathematical Physics Laboratory at to random matrices, and the corresponding cor- the CRM. relation functions. John Harnad has been invited to give a plenary lecture during the 2006 CAP He began his career as an elementary particle (Canadian Association of Physicists) Congress at physicist. Turning towards non-Abelian gauge Brock University in St. Catharines, Ontario (June theories, he developed, with collaborators and 11 – 14, 2006). students, the theory of dimensional reduction and applied it to obtain a great number of ex- A detailed description of the achievements act invariant solutions of the classical Yang – of John Harnad may be found in Le Bul- Mills equations and their supersymmetric exten- letin du CRM (Fall 2006), at the address sions. Those investigations are still quoted by www.crm.umontreal.ca/rapports/bulletin/ both mathematicians and physicists. bulletin12-2.pdf. Since the early 1980s, John Harnad has been mainly working on the theory of classical and quantum integrable systems and has become one of the world leaders in this field. Numerous The CAP – CRM Prize and important, his contributions include: nonlinear superposition formulas for certain types The Centre de recherches mathématiques (CRM) of nonlinear ordinary differential equations that and the Canadian Association of Physicists later turned out to figure as Bäcklund transfor- (CAP) created in 1995, on the occasion of the mations for soliton type equations; the introduc- 50th anniversary of the CAP, a joint prize for rec- tion of the soliton correlation matrix in soliton ognizing exceptional achievements in theoreti- theory, relating the inverse spectral approach to cal and mathematical physics. The prize consits the holonomic quantum field approach of Sato of a $2,000 award and a medal. et al.; the Hamiltonian theory of quasi-periodic The previous recipients of the prize are Werner solutions of integrable partial differential equa- Israel (1995), William G. Unruh (1996), Ian tions and the introduction of spectral Darboux Affleck (1997), J. Richard Bond (1998), David coordinates; the introduction of “dual isomon- J. Rowe (1999), Gordon W. Semenoff (2000), odromic deformations” in the general frame- André-Marie Tremblay (2001), Pavel Winternitz work of the Hamiltonian theory of isomon- (2002), Matthew Choptuik (2003), Jiˇrí Patera odromic deformations. (2004), and Robert C. Myers (2005).

CRM – SSC Prize 2006 Awarded to Jeﬀrey Rosenthal

Jeffrey Rosenthal, Profes- in this area. Jeffrey Rosenthal is a powerful re- sor in the Department of searcher, gifted with a natural ability to explain Statistics at the University difﬁcult concepts. His extensive collaborations of Toronto, is the 2006 win- reﬂect his expansive interests and his emphasis ner of the CRM – SSC prize. on practical aspects of theoretical results. Dr. Rosenthal’s elegant and Jeffrey Rosenthal received his B.Sc. from the Uni- landmark results set him as versity of Toronto in 1988, and his M.A. (1990) one of the leaders in the and Ph.D. (1992) from Harvard University. His development of Markov Chain Monte Carlo Ph.D. supervisor was Persi Diaconis and it was methods. Within 15 years of his Ph.D., Jeffrey at Harvard that Jeffrey Rosenthal’s interest in ap- Rosenthal has made outstanding contributions plications and practical issues was piqued. In to asymptotic theory related to Markov pro- a series of elegant papers rich in mathemati- cesses and, with great insight and ingenuity, to cal analysis, Jeffrey Rosenthal has studied con- clarifying the practical implications of the theory

48 CRMPRIZES vergence rates of MCMC algorithms for hybrid the address www.crm.umontreal.ca/rapports/ samplers, slice samplers, time-inhomogeneous bulletin/bulletin12-2.pdf. chains and time-sampled chains. He has published several key theoretical papers in the An- The CRM – SSC Prize nals of Applied Probability, the Annals of Probabil- ity, the Annals of Statistics, and Advances in Ap- The SSC, founded in 1977, is dedicated to the plied Mathematics, while papers in the Journal of promotion of excellence in statistical research the American Statistical Association, Statistical Sci- and practice. This prestigious award, jointly ence and the SIAM Review pay great attention to sponsored by the SSC and the Centre de recher- practical issues. Jeffrey Rosenthal has received ches mathématiques (CRM), is given each year many honours and awards over his career, in- to a Canadian statistician in recognition of out- cluding his election as IMS Fellow in 2005. standing contributions to the discipline during the recipient’s ﬁrst 15 years after earning a doc- This announcement of the 2006 CRM – SSC Prize torate. was made at University of Western Ontario in London, site of this year’s Annual Meeting of Jeffrey Rosenthal is the eighth recipient of the the Statistical Society of Canada. A detailed de- CRM – SSC Prize. The previous winners of the scription of the work of Jeffrey Rosenthal may award are Christian Genest (1999), Robert J. Tib- be found in Le Bulletin du CRM (Fall 2006), at shirani (2000), Colleen D. Cutler (2001), Larry A. Wasserman (2002), Charmaine B. Dean (2003), Randy Sitter (2004), and Jiahua Chen (2005).

49 CRM Outreach Program CRMOUTREACH PROGRAM

HE CRM is eager to fulﬁll the public’s desire for understanding the latest developments in the Tmathematical sciences. To this end, the CRM initiated in the spring of 2006 a series of lectures called the Grandes Conférences du CRM, which will feature outstanding lecturers able to convey the beauty and power of mathematical research to a wide audience. This year two lecturers were invited within the framework of this new outreach program, Jean-Marie De Koninck and Ivar Ekeland.

Jean-Marie De Koninck

The first lec- on Canal Z, Canal Savoir and TFO. He is also a ture in the se- regular guest on many scientific radio and tele- ries of Grandes vision programs, and whenever he is invited to Conférences du do so, his enthusiasm and talent for populariza- CRM took place tion of mathematics and science allows him to on Wednesday, reach the general public. Thanks to Jean-Marie March 29, at 8PM De Koninck, the drivers of Quebec can learn in the Pavillon about the Riemann hypothesis while fighting Jean-Coutu of the Université de Montréal. The morning traffic! speaker was Jean-Marie De Koninck of Uni- Jean-Marie De Koninck’s lecture was followed versité Laval, a mathematician well-known for by more than 250 people, among them, of course, his scientific achievements and for his involve- his fellow mathematicians, but also students at ment in the introduction of mathematics to a all levels (university, CEGEP, high school), and general audience. In 2005, Jean-Marie De Kon- scientists from many disciplines. His talk, enti- inck received the “Scientifique de l’année” Prize tled When reality outplays intuition, focused on from the Société Radio-Canada, which has rec- certain mathematical questions where intuition ognized, for twenty years, the involvement and can be misleading, such as the famous Birth- achievements of a Québec scientist. It was the day Paradox. If we want to invite enough peo- first time that this honor was awarded to a math- ple to guarantee that two of them were born the ematician. The jury of the Prize wanted to ac- same day of the year, we need of course 367 knowledge the involvement of Jean-Marie De persons (let’s not forget leap years!). But if we Koninck in the project Sciences et mathématiques only want to achieve a 50% probability that two en action (SMAC). The Web site of the project, guests have the same birthday, it is enough to and the humoristic Show Math presented to more invite 23 guests. And if we invite 60 guests, the than 3000 high school students, illustrate the use probability of having two guests with the same of mathematics in everyday life. This prize is birthday is greater than 99%! With several simi- only one of the numerous distinctions awarded lar examples from geometry, number theory and to Jean-Marie De Koninck in the course of his probability, Jean-Marie De Koninck showed how career; other distinctions include the Order of intuition can mislead us. Canada in 1994, the National Order of Quebec in 1999, and the Adrien-Pouliot Prize of the Cana- Jean-Marie De Koninck concluded his lecture dian Mathematical Society in 2004. by a problem that still concerns researchers in number theory, namely a well-known conjecture Jean-Marie De Koninck is a well-known figure posed by Hardy and Littlewood in 1922. Accord- in Quebec: since 1976, he has been a sports ana- ing to this conjecture, there are infinitely many lyst for the Olympic games swimming competi- twin primes, i.e., primes p such that p + 2 is tions and other sports events at Radio-Canada, also a prime, for example 5 and 7, 11 and 13, and he is also the founder of Opération Nez or 101 and 103. We can generalise this conjec- Rouge, which was launched in Quebec City in ture to triplets of prime numbers, for example 1984 to prevent car accidents caused by drinking primes p such that p + 2 and p + 6 are also prime, and driving in the holiday season. This highly for instance 11, 13 and 17, or 41, 43 and 47. We original and efficient program then spread to can also generalize the conjecture to quadruplets every region of Quebec, and has now crossed of prime numbers, and so on. The Generalised national boundaries; indeed, similar programs Twin Prime conjecture of Hardy and Littlewood have been adopted in France, Switzerland and contains all those particular cases. Even if no Portugal. In 2000 and 2001, Jean-Marie De Kon- case of the conjecture has been solved, there is inck was also the host of 29 installments of the a lot of evidence, both theoretical and computa- television show C’est mathématique!, which aired tional, for the validity of the conjecture.

51 CENTRE DE RECHERCHES MATHÉMATIQUES

Another conjecture of Hardy and Littlewood misleading? We can now show that if the Gener- says that the function π(x), which represents the alised Twin Prime conjecture is true (this is what number of primes at most equal to x, is convex, most of the experts believe), then there exists an i.e., there are always more primes in the inter- interval [x0, x0 + 4893] containing more primes val [1, y] than in any of the intervals [x, x + y] for than the interval [1, 4893]. But we can also esti- any value of x. In this case also, computer test- mate empirically that to write x0, between 1057 ing seems to indicate the validity of the conjec- and 1590 decimal digits are necessary! ture. But it was shown in 1973 by Hensley and With his lecture, Jean-Marie De Koninck suc- Richards that the two conjectures of Hardy and ceeded once more in his role as ambassador of Littlewood are incompatible, which means that mathematics to the wide audience attending his both cannot be true! How can our intuition be so talk, while intriguing his fellow mathematicians.

Ivar Ekeland

On May the 4th 2006, at both questions at the same time through his vari- the IBM amphitheater of the ational principle of least action. École des HÉC de Montréal, As pointed out by our lecturer, this principle Professor Ivar Ekeland de- found its origin in the theory of light. Already in livered to a large and en- Antiquity, Hero of Alexandria had derived the thusiastic audience the sec- law of reflection by assuming that light follows ond of the Grandes Conférences a path of minimal length. In the 17th Century, du CRM. This distinguished Descartes thought he had proved the law of re- mathematician, who has been the Director of fraction, wrongly so, though, since he had at- PIMS since 2003, holds a Canada Research Chair tributed light a greater speed in water than in in Mathematical Economics at UBC. Educated at air! Assuming the opposite, Fermat managed to the École Normale, he taught at the Université recover this law by assuming that light travels de Paris-Dauphine from 1970 to 2003 and was from one point to another in such a way as to its President from 1989 to 1994. He was also the minimize the time spent. Director of the Centre de Recherche en Mathé- matiques de la Décision and the Institut Finance According to Maupertuis, light follows neither Dauphine. His scientific achievements were ac- the shortest, nor the fastest path: it travels so as knowledged with prizes from the Académie des to minimize the action, an ill-defined quantity Sciences de Paris, the Société Mathématique de that he chose in such a way as to recover the France as well as the Académie des Sciences de law of refraction when using Descartes’ wrong Belgique. assumption about the speed of light. Such a du- bious achievement could hardly have secured Anxious to reach a large audience, he wrote Maupertuis immortality, had he not decided to books of popularization and personal thoughts, generalize his principle of least action so that all such as Le calcul, l’imprévu and Au hasard, for the laws of classical mechanics could be derived which he was awarded the Prix Jean-Rostand from it. According to this principle, amongst of the Association des Écrivains Scientifiques de all possible paths nature chooses precisely that France and the Prix d’Alembert of the Société one for which action is a minimum, a notion Mathématique de France. His May 4th lecture that seems to ascribe a decisional power to na- borrowed the title of his latest book, Le meilleur ture. Maupertuis quickly took the step that led des mondes possibles. him to conclude that his principle is a bridge Ekeland started his lecture by drawing a par- between physics and metaphysics. Indeed, he allel between the fate of la Sagouine, Antonine writes: “Once it is known that all the laws of Maillet’s character, who wonders why the world motion stem from the principle of the best, one is the way it is, and that of Archimedes, who, cannot doubt that they have been settled by an for the sheer sake of science, wonders how the almighty Being full of wisdom.” world is. Why and how, two drastically differ- Maupertuis suffered a miserable end. Koenig, ent questionings that did, nevertheless, intersect once a friend, claimed that Leibniz had stated at a given point of History, when, in 1744, Pierre the principle of least action before Maupertuis Moreau de Maupertuis fancied he could answer in a letter that he was unable to find again. Mau- pertuis’ reaction triggered a quarrel followed by

52 CRMOUTREACH PROGRAM a flood of lampoons. Voltaire intervened and left rapidly the situation in other fields. He men- posterity a ridiculous image of Maupertuis and tioned Darwin, according to whom perfection Leibniz in L’histoire du docteur Akakia and Can- is not absolute since a species may be perfectly dide. Still, although incompetent at physics and well adapted here without being so elsewhere, mathematics, Maupertuis had had a right intuti- as well as Hayek, an economist for whom the tion. It would fall to Euler and Lagrange to de- best is the enemy of the good. And he con- fine action correctly and to formulate the vari- cluded very wisely that both Archimedes and ational principle that makes it stationary. The la Sagouine would have advantage to meet: he metaphysical dimension would be cast aside. would encourage her to think on her own, while Physics gives us no reason to think that our she would convince him that he should commu- world is organized in view of a given end, or nicate better and ponder over real problems. A that is is better or worse than any other world. piece of advice she could certainly not give Ivar At the end of his talk, Ivar Ekeland reviewed Ekeland: his talk, full of stimulating thoughts, was a real tour de force: not a single equation!

53 CRM Partnerships CRMPARTNERSHIPS

HE CRM is strongly committed to its national mission and takes measures to ensure that as many TCanadian scientists as possible benefit from its activities and become involved in their planning. For instance, it appoints to its Scientific Advisory Committee eminent Canadian scientists from various parts of the country; it is present in all important forums where the future directions of the Cana- dian mathematical sciences are discussed; it urges its organizers to ensure that Canadian specialists are included in their activities; it organizes and supports scientific events across the country; it collaborates with Canadian institutes, societies and associations. A specific budget is set aside each year for the participation of Canadian graduate students in its programs. The CRM is the only national institute that operates in the two official languages of Canada and it is highly visible on the international scene. In keeping with its national role, it coordinates its activities with the Fields Institute, PIMS, the Canadian Mathematical Society (CMS), MITACS, the Canadian Applied and Industrial Mathematics Society (CAIMS), the Statistical Society of Canada (SSC), the Canadian Association of Physicists (CAP), as well as with other societies and institutes abroad.

CRM Partners

The Fields Institute (FI) and the Pacific two series of joint publications, the CRM Mono- Institute for the Mathematical Sciences graph Series and the CRM Proceedings and Lec- (PIMS) ture Notes Series. Two CRM series, in statistics and in mathematical physics, are published by Since the early 1990s two other research insti- Springer. The CRM has exchange agreements tutes have joined the CRM on the Canadian with the Fields Institute, PIMS, MSRI, the Insti- scene: Toronto’s Fields Institute (FI) and the tute for Mathematics and its Applications (IMA), Pacific Institute for the Mathematical Sciences the École Normale Supérieure (France), the Isaac (PIMS). As well as coordinating their scien- Newton Institute, the Institut des Hautes Études tific activities, the three institutes have worked Scientifiques (IHÉS, France), and BIRS. closely on a variety of initiatives, the most important of which is the Mathematics of Infor- Associations and Professional Societies mation Technology and Complex Systems network (MITACS). The three institutes were also The CRM maintains close ties with the different involved in other initiatives, such as the CRM – professional societies in the mathematical sci- Fields Prize awarded in recognition of outstand- ences: CMS, CAIMS, SSC and CAP. The presi- ing accomplishments in the mathematical sci- dent of the CMS is an ex-officio member of the ences in Canada. It was created in 1994 and in CRM Scientific Advisory Committee. The CRM 2006 became the CRM – Fields – PIMS Prize. The also supports financially certain initiatives of the administrative responsibility for this prize will CMS, such as the mathematical camps. Together rotate between the three institutes. with the other institutes, the CRM organizes or sponsors special sessions at the CMS, CAIMS International and National Collaborations and SSC meetings. The CRM awards a prize each year jointly with the SSC; similarly, it awards a In 2005 – 2006, the CRM collaborated with or prize each year with the CAP in mathematical received financial assistance from the follow- and theoretical physics. ing institutions: the National Science Founda- tion (NSF), INSERM (Paris), the Clay Founda- The Mathematics of Information Technol- tion, DIMATIA (Prague), IBM, INRIA, the AL- ogy and Complex Systems Network (MI- GANT programme, École Nationale des Ponts et TACS) Chaussées, Mathematical Sciences Research In- stitute (MSRI), the University of Havana (Cuba), MITACS was conceived by the three Cana- the Banff International Research Station (BIRS), dian mathematical sciences institutes. They en- the Groupe d’études et de recherche en analyse visioned a pan-Canadian network of projects des décisions (GERAD), and the Regroupement each using sophisticated mathematical tools for québécois sur les matériaux de pointe (RQMP). modelling industrial problems in key sectors of In its publishing activities, the CRM is contin- the Canadian economy. MITACS was officially uing its partnership with the American Mathe- launched on February 19, 1999. By March 1999, matical Society (AMS), in particular through its all 21 initial research projects were under way.

55 CENTRE DE RECHERCHES MATHÉMATIQUES

MITACS leads Canada’s effort in the genera- gram by the institutes. The National Program tion, application and commercialization of new was conceived as a model for a national net- mathematical tools and methodologies within a work in the statistical sciences, in partnership world-class research program. The network ini- with the mathematics institutes. The broad goal tiates and fosters linkages with industrial, gov- of the proposal is to foster nationally coordi- ernmental, and not-for-profit organizations that nated projects with substantial interactions with require mathematical technologies to deal with the large community of scientists involved in problems of strategic importance to Canada. MI- the analysis of complex data sets, and to estab- TACS is driving the recruiting, training, and lish a framework for the national networking placement of a new generation of personnel of research activities in the statistical commu- with highly mathematical skills that is vital to nity. The original proposal targeted the develop- Canada’s future social and economic well-being. ment and application of statistical methods for MITACS creates links between academia, indus- the analysis of data obtained from complex sur- try and the public sector to develop cutting edge vey sample designs and longitudinal biological, mathematical tools vital to a knowledge-based epidemiological and medical studies. More spe- economy. The only Network of Centres of Excel- cific objectives of the program include the de- lence (NCE) for the mathematical sciences, MI- velopment of collaborations between university TACS currently has 305 scientists, 611 students and extra-university researchers, and the provi- and 169 partner organizations working on 32 on- sion of training for graduate students in impor- going projects, involving 48 Canadian universi- tant scientific areas through these collaborations. ties. To improve Canada’s international compet- itiveness, MITACS research focuses on five key NPCDS Projects sectors of the economy: Statistical Methods for Complex Survey Data • biomedical and health; Project Leader: Changbao Wu (Waterloo) • environment and natural resources; Canadian Consortium on Statistical Genomics • information processing; Project Leader: Rafal Kustra (Toronto) • risk and finance; • communication, networks and security. Data Mining with Complex Data Structures Project Leaders: Hugh Chipman (Acadia), Anto- MITACS Inc. is a federally incorporated not-for- nio Ciampi (McGill), Theodora Kourti (McMas- profit society formed to administer the MITACS ter), Helmut Kröger (Laval) Network of Centres of Excellence. MITACS also gives financial support to some Design and Analysis of Computer Experiments events organized by the CRM and other infor Complex Systems stitutions. For instance, in 2005 – 2006, it gave Project Leader: Derek Bingham (Simon Fraser) support to three workshops partially sponsored Forests, Fires and Stochastic Modeling by the CRM, whose reports are included in Project Leaders: John Braun (Western Ontario), the section on the CRM multidisciplinary and Charmaine Dean (Simon Fraser), Dave Martell industrial program: the Fifth Summer School (Toronto) in Quantum Computing, the MITACS – MSRI – AFMnet – CRM Workshop on Therapeutic Effi- NPCDS Workshops cacy in Population Veterinary Medicine, and the NPCDS/MITACS Spring School on Statistical Workshop on Spatial/Temporal Modeling for and Machine Learning. Marine Ecosystems August 17 – 19, 2005, Dalhousie University Organizers: Mike Dowd (Dalhousie), Chris Field National Program on Complex Data Struc- (Dalhousie), Joanna Mills Fleming (Dalhousie) tures (NPCDS) Workshop on Current Issues in the Analysis of Incomplete Longitudinal Data This initiative was developed in partnership October 13 – 15, 2005, Fields Institute with the three mathematical sciences insti- Organizers: Peter Song (Waterloo), Michal Abra- tutes and the reallocations committee during hamowicz (McGill), Richard Cook (Waterloo), the recently completed reallocations exercise at Paul Gustafson (UBC), Liqun Wang (Manitoba) NSERC. The program was funded by NSERC for four years for a total of $687,000. An addi- Workshop on Data Mining tional $200,000 has been committed to the pro- November 10 – 12, 2005, Fields Institute

56 CRMPARTNERSHIPS

Organizers: Hugh Chipman (Acadia), Antonio August 17 – 19, 2005, Dalhousie University Ciampi (McGill), Theodora Kourti (McMaster), Organizers: Mike Dowd (Dalhousie), Chris Field Helmut Kröger (Laval), Michael Vainder (Gen- (Dalhousie), Joanna Mills Fleming (Dalhousie) eration 5) APICS 2005: Symposium on Graph Theory and NPCDS/MITACS Spring School on Statistical Combinatorics and Machine Learning: Topics at the Interface October 21 – 23, 2005, Acadia University May 23 – 27, 2006, CRM Organizer: Nancy Clarke (Acadia) Organizers: Yoshua Bengio (Montréal), Hugh A. APICS 2005: Workshop on Robust and Compu- Chipman (Acadia), Russell Steele (McGill) tationally Intensive Statistical Models Atlantic Association for Research in the October 21 – 23, 2005, Acadia University Organizer: Hugh Chipman (Acadia) Mathematical Sciences (AARMS) Atlantic Analysis Days AARMS was founded in March 1997 at a time January 20 – 21, 2006, Dalhousie University when the National Network for Research in the Organizer: John Borwein (Dalhousie) Mathematical Sciences was being discussed and East Coast Combinatorics Conference planned. AARMS exists to encourage and ad- April 1-2, 2006, University of Prince Edward Is- vance research in all mathematical sciences, in- land cluding statistics and computer science, in the Organizer: Shannon Fitzpatrick (Prince Edward Atlantic region. In addition, AARMS acts as a Island) regional voice in discussions of the mathematical sciences on a national level. Since its incep- Atlantic Canada General Relativity Meeting tion, AARMS has played an important role in the University of New Brunswick, May 5 – 7, 2006 research activities in the Atlantic region, spon- Organizers: Arundhati Dasgupta (New soring or co-sponsoring numerous meetings and Brunswick), Jack Gegenberg (New Brunswick), workshops. In the summer of 2002, AARMS Robert McKellar (New Brunswick) initiated an annual Summer School for graduate students and promising undergraduates. AARMS is grateful to Canada’s three mathemat- Academic Partners ical institutes, the Centre de recherches mathé- All the activity of the CRM rests on a solid ba- matiques, the Fields Institute, and the Pacific In- sis of cooperation with universities in the region, stitute for the Mathematical Sciences, as well as in particular the Montréal universities, and most to the member universities, for providing fund- particularly the Université de Montréal, whose ing for its activities. Its member universities are support for the CRM has been unfailing. The Acadia University, Dalhousie University, Memo- Université de Montréal releases five of its fac- rial University, Mount Allison University, Saint ulty members to work at the CRM each year, and Francis Xavier University, Saint Mary’s Univer- the support of these faculty members is an es- sity, the University of New Brunswick and the sential asset for the CRM’s scientific activities. University of Prince Edward Island. There is in addition a regular program of teach- AARMS Scientific Activities ing releases with the other Montréal universities, bringing the equivalent of another two po- Sixth Annual Bluenose Numerical Analysis Day sitions to the CRM each year. On an ad-hoc ba- June 10, 2005, Cape Breton University sis linked to the thematic program, the CRM has Organizer: Shaohua George Chen (Cape Breton) also been arranging the release of research per- AARMS Summer School 2005 sonnel from nearby universities such as Laval, July 17 – August 14, 2005, Dalhousie University Sherbrooke, Queen’s and Ottawa. The partner- Organizers: Renzo Piccinini (Milano-Bicocca), ships of the CRM with the other research insti- Tony Thompson (Dalhousie) tutes in the Montréal area have been very prof- itable. Christopher Field Retirement Symposium With the financial support of the Université August 15, 2005, Dalhousie University de Montréal, McGill University, the Université Organizers: Joanna Mills Fleming (Dalhousie), du Québec à Montréal, Concordia University, David Hamilton (Dalhousie) and Université Laval, as well as grants from NPCDS Workshop: Spatial/Temporal Modeling NSERC and the Fonds québécois de recherche for Marine Ecosystems sur la nature et les technologies (FQRNT), the

57 CENTRE DE RECHERCHES MATHÉMATIQUES

CRM finances the activities of its eight laborato- More information on this workshop may be ries, which collectively represent the most active found in the “General Program” section of this branches of the mathematical sciences. These report. laboratories are the perfect illustration of scientific vitality and serve to feed the national and Network for Computing and Mathematical international scientific programs of the CRM. Modeling (ncm2) Please refer to the section “Research Laborato- ries” for reports describing the activities of each The CRM is one of the founding members of of these laboratories. the Network for Computing and Mathemati- cal Modeling (ncm2), a network created by several research centres in order to respond to Association with the University of Ottawa the needs of industry in fields related to computing and mathematical modeling. The re- In 2003, the Department of Mathematics and search of the network focuses on five major Statistics of the University of Ottawa became a themes: risk management, information process- member of the Centre de recherches mathéma- ing, imaging and parallel computing, transport tiques (CRM). In partnership with the Univer- and telecommunications, and health and elec- sity of Ottawa, the CRM co-finances the CRM – tronic commerce. The ncm was founded by University of Ottawa Distinguished Lecture Series, 2 the CRM, the Centre de recherche en calcul postdoctoral fellowships, and teaching releases appliqué (CERCA), the Center for Interuniver- so that University of Ottawa faculty members sity Research and Analysis of Organizations can undertake research with colleagues in the (CIRANO), the Center for Research on Trans- CRM’s laboratories or participate in CRM scien- portation (CRT), and the Group for Research in tific activities. The activities below were made Decision Analysis (GERAD). Since then, three possible through sponsorship by the CRM. new members have joined the network: the Co- operative Centre for Research in Mesometeo- CRM – University of Ottawa Distinguished Lec- rology (CCRM), the Centre de Recherche Infor- ture Series matique de Montréal (CRIM), and the Institut National de la Recherche Scientifique-Énergie, The series features talks by prominent mathe- Matériaux et Télécommunications (INRS-EMT). maticians from Canada and abroad on topics at the forefront of today’s mathematical research. Laboratoires universitaires Bell (LUB) Cocycles and cocycle categories Rick Jardine (University of Western Ontario), The CRM is an active participant in Laboratoires October 21, 2005 universitaires Bell, a joint project between the ncm2 and Bell. The goal of the Laboratories is to Algebraic Topology as a Tool for the Analysis of High- make innovations in the field of multimedia re- Dimensional Data search and applications (mainly interactive ap- Gunnar Carlsson (Stanford University), Febru- plications aimed at the general public, electronic ary 10, 2006 commerce applications and new generations of Putting a Match to Square Ice networks), as well as to promote the training of a Georgia Benkart (University of Wisconsin at highly qualified, international calibre workforce Madison), March 24, 2006 in these areas. Coupled Systems: Theory and Examples Québec Neuroimaging Initiative (RNQ) Marty Golubitsky (University of Houston), April 28, 2006 In recent years, CRM’s PhysNum laboratory has developed a strong collaborative network with various partners in neuroimaging in the Workshop on Probabilistic Symmetries and Montréal area. This network became an offi- Their Applications cially recognized network with the founding May 15 – 17, 2006, University of Ottawa of the “Regroupement Neuro-imagerie Québec” Sponsored by the Fields Institute, the University (RNQ), under the umbrella of the Institut Uni- of Ottawa and the CRM versitaire de Gériatrie in Montréal. RNQ, with Organizers: Gail Ivanoff (Ottawa), Raluca its 70 researchers, has recently purchased some Balan (Ottawa) key equipment in neuroimaging thanks to a very

58 CRMPARTNERSHIPS large grant ($11M). One of the strongest alliances with the INSERM laboratory for brain imaging of the CRM within that network is its association at Jussieu – La Salpêtrière (Paris), whose director is Dr. Habib Benali.

Joint Initiatives

The annual meetings of the CMS, SSC and Complex Variables CAIMS, as well as some of their training and Organizers: Thomas Bloom (Toronto), Paul Gau- promotion activities, are jointly sponsored by thier (Montréal) the CRM, the Fields Institute, PIMS and MI- Discrete and Computational Geometry TACS. The reader will find below brief sum- Organizers: Leroy J. Dickey (Waterloo), Asia Ivic maries of the meetings that took place in 2005 – Weiss (York) 2006, as well as a report on the 17th Canadian Conference on Computational Geometry. Dynamical Systems Organizers: Sue Ann Campbell (Waterloo), Yum- ing Chen (Wilfrid Laurier), Huaiping Zhu (York) CMS/CSHPM Summer 2005 Meeting June 4 – 6, 2005, University of Waterloo Exploratory Classroom Problems in Calculus Organizer: Peter Taylor (Queen’s) Meeting director: Alexandru Nica (Waterloo) Functional Equations and Their Applications The Summer 2005 Meeting of the Canadian Organizers: Janos Aczel, Che-Tat Ng (Waterloo) Mathematical Society welcomed a record number of 540 participants — the first meeting to General Topology and Its Applications have more than 500 participants. This was a joint Organizers: E.D. Tymchatyn (Saskatoon), A. meeting with CSHPM (the Canadian Society for Karassev, M. Tuncali, V. Valov (Nipissing) the History and Philosophy of Mathematics). Geometric Topology The public lecture was given by Moshe Milevsky Organizers: Hans Boden (McMaster), Doug Park, from York University and was titled The math- Mainak Poddar (Waterloo) ematics of silly investment strategies, or how to win the Globe and Mail’s stock picking contest. History and Philosophy of Mathematics The plenary speakers were Len Berggren (Si- (CSHPM Session) mon Fraser), Keith Devlin (Stanford), Dan Freed Organizer: Duncan Melville (St. Lawrence) (Texas at Austin), Robert McCann (Toronto), An- History of Mathematics from Medieval Islam to drei Okounkov (Princeton), Gilles Pisier (Paris 6 Renaissance Europe (CSHPM Session) and Texas A&M), and Ken Ribet (Berkeley). Organizers: Rob Bradley (Adelphi), Glen van The CMS was pleased to present lectures from Brummelen (Bennington College) its research prize winners, namely, the Krieger – Invariant Theory and Differential Geometry Nelson Prize Lecture, given by Barbara Lee Key- Organizers: Ray MacLenaghan (Waterloo), Ro- fitz (Fields Institute and the University of Hous- man Smirnov (Dalhousie) ton), and the Jeffery-Williams Lecture, given jointly by Edward Bierstone and Pierre Mil- L-Functions and Algebraic Curves man (both from the University of Toronto). The Organizers: Yu-Ru Liu, David McKinnon, CMS Excellence in Teaching Lecture was given Michael Rubinstein (Waterloo) by Philip Loewen (UBC). The meeting hosted Mathematical Aspects of Quantum Information a record number of 23 parallel special sessions, Organizers: Daniel Gottesman (Perimeter), covering a wide range of mathematical research Achim Kempf (Waterloo), David Kribs (Guelph), interests, and also aspects of mathematics educa- Mike Mosca (Waterloo) tion and of the history and philosophy of mathematics. The special sessions and their organizers Mathematics from Ancient to Modern Times may be found below. Organizers: Richard O’Lander, Ronald Sklar (St John’s) Automatic Sequences and Related Topics Organizers: Jean-Paul Allouche (Orsay), Jeffrey Mathematics of Actuarial Finance Shallit (Waterloo) Organizer: Tom Salisbury (York & Fields Insti- tute) Combinatorics and Geometry Organizer: Ian Goulden (Waterloo)

59 CENTRE DE RECHERCHES MATHÉMATIQUES

Mathematics of Computer Algebra and Analysis the CRM – SSC Award Address by Jiahua Chen Organizers: Keith Geddes, Mark Giesbrecht, (Waterloo). The Pierre-Robillard Award Address George Labahn, Arne Storjohann (Waterloo) was given by Zeny Zhe-Qing Feng (Waterloo & Yale), and the Canadian Journal of Statistics Award Nonlinear Partial Differential Equations Address was given by Naomi S. Altman (Penn Organizers: Robert McCann (Toronto), Walter State) and Julio C. Villarreal (Cornell). The Spe- Craig (McMaster), Catherine Sulem (Toronto) cial Invited Addresses of the Sections were given Operator Algebras, Operator Spaces and Har- by Jerry Lawless (Waterloo), Randy Sitter (Si- monic Analysis mon Fraser) and Gerald van Belle (University of Organizers: Ken Davidson, Brian Forrest (Water- Washington). loo) Random Graphs and Their Applications CAIMS Annual Meeting 2005 Organizers: Anthony Bonato (Wilfrid Laurier), June 16-18, 2005, University of Manitoba Penny Haxell, Nicholas Wormald (Waterloo) Organizers: Abba Gumel (Manitoba), Rob Representation Theory McLeod (Manitoba) Organizer: Wentang Kuo (Waterloo) This meeting featured six themes, each of which String Theory and Integrable Systems was addressed by a plenary speaker. Here are Organizers: Lisa Jeffrey (Toronto), Boris Khesin the themes, with the names of the plenary speak- (Toronto), Rob Myers (Perimeter Institute) ers within parentheses: dynamical systems and mathematical biology (Michael Mackey, McGill); Contributed Papers Session signal processing (Simon Haykin, McMaster); Organizer: Peter Hoffman (Waterloo) mathematics in industry (Heinz Engl, Austrian The Meeting Committee gratefully acknowl- Academy of Sciences, and Sam Howison, Ox- edges the support of the following institutions: ford); bioinformatics (Ruben Zamar, UBC); com- the University of Waterloo (Faculty of Mathe- putational mathematics (Sebastian Reich, Im- matics and Department of Pure Mathematics), perial College); pattern recognition (Tin Kam the CRM, the Fields Institute, MITACS, PIMS, Ho, Bell Laboratories). The Research Prize Lec- A.K. Peters, the Institute for Quantum Comput- ture was given by Michel Fortin (Laval), and ing (IQC), Springer, the University of Guelph, two Doctoral Dissertation Award Lectures were and Queen’s University (Department of Mathe- given by Ovidiu Voitcu (Alberta) and Lindsay matics and Statistics). Anderson (Western Ontario), respectively. The CAIMS meeting also featured contributed lectures and 32 invited lectures. The meeting was Annual Meeting of the Statistical Society sponsored by the University of Manitoba (in- of Canada cluding the Institute of Industrial Mathematical June 12 – 15, 2005, University of Saskatchewan Sciences), the CRM, the Fields Institute, PIMS, MITACS and Western Economic Diversiﬁcation Organizers: Program Committee Chair, Augus- Canada. tine Wong (York); Biostatistics Section, Gordon Fick (Calgary); Business and Industrial Statistics Section, Stefan Steiner (Waterloo); Survey Meth- 17th Canadian Conference on Computa- ods Section, Changbao Wu (Waterloo) tional Geometry August 10-12, 2005, University of Windsor The thirty-third Annual Meeting of the Statisti- cal Society of Canada has brought together re- Organizer: Asish Mukhopadhyay (Windsor) searchers in statistics and probability and users Computational Geometry deals with geometric from academia, government and industry. The problems from an algorithmic point of view. The meeting featured three workshops, some 40 in- Canadian Conference on Computational Geom- vited paper sessions and a number of con- etry has played a pioneering role in the nur- tributed paper sessions. SSC 2005 was sponsored ture and development of this area. The num- by the CRM, the Fields Institute, PIMS, MITACS, ber of attendees at the 17th Canadian Confer- the University of Saskatchewan, AON Consult- ence on Computational Geometry was 91, with ing, MyTravel Sinfonia and W.H. Freeman. students accounting for nearly a third of the to- The Presidential Invited Address was given by tal. A total of 75 papers were accepted for pre- Barbara Lee Keyﬁtz (Fields Institute), the Gold sentation at the Conference. The presentations Medal Address by Keith Worsley (McGill) and were organized into two parallel sessions with

60 CRMPARTNERSHIPS each presentation lasting 20 minutes, includ- Discrete and Convex Geometry ing a question period. The main highlights of Organizers: Karoly Bezdek (Calgary), Jozsef Soly- the Conference were three invited talks, one on mosi (UBC) each day of the Conference, and an open prob- Ergodic Theory lems session, chaired by Erik Demaine (MIT) Organizers: Christopher Bose (Victoria), Andres and Joseph O’Rourke (Smith College). The ﬁrst del Junco (Toronto) invited talk was by Jeffe Erickson (Illinois at Urbana-Champaign). Dr. Erickson spoke about Graph Theory computing optimal graph structures in topo- Organizers: Jing Huang (Victoria), Kieka Myn- logical spaces and posed a host of interesting hardt (Victoria), Wendy Myrvold (Victoria) open problems. The second invited talk was History of Mathematics the Erd˝osmemorial lecture by Joseph O’Rourke Organizer: Len Berggren (Simon Fraser) (Smith College). Dr. O’Rourke held the audience in thrall by revealing the connections be- Life Beyond Calculus tween his current work on linkages that lock and Organizers: Malgorzata Dubiel (Simon Fraser), protein folding. The third invited talk was by Veselin Jungic (Simon Fraser) Sudipto Guha (University of Pennsylvania). Dr. Mathematics Inspired by Biological Models Guha spoke about the applicability of geometry Organizers: Fred Brauer (UBC), Pauline van den to the resolution of nonlinear problems in the Driessche (Victoria) streaming model of computation. The Confer- ence was supported by the University of Wind- Matrix Analysis sor, the CRM, the Fields Institute and PIMS. Organizers: Man-Duen Choi (Toronto), Douglas Farenick (Regina) CMS Winter 2005 Meeting Nonlinear Analysis December 10 – 12, 2005, University of Victoria Organizers: Martial Agueh (Victoria), Ivar Eke- land (PIMS), Robert McCann (Toronto) Meeting director: Ahmed R. Sourour (Victoria) Operator Algebras The Winter 2005 Meeting of the Canadian Math- Organizers: Marcelo Laca (Victoria), John Phillips ematical Society welcomed 322 participants. The (Victoria) plenary speakers were Robert Guralnick (South- ern California), Uffe Haagerup (South Den- Probability mark), Bryna Kra (Northwestern), Andrew Ma- Organizers: Martin Barlow (UBC), Edwin Perkins jda (Courant), and Oded Schramm (Microsoft). (UBC) The CMS was pleased to present lectures from its Topology prize winners, namely, the Coxeter-James Prize Organizer: Dale Rolfsen (UBC) Lecture, given by Robert McCann (Toronto), the Doctoral Prize Lecture, given by Vasil- Variational Analysis and Optimization isa Shramchenko (Concordia), and the Adrien- Organizers: Jiming Peng (McMaster), Jane Ye Pouliot Prize Lecture, given by Katherine Hein- (Victoria) rich (Regina). Professor Yu-Ru Liu (Waterloo) re- Contributed Papers Session ceived the G. de B. Robinson award. The invited Organizer: C. Robert Miers (Victoria) sessions and their organizers may be found below. The following institutions sponsored the CMS Winter 2005 Meeting: the University of Victoria Applied Partial Differential Equations (Department of Mathematics and Statistics, Fac- Organizers: Anne Bourlioux (Montréal), Rein- ulty of Science, Faculty of Engineering, Faculty hard Illner (Victoria), Boualem Khouider (Victo- of Graduate Studies), the CRM, the Fields In- ria) stitute, MITACS, PIMS, Simon Fraser University Combinatorics (Department of Mathematics and Statistics), and Organizers: Peter Dukes (Victoria), Frank Ruskey the University of British Columbia (Department (Victoria) of Mathematics and Faculty of Science).

61 Mathematical Education MATHEMATICAL EDUCATION

S part of its mandate to promote and stimulate research in the mathematical sciences, at every Alevel, the CRM provides funding and support for many activities and programs related to mathematical education and the training of researchers. Many of these activities and programs are carried out jointly with the ISM (Institut des sciences mathématiques) that the CRM created in 1991.

Institut des sciences mathématiques (ISM)

Created in 1991 by the departments of mathe- Promotion of the mathematical sciences matics and statistics of the four Montréal uni- The ISM produces the Accromαth journal and versities on the iniative of the CRM, the ISM is distributes it freely in all the cégeps and sec- a consortium of seven Québec universities (Con- ondary schools in Québec. In this way, it concordia, Laval, McGill, Université de Montréal, tributes to spreading mathematical knowledge UQÀM, UQTR and Université de Sherbrooke), among teachers, young students and the gen- six of which offer a Ph.D. program in mathe- eral public. Each year, ISM professors give talks matics. As an institute to which belong almost attended by thousands of cégep students; these all the Québec researchers in the mathematical talks present the latest breakthroughs in mathe- sciences, the ISM has at its disposal vast mate- matics and the careers available to mathematics rial and intellectual resources, and as a result, graduates. Montréal and Québec itself have become one of As the above list demonstrates, the CRM has the main centers of training and research in the several joint activities with the ISM, in partic- mathematical sciences in North America. The ular two colloquia, a joint program of postdoc- ISM is funded by the Ministère de l’Éducation, toral fellowships, and the planning of gradu- du Loisir et du Sport du Québec and by the ate courses related to the thematic programs of seven universities in the consortium. the CRM. Since the summer of 2003, the CRM The reader will find below an overview of the has also supported the Undergraduate Summer activities and programs of the ISM. Scholarships program, which allows postdoc- Coordination and harmonisation of graduate toral fellows to supervise undergraduate stu- programs dents doing research. The ISM was created to bring together the CRM – ISM Postdoctoral Fellowships strengths of its member departments, in order to turn them into a great school of mathematics. The CRM – ISM postdoctoral fellowships enable Thus the ISM coordinates the graduate studies promising young researchers to devote them- of the mathematics departments, supports the selves to their research work. The ISM orga- sharing of expertise among its researchers and nizes a single competition on behalf of the seven facilitates student mobility between the Mont- universities of the consortium, and it receives réal universities. a large number of applications, which are then Scholarships and financial support evaluated by the 150 ISM professors. The selec- The ISM helps students and beginning re- tion of the fellows is rigorous and only one in searchers carry out their research activities in forty applicants is awarded a fellowship. The ap- several ways, for instance through the ISM plications are handled electronically in order to Scholarships for Graduate Studies, the Carl Herz streamline the selection process and economize Scholarship (financed by the Carl Herz Founda- the resources consumed during the selection. tion), the Travel Bursaries, the Undergraduate The postdoctoral fellows play a crucial role in Summer Scholarships and the CRM – ISM post- the Montréal universities: they collaborate with doctoral fellowships. the established researchers, stimulate their work and bring new ideas from other great centres of Scientific activities mathematical research. Also they are a vital link Since its creation, the ISM has initiated several between the professors and the students, espe- activities that are by now an integral part of the cially when they organize on their own study Québec scientific scene: the CRM – ISM Math- groups on emerging topics. ematics Colloquium, the CRM – ISM – GERAD Statistics Colloquium, the ISM Graduate Student 2005 – 2006 Postdoctoral Fellows Conference and the ISM Graduate Student Sem- inar. Abdellatif Bourhim (Ph.D. 2001, Rabat) worked in analysis with Thomas Ransford, from

63 CENTRE DE RECHERCHES MATHÉMATIQUES

Laval University. He has accepted a faculty po- Supervisor: Benoit Charbonneau sition at the Université de Moncton. This scholarship was cofinanced by Paul Tup- Harald Helfgott (Ph.D. 2003, Princeton) per’s research funds. worked with Andrew Granville, from the Uni- Christelle Vincent (McGill) versité de Montréal, on number theory, elliptic Topic: Évacuation de tableaux de Young, deux curves, and automorphic forms and combina- conjectures de Schützenberger torics. He has accepted a faculty position at the Duration: 2 months University of Bristol, in England. Supervisor: Aaron Lauve Emmanuel Lorin de la Grandmaison (Ph.D. This scholarship was cofinanced by Benoit 2001, ENS Cachan) worked in applied mathe- Larose’s research funds. matics with André Bandrauk, from the Univer- Martin Gariépy (Université de Montréal) sité de Sherbrooke. He is pursuing his postdoc- Topic: Théorie du revêtement en géométrie toral studies at the Université de Sherbrooke. Duration: 4 months Joseph Maher (Ph.D. 2002, UC Santa Barbara) Supervisor: Samuel Lisi worked in geometry and topology with Steven This scholarship was cofinanced by François Boyer, from UQÀM. He has accepted a faculty Lalonde’s research funds. position at the Oklahoma State University. Andrew McIntyre (Ph.D. 2002, SUNY Stony ISM Graduate Student Conference Brook) has worked in mathematical physics and analysis with Dmitry Korotkin, from Concordia The eighth ISM Graduate Student Conference University. He is pursuing his postdoctoral stud- (Colloque panquébécois annuel des étudiants) ies at Concordia University. took place at Université Laval on May 23 – 25, Ye Tian (Ph.D. 2003, Columbia) worked in 2006. It was attended by 104 participants, in- number theory with Henri Darmon, from McGill cluding 90 students from eight Canadian uni- University. He has accepted a faculty position in versities. The Conference offered the students a China. great opportunity to meet, to present their re- Jensen Bernt Tore (Ph.D. 2003, NTNU) worked search work and to exchange ideas with their in algebra with Thomas Brüstle, from the Uni- peers. The Conference had three streams: statis- versité de Sherbrooke. Jensen Bernt Tore has ac- tics, pure mathematics and applied mathematics. cepted a postdoctoral fellowship from the Nor- Two of the six plenary lectures were reserved for wegian University of Science and Technology each stream, and 30 lectures were given by stu- (NTNU), in Trondheim (Norway). dents. Each stream had its own meeting room, and thus the participants could go on discussing Undergraduate Summer Scholarships mathematics after the lectures. The Conference was also an opportunity to promote the mathe- In collaboration with the CRM and the ISM pro- matical sciences in front of a wide audience; on fessors, the ISM awards summer scholarships to Tuesday, May 23, Jean-Marie De Koninck (Uni- promising undergraduates who want to do re- versité Laval) presented ShowMath, his mathe- search during the summer and plan to study matical show for the general public. This show mathematics at the graduate level. These un- was attended by the Conference participants, dergraduates are supervised by postdoctoral fel- but also by about 100 other persons: students lows, who in general are supervising students from all levels (grade school, high school and for the first time. The reader will find below the college) and some parents and teachers. list of the undergraduate scholars. The organizers wanted the students to present Agnès Beaudry (McGill) their research work in a lucid way, and they de- Topic: Euclidean algorithms in k-steps in real cided to award prizes to the two best presen- quadratic number fields tations in each of the three streams. They en- Duration: 4 months listed the support of some institutions, which Supervisor: Pierre Charollois responded with enthusiasm and provided their This scholarship was cofinanced by Henri Dar- own selection committees. In statistics, the mon’s research funds. prizes were awarded by the ASSQ and the Yuriy Svyrydov (McGill) Canada Research Chair of Professor Louis-Paul Topic: Different modes of convergence for the nu- Rivest (Université Laval). In applied mathemat- merical solution of stochastic differential equa- ics, the prizes were awarded by GIREF (Uni- tions versité Laval) and DRDC Valcartier, which had Duration: 2 months (May – June) a kiosk on the conference site and contributed

64 MATHEMATICAL EDUCATION substantially to the Conference. In pure math- ISM universities, of which around ﬁfteen gave ematics, the prizes were awarded by CICMA, talks. the Analysis Group of the Mathematics Depart- ment and the Canada Research Chair of Profes- Plenary lectures sor Thomas Ransford (Université Laval). Fonctions analytiques discrètes ou empilements de ISM “Sur la Route” Colloquium cercles Virginie Charette, Université de Sherbrooke In the same vein as the ISM Graduate Student Systèmes dynamiques chaotiques et indice de Conley Conference, the “Sur la Route” Colloquium is or- Sara Derivière, Université de Sherbrooke ganized by and geared towards students. This colloquium was initiated by students from the La conjecture de dimension ﬁnitiste Université de Sherbrooke, and this year, it took François Huard, Bishop’s University place on October 14 – 16, 2005, at the Camp Les Organizing committee: Jennifer Bélanger, Syl- Sommets, in the Eastern Townships. It was at- vain Bérubé, Julie Dionne, Jean-Philippe Morin, tended by approximately forty students from the Charles Paquette, David Smith

Other Joint Initiatives

ESSO/CMS Math Camps 2005 University, the University of Ottawa, the Univer- sity of Calgary, Brock University, the University The ESSO/CMS Math Camp Program started of Western Ontario, the University of Manitoba in 1999 with three camps, and the program has and the University of Regina. now grown to include at least one camp in every Finally, the 2005 IMO Training Seminar, de- province. The support received from the spon- signed to prepare a team of Canadian students sors enables the Canadian Mathematical Society for the International Mathematical Olympiad to make these camps accessible to students from (IMO), took place from June 25 to July 10, 2005, across Canada who demonstrate an interest and and was organized by the University of Calgary excellence in mathematics. In 2005, there were and BIRS (Banff International Research Station). thirteen regional math camps in ten provinces, as well as a national camp. The sponsors of the Math Camp Program are: the Imperial Oil Foundation, the Canadian Organized by Daniel Gatien and Matthieu Du- Mathematical Society, NSERC PromoScience, four, the national camp was held at the John CRM, the Fields Institute, the Pacific Institute Abbott cegep from July 3 to 9, 2005. The Na- for the Mathematical Sciences, the Association tional Camp is designed primarily for younger Mathématique du Québec, the host universities, Canadian students with at least two years re- and the governments of New Brunswick, Al- maining in high school and with the potential berta, the Northwest Territories, Newfoundland to compete at the Mathematical Olympiad level. and Labrador, Nova Scotia, Québec, Ontario and The selection of invited students is based upon Saskatchewan. their results in various mathematics competitions. Presentations on specific topics and the 2005 AMQ Mathematics Camp various problem solving sessions are run by local area teachers and faculty members as well as June 18 – July 1, 2005, UQÀM former IMO team members. Organizers: Pierre Bouchard (UQÀM) and The Regional Camps are intended to provide Matthieu Dufour (UQÀM) some mathematics enrichment in a fun and re- For the fifth year in a row, the Camp was held warding environment. Each camp invites be- at UQÀM. In 2005, there were 22 participants, tween 20 and 30 students (from grade 9 to 11) who had the opportunity to meet with mathe- on the basis of national or regional mathemat- maticians and people who use mathematics in ics competitions as well as recommendations their work. Every day, one or more lecturers pre- from teachers. The 2005 regional camps took sented topics of interest, and the participants place at the Sir Wilfred Grenfell College, the shared in an unforgettable experience with more University of New Brunswick, the University of than twenty other "fans" of mathematics. For the Prince Edward Island, the Université du Québec duration of the camp, the participants could use à Rimouski, Simon Fraser University, Dalhousie the UQÀM computers. In 2005 (as in 2003 and

65 CENTRE DE RECHERCHES MATHÉMATIQUES

2004), they visited the national park of Mont- Mégantic, in particular the telescope and the ob- servatory.

66 Research Laboratories CENTRE DE RECHERCHES MATHÉMATIQUES

HE nine CRM research laboratories are where a substantial part of the Canadian research effort Tin the mathematical sciences takes place. They span 12 universities in Quebec and Ontario (Mon- treal, McGill, UQÀM, Concordia, Laval, Sherbrooke, École Polytechnique, HÉC, UQTR, Ottawa, Car- leton, Queen’s). Each of the laboratories hosts an average of 20 professors, 50 graduate students, and 15 postdoctoral fellows, organizes workshops and inter-university seminars on a regular basis, and coordinates a uniﬁed graduate school (involving ﬁve, six or seven universities), with funding coming from a wide variety of sources. The dedicated involvement of lab members in the CRM’s activities is a driving force in bringing leading scientists to the Center. It also ensures that students and postdoctoral fellows receive an excellent preparation for the thematic programs, through special advanced courses, mini-courses, and student seminars. These labs are the most effective way to transfer the results of our international programming to Canadian scientists.

Applied Mathematics

Description

Applied and computational mathematics is a One characteristic of this laboratory is the sus- very active area of research with a long tradi- tained collaboration of its members with re- tion, as well as many young faculty members, in searchers in other fields: for instance, André the greater Montreal area. With modern comput- Bandrauk and Nilima Nigam are members of ing equipment, it has become possible to simu- RQMP (Regroupement québécois des matériaux late problems and compute solutions that were de pointe), Sebius Doedel and Jacques Bélair out of reach a few decades ago: this has been are members of the Centre for Nonlinear Dy- a tremendous driving force in recent develop- namics in Physiology at McGill, Martin Gan- ments in applied and computational mathemat- der and Michel Delfour are members of GIREF, ics. Anne Bourlioux collaborates with computer sci- The objective of the Laboratory is to encour- entists and mechanical engineers in an indus- age further scientific exchanges both amongst its trial project sponsored by MITACS, while Pe- members and outside the group. It is character- ter Bartello, André Bandrauk, and Sebius Doedel ized by the intensity of its multidisciplinary col- hold positions completely or partly outside laborations, with all the members working on mathematics departments. the development of mathematical models and The Laboratory organizes the Montreal Scien- numerical methods for applications to science tific Computing Days each February, as well as and engineering. The members of the Labora- other workshops. It has two regular seminars tory work in a wide range of applications (fluids, running during the academic year, a weekly ap- solids, physics, biology, etc.), using a wide va- plied mathematics seminar and a biweekly com- riety of tools (optimization, numerical analysis, putational science and engineering seminar. It dynamical systems, etc.), and are very active in also supports postdoctoral fellows and summer both research and training, supervising a large students as well as Canadian and international number of graduate students and postdoctoral visitors. fellows.

News and highlights

The Laboratory and its members remain very ac- and Jacques Bélair organized workshops, de- tive, as it welcomed two new members this year: scribed below. The Laboratory members are also Tucker Carrington (Montréal) and Thomas Wih- very visible at the national and international lev- ler (McGill). The Laboratory organizes two sem- els in applied and industrial mathematics. An- inars, described below, and the Montreal Scien- dré Bandrauk was awarded the 2005 Urgel Ar- tiﬁc Computing Days in February, whose pur- chambault Prize by ACFAS (l’Association fran- pose is to bring together people in the nearby cophone pour le savoir), and is the second lab- scientiﬁc computing community so that they oratory member honored in this way, follow- learn about the latest techniques and exchange ing Michel Delfour who was honored in 1995. ideas. In addition, Sebius Doedel, Nilima Nigam Paul Tupper was awarded the Twelfth Leslie Fox

68 RESEARCH LABORATORIES

Prize in June 2005, an award given once every Paul Tupper and Nilima Nigam have both been two years to a Numerical Analyst less than 31 invited to the Abel Symposium in May 2006. Nil- years old. Anne Bourlioux continues to serve on ima Nigam was on the organizing committee for the board of directors of CAIMS. the Fields – MITACS Industrial Problem-Solving Laboratory members were also very active in Workshop in August 2006. André Bandrauk is workshop and conference organization, in addi- co-director of the Attosecond Science Workshop tion to the Laboratory sponsored events. Michel that took place at the University of California at Delfour and André Bandrauk along with Claude Santa Barbara in August/September 2006. Anne Le Bris organized the High-dimensional Partial Bourlioux was a plenary speaker at the Cana- Differential Equations in Science and Engineering dian Combustion Institute Spring Meeting in workshop at the CRM in August 2005. At BIRS, May 2006, and organized a session on Scien- Paul Tupper was one of the organizers of Math- tiﬁc Computing at the joint CAIMS/MITACS ematical Issues in Molecular Dynamics in June Meeting in June 2006. Tucker Carrington orga- 2005, and Jacques Bélair was a member of the nized an invited mini-symposium on Eigenvalues organizing committee for the MITACS – MSRI – in computational chemistry at the GAMM – SIAM AFMnet – CRM Workshop on Therapeutic Efﬁcacy Applied Linear Algebra Conference in Germany in Population Veterinary Medicine in October 2005. in July 2006. Sebius Doedel was a member of Anne Bourlioux organized a session on Ap- the program committee for the workshop Ap- plied PDEs at the 2005 CMS Winter Meeting in plied Dynamical Systems, held at the University Victoria. Sebius Doedel also organized a mini- of Ghent in June 2006. Finally, Tony Humphries, symposium on Numerical Bifurcation Techniques Sebius Doedel, Paul Tupper and Jacques Bélair at the Euromech Nonlinear Dynamics Confer- are all involved in the organization of the The- ence in the Netherlands in August 2005. The matic Semester on Applied Dynamical Systems members also gave countless invited lectures that will take place at the CRM in the Summer and conference presentations, including Martin and Fall of 2007. Gander who gave an invited topical talk at the 2005 SIAM Annual Meeting.

Students, postdoctoral fellows and visitors

The Laboratory hosted a number of scientiﬁc (INRIA), and in total over 25 seminar speakers visitors including Steve Thomas (NCAR), An- came from outside Québec. In 2005 – 2006, 2 un- nalisa Buffa (IMATI, Italy), Jay Gopalakrishnan dergraduate students, 23 master’s students, 26 (Florida), Alain Dervieux (INRIA, France), Anita Ph.D. students and 11 postdoctoral fellows were Layton (Duke), Jiannong Fang (EPFL, Switzer- supervised by Laboratory members. land), Marc Thiriet (INRIA), Jean-Paul Zolésio

Seminars

The regular core activity of the Laboratory is the community, and provides a weekly occasion for weekly Monday Applied Mathematics seminar. the Montreal applied mathematics community This year, it was organized by Robert Owens, to congregate. who lined up 28 speakers covering a very wide Complementary to that core seminar, and in line range of interesting topics in applied mathemat- with the strong multidisciplinary orientation of ics. The seminars were held at McGill and at the this group, the Laboratory was also involved in CRM, and the series included one joint semi- organizing and sponsoring the biweekly Com- nar with Computational Science and Engineer- putational Science and Engineering (CSE) Sem- ing. The seminar series remains well attended inar at McGill, organized this year by Abdelka- not just by Laboratory members along with their der Baggag (CLUMEQ, McGill), which featured students and post-doctoral fellows, but by many 11 speakers, in addition to one joint Applied members of the Montreal applied mathematics Mathematics/CSE seminar.

69 CENTRE DE RECHERCHES MATHÉMATIQUES

Workshops, special sessions and others

Under the sponsorship of the Applied Mathe- simulation of electromagnetic, elastic and acous- matics Laboratory, members of the Laboratory tic scattering problems, with expertise ranging organized the following workshops in 2005 – from finite element methods to geometrical op- 2006. Descriptions of the first and third of these tics, asymptotics and boundary element meth- workshops may be found in the “General Pro- ods. The mathematicians in attendance included gram” section of this report, and a description some of the very top names in the field. This of the second may be found in the “Multidisci- was an opportunity for the community to share plinary and Industrial Program” section. the latest results in the area, and also to map Mini-workshop on Computational Aspects of out open problems and challenges for the future. Dynamical Systems A collection of these open problems will be re- July 15, 2005, Concordia leased soon as a Banff Report. Organizer: Sebius Doedel (Concordia) The meeting also offered several opportunities for informal discussions between experts and International Workshop on Applied Dynami- young mathematicians (graduate students and cal Systems — Mechanics, Turbulence, Knots, postdocs), and many new collaborations were Cockroaches, and Chaos started. A novel poster-session idea was imple- October 15 – 16, 2005, CRM mented, and was very successful in sparking Organizers: Jacques Bélair (Montréal), Sue Ann discussions between participants. Another novel Campbell (Waterloo), Jeff Moehlis (UC Santa feature of the meeting was the informal “intro- Barbara), N. Sri Namachchivaya (Illinois at ductory lectures” given by world experts to the Urbana-Champaign), Steve Shaw (Michigan attending graduate students, including lectures State) on mixed finite elements, combined boundary- The Third Montreal Scientific Computing field methods, high-frequency integral equation Days solvers, and edge finite elements. A direct con- February 25 – 26, 2006, CRM sequence of this interaction was that at least four Organizers: Paul Tupper (McGill), Anne of the graduate students found interesting open Bourlioux (Montréal), Thomas Wihler (McGill) problems to work on during their doctoral studies. Advances in Computational Scattering The Applied Mathematics Laboratory funded February 18 – 23, 2006, Banff International Re- the travel of the graduate students from Québec search Station (BIRS) to Banff. This support benefited the graduate Organizers: David Nicholls (Illinois at Chicago), students themselves, but in addition freed other Nilima Nigam (McGill), Fernando Reitich (Min- sources of funding that will be used to attract nesota) graduate students and postdocs from abroad. This 5-day workshop was a very successful event, drawing together experts in the numerical

Members of the Laboratory

Regular members Jacques Bélair (Montréal) Dynamical systems in physiology. Robert G. Owens (Montréal) Director Mechanics, numerical simulation of complex Anne Bourlioux (Montréal) fluids. Modeling, numerical simulation in turbulent combustion. Antony R. Humphries (McGill) Director Numerical analysis, differential equations. Michel C. Delfour (Montréal) Control, optimization, design, shells, calculus, Paul Arminjon (Montréal) biomechanics. Numerical methods in fluid mechanics. Eusebius J. Doedel (Concordia) André D. Bandrauk (Sherbrooke) Numerical analysis, dynamical systems, differ- Quantum chemistry. ential equations, bifurcation theory, scientific Peter Bartello (McGill) software. Turbulence, CFD.

70 RESEARCH LABORATORIES

Sherwin A. Maslowe (McGill) Jian-Jun Xu (McGill) Asymptotic methods, ﬂuid mechanics. Asymptotics and numerical analysis, nonlinear PDEs, material science. Nilima Nigam (McGill) Applied analysis, numerical methods in electro- Associate Members magnetism. Tucker Carrington (Montréal) Paul F. Tupper (McGill) Chemical dynamics. Numerical analysis, stochastic processes, statistical mechanics. Martin J. Gander (Genève) Domain decomposition, preconditioning. Thomas P. Wihler (McGill) Numerical analysis, computational methods for Jean-Paul Zolésio (INRIA Sophia-Antipolis) PDEs. Control, optimization.

CICMA

Description

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

News and highlights

In 2005 – 2006, most of the scientiﬁc activities or- Hida, Tilouine and Colmez dealt with these ganized by CICMA were part of the thematic timely topics, in particular the proof by Colmez year on analysis (p-adic or classical) in number of the p-adic Langlands correspondence for theory. Analysis in number theory is a broad GL(2) (based on the theory of (φ, Γ)-modules), theme, including such diverse topics as the p- and the study by Tilouine of the p-adic families adic Langlands program, arithmetic cycles on and Galois representations related to the Siegel Shimura varieties, the analytic properties of L- modular forms. The workshop that took place functions and additive combinatorics. The ﬁrst in September was an opportunity to emphasize half of the year (i.e., the fall of 2005) was devoted the many remarkable advances due to Breuil, to the applications of p-adic analysis to arith- Colmez, Emerton, Khare et Kisin. metic and number theory, while the second half In the fall of 2005 the conjectures of Stark and (i.e., the winter and spring of 2006) was devoted their versions in the context of elliptic curves to analytic number theory. were also an important topic. A workshop that The beginning of the year (September and Octo- took place in November was attended by Stark ber 2005) featured activities organized by Adrian himself and enabled several members of CICMA Iovita on p-adic families of modular forms and (e.g., Eyal Goren, David Dummit and Henri Dar- the p-adic Langlands program. The lectures by mon), as well as several postdocs and visitors

71 CENTRE DE RECHERCHES MATHÉMATIQUES

(e.g., Pierre Charollois, Mak Trifkovic and Samit School on Additive Combinatorics was followed Dasgupta), to present their results, which throw by a workshop on the same topic, one of the a new light on Stark’s conjectures. most successful workshops ever organized by The third theme of the first half of the thematic the CRM since it was attended by more than year was the intersection of algebraic cycles on 145 participants. Several of the world leaders in Shimura varieties and the relationship between analysis, Bourgain, Gowers, Tao, Green, Konya- these intersection numbers and the Fourier coef- gin (a group including Fields medallists and ficients of automorphic forms. Several lecturers potential Fields medallists) attended this work- (such as Burgos, Kramer and Bruinier) presented shop. the latest approaches to the theory of arithmetic The thematic year was especially successful in intersection, based on Arakelov theory. Other re- that many visitors, young researchers and post- searchers (Bruinier and Kudla) spoke on the rela- doctoral fellows spent several months and even tionships with the theory of automorphic forms the whole academic year at the CRM. The regu- and theta-correspondences. lar members of CICMA were thus able to initiate The activities of the second half of the year, or- collaborations with them. For instance, in collab- ganized mainly by Chantal David and Andrew oration with Guillaume Ricotta and Djordje Mil- Granville, revolved around analytic number the- icevic, Chantal David studied the non-vanishing ory. This semester featured several highlights. of cubic twists of elliptic curves on a field con- The first activity was a workshop on the analytic taining the cube roots of unity. In collaboration properties of L-functions, organized by Chan- with Alina Cojocaru and Antal Balog, Chantal tal David, and featuring a series of lectures by David is pursuing a different project on a con- Philippe Michel on problems of equidistribution jecture of Koblitz that can be considered as the and a series of lectures by Soundararajan, one of analogue of the twin prime conjecture in the con- the Aisenstadt chairs of the thematic year. text of elliptic curves. Antal Balog, another visitor to the CRM, has studied these conjectures in The second activity was a workshop on the the past and made progress on them. anatomy of integers that took place on March 13 – 17 and was attended by 70 participants. This Henri Darmon was able to embark on new re- workshop highlighted the proof of the existence search projects with four of the postdoctoral fel- of “small gaps” between prime numbers, due to lows and two visitors to the CRM (Pierre Charol- Goldston, Pintz and Yildirim and based on sieve lois, Samit Dasgupta, Kartik Prasanna, Ye Tian, theory. Goldston himself gave a series of lec- Gonzalo Tornaria and Mak Trifkovic). During tures on this work. Kevin Ford also gave a series the stay of Soundararajan at the CRM as Aisen- of beautiful lectures on his work regarding the stadt Chair holder, Andrew Granville developed divisor distribution of an integer. Soundarara- his projects with him on the distribution of val- jan spoke of his improvement of the Polya – ues taken by multiplicative functions. Granville Vinogradov inequality (obtained with Andrew also collaborated with Antal Balog on this topic. Granville), and of his work with Lagarias on Eyal Goren continued his collaboration with smooth solutions of the equation a + b = c. Payman Kasaei on the Katz-style geometric ap- The CRM – Clay School on Additive Combina- proach to the theory of p-adic modular forms; torics took place at the Université de Mont- he also continued his collaboration with Fab- réal from March 30 to April 5, and was at- rizio Andreatta. The visits by Bruinier and Kudla tended by more than 100 participants. The series in December 2005 may result in collaborations of lectures given by the two organizers, Jozsef between them and Eyal Goren and increased Solymosi (UBC) and Andrew Granville (Uni- Goren’s desire to further his understanding of versité de Montréal), were followed by the ple- Borcherds theory. Adrian Iovita had further ex- nary talks of the world-renowned mathemati- changes with Tilouine and Hida, which may cians Ben Green (University of Bristol) and Terry lead to discoveries regarding the p-adic families Tao (UCLA). Green and Tao explained Gowers’ of automorphic forms on higher-order reductive approach to proving Szemeredi’s theorem. The groups.

72 RESEARCH LABORATORIES

Students, postdoctoral fellows and visitors

The above summary of the thematic year shows report. Also, in 2005 – 2006, 2 undergraduate stu- that CICMA hosted a great number of visitors in dents, 25 master’s students, 29 Ph.D. students 2005 – 2006, and the names of many visitors ap- and 20 postdoctoral fellows were supervised by pear in the “Thematic Program” section of this Laboratory members.

Seminars

The Québec – Vermont Number Theory Seminar mon was the Seminar coordinator from Septem- is the main scientiﬁc activity of CICMA (when ber to December 2005, and Chantal David was there is no thematic program on number the- coordinator from January to May 2006. The Sem- ory!). The Seminar is held every second Thurs- inar consisted of 49 lectures, including several day for a full day and is attended by about lectures on the ﬁnite subgroups of Lie groups by 30 regular participants from Montréal, Vermont, Jean-Pierre Serre. Québec and Ottawa. In 2005 – 2006, Henri Dar-

Workshops, special sessions and others

We refer the reader to the “Thematic Program” section of this report.

Members of the Laboratory

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

73 CENTRE DE RECHERCHES MATHÉMATIQUES

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

CIRGET

Description

Geometry and topology are fundamental disci- Québec universities. The research centre, based plines of mathematics whose richness and vi- at UQÀM, now comprises seventeen professors tality have been evident throughout human his- together with a large number of postdoctoral fel- tory and reflect their deep link to our experience lows and graduate students. The main themes of the universe. They are a focal point of mod- to be pursued in the coming years include Dehn ern mathematics and in effect several domains of surgery and Thurston geometrization; quantiza- mathematics have recently shown a strong trend tion of Hitchin systems and the geometric Lang- towards a geometrization of ideas and meth- lands program; classification of special Kähler ods: two cases in point are mathematical physics metrics; the study of symplectic invariants, espe- and number theory. During the last twenty-five cially in dimension 4; and Hamiltonian dynami- years, several researchers of international calibre cal systems. in geometry and topology have been hired by

News and highlights

Virginie Charette (Ph.D. from Maryland in 2000, give the Distinguished Visitor Lecture Series at postdoctoral fellowship at McMaster in 2000 – Stanford University in the fall of 2005 and he 2002) will ofﬁcially become a member of CIR- has been invited to give a 45-minute talk in the GET on June 1, 2006. She took up a position geometry section of the ICM Madrid 2006. John at the Université de Sherbrooke in 2005 af- Harnad was awarded the 2006 CAP – CRM Prize ter spending several years at the University of in theoretical and mathematical physics, Niky Manitoba. Her research focuses on the study Kamran is the recipient of a Killam fellowship of discrete group actions on afﬁne manifolds for the years 2006 – 2008, and Iosif Polterovich and Lorentz geometry. Various honours were was awarded the 2006 André-Aisenstadt Prize, bestowed on CIRGET members over the last which recognizes outstanding research achieve- twelve months. François Lalonde was invited to ment by a young mathematician.

Students, postdoctoral fellows and visitors

CIRGET had an impressive group of postdoc- Sydney, Australia. CIRGET members have su- toral fellows this year: Benoit Charbonneau, pervised nine undergraduate research students Jianjun Chuai, David Duchemin, Nicola Gam- and one cégep student during the summer of bino, Paolo Ghiggini, Shengda Hu, Alexander 2006. Altogether, in 2005 – 2006, 10 undergradu- Ivrii, Samuel Lisi, Joseph Maher, Ramin Moham- ate students, 30 master’s students, 14 Ph.D. stu- madalikhani, Erwan Rousseau, Stephan Till- dents and 16 postdoctoral fellows were super- mann, and Mark Weber. Charbonneau, Chuai, vised by Laboratory members. Duchemin, Gambino, Ghiggini, Hu, Lisi, and In addition to its many seminar and confer- Rousseau will be continuing in Montréal next ence visitors, CIRGET also welcomed many year. Alexander Ivrii has accepted a postdoc- researchers. Davide Batic (ETH) visited Niky toral position at Technion, Joseph Maher will be- Kamran; Baojun Bian (Shanghai) visited Pengfei gin a tenure-track position at Oklahoma State Guan; Stephan De Bièvre (Lille) visited Niky University in September, Stephan Tillmann will Kamran; Alberto Encisco (Universidad Com- begin a postdoctoral position at the University plutense, Madrid) visited Niky Kamran; Michael of Melbourne, and Mark Weber has obtained a Levitin (Heriot-Watt, Edinburgh) visited Iosif postdoctoral position at Macquarie University in Polterovich; Susan Nieﬁeld (Union College) vis-

74 RESEARCH LABORATORIES ited André Joyal; Louis Nirenberg (NYU) vis- veira (Campinas, Brazil) visited Octav Cornea; ited Pengfei Guan; Ketty de Rezende (Campinas, Xi Zhang (Zhejiang University) visited Pengfei Brazil) visited Octav Cornea; Richard Schoen Guan; Xingru Zhang (SUNY Buffalo) visited (Stanford) visited Pengfei Guan; Mariana Sil- Steven Boyer.

Seminars

CIRGET’s everyday scientific life revolves tended at least two seminars, if not three, on a around its weekly seminars and working groups regular basis. Indeed, scientific activity at CIR- where professors, postdoctoral fellows and stu- GET truly flourished this year, thanks in large dents meet on a regular basis. The CIRGET Ge- part to the high mathematical level and commit- ometry and Topology Seminar, organized by ment of the postdoctoral fellows, whose pres- Olivier Collin, is a general seminar series at- ence stimulated faculty members and students tended by all CIRGET members. Most of the alike. talks in this seminar are given by invited speak- CIRGET graduate students from UQÀM, Uni- ers who stay at the centre for short research vis- versité de Montréal and McGill continued to its. To complement this general seminar, CIR- participate in the CIRGET Junior Seminar, orga- GET organized two more specialized seminars nized by a doctoral student, Baptiste Chantraine. and one working group, so that three poles of re- This seminar gives graduate students a forum to search were developed: geometric group theory present their research to their peers and to prac- (organized by Dani Wise), symplectic topology tice giving talks in a relaxed setting. It has also (organized by Octav Cornea), and 3-dimensional created a natural meeting place for the students, topology (organized by Steven Boyer). There who now form a cohesive interuniversity stu- was a healthy amount of interaction between dent body. these three poles as many CIRGET members at-

Workshops, special sessions and others

The following workshops were organized by Homotopy Theory Conference in Honor of Joe members of CIRGET, and their descriptions may Neisendorfer’s 60th Birthday be found in the “General Program” section of November 18 – 20, 2005, CRM this report. Organizer: Octav Cornea (Montréal) Short Program on Random Matrices, Random In addition, as a follow-up to the thematic Processes and Integrable Systems semester in symplectic topology held in the fall June 20 – July 8, 2005, CRM of 2004, Octav Cornea, David Ellwood, Hel- Organized with the Mathematical Physics Labo- mut Hofer, François Lalonde, and Katrin Wer- ratory heim organized a workshop on the Cluster- Organizers: John Harnad (Concordia), Jacques Polyfold setup for Lagrangian Floer homology. Hurtubise (McGill) This workshop was held on October 10 – 05, at the Institute for Advanced Study in Princeton, CIRGET – CRM Workshop on Khovanov Ho- and was partially subsidized by CIRGET. It has mology led to a major research collaboration between September 30 – Oct 2, 2005, UQÀM Cornea, Hofer, Lalonde and Werheim on the an- Organizer : Olivier Collin (UQÀM) alytical foundations of the cluster theory.

Members of the Laboratory

Regular members Abraham Broer (Montréal) Algebraic transformation groups, invariant the- Steven Boyer (UQÀM) Director ory. Topology of manifolds, low-dimensional geometry and topology. Olivier Collin (UQÀM) Invariants of knots and 3-manifolds arising from Vestislav Apostolov (UQÀM) global analysis. Complex geometry, Kähler geometry.

75 CENTRE DE RECHERCHES MATHÉMATIQUES

Octav Cornea (Montréal) Iosif Polterovich (Montréal) Algebraic topology, dynamical systems. Geometric analysis, spectral theory, functional analysis, differential geometry, partial differen- Pengfei Guan (McGill) tial equations. Partial differential equations, geometric analysis, several complex variables. Peter Russell (McGill) Algebraic geometry. Jacques Hurtubise (McGill) Algebraic geometry, integrable systems, gauge Daniel T. Wise (McGill) theory, moduli spaces. Geometric group theory, low-dimensional topology. André Joyal (UQÀM) Algebraic topology, category theory. Associate members Niky Kamran (McGill) Syed Twareque Ali (Concordia) Geometric approach to partial differential equa- Coherent states, wavelets, quantization tech- tions. niques, harmonic analysis, Wigner functions. François Lalonde (Montréal) John Harnad (Concordia) Symplectic topology and geometry, global anal- Mathematical physics, classical and quantum ysis on manifolds, inﬁnite-dimensional transfor- physics, geometrical methods, integrable sys- mation groups. tems, group theoretical methods, random ma- Steven Lu (UQÀM) trices, isomonodromic deformations, isospectral Chern number inequalities, semi-stability of ten- ﬂows. sorial sheaves, log jets, log and hyperbolic geom- John A. Toth (McGill) etry, algebraic degeneracy. Microlocal analysis, partial differential equations.

LaCIM

Description

LaCIM is a research laboratory of the Univer- tions to other scientiﬁc domains, such as the sité du Québec à Montréal, which was ofﬁcially analysis of algorithms, statistical mechanics and established in 1989. Its research activities con- computational biology. LaCIM has been one of centrate on enumerative algebra, algebraic com- the eight research laboratories of the CRM since binatorics, computer science and their applica- 2002.

Research areas

Discrete mathematics has lately become an im- by highlighting constructive geometric meth- portant field of practical research, reflected in ods. Moreover, combinatorics can be applied to a new heading in Mathematical Reviews (Al- computer science (theory of automata, analy- gebraic Combinatorics, 05E), with subheadings sis of algorithms), to statistical physics (com- indicating interactions with the newest areas putation of configuration spaces and of critical of mathematics, such as group representations, exponents, discrete models), and bioinformat- quantum groups, discrete algebraic geometry, ics (combinatorics of words applied to genomic and special functions. Combinatorics benefits sequences). The usefulness and applicability of from the revival of the concrete computational this dynamic research field are especially obvi- aspect in mathematics after decades of abstract ous in the modern world, where discrete struc- structuralism. Algebra is enriched in a funda- tures (trees, graphs, permutations) play an in- mental manner by combinatorics, as the commu- creasingly important role in communications, tative algebra book by Eisenbud demonstrates networks and search engines.

76 RESEARCH LABORATORIES

News and highlights

Srecko Brlek is the new director of LaCIM and du Québec and Christophe Reutenauer to the ed- the members of LaCIM are serving on many sci- itorial board of the Journal of Algebraic Combi- entiﬁc committees. For instance, in 2005 – 2006, natorics. Pierre Leroux belongs to the editorial François Bergeron was President of a Grant Se- boards of the journal Discrete Mathematics and lection Committee (GSC 337) for NSERC. Srecko the Electronic Journal of Combinatorics. Brlek was consulted as an expert by the Italian The NSERC University Faculty Award of Sylvie equivalent of NSERC, i.e., the Italian commis- Hamel was renewed for two years (2006 – 2008). sion for the evaluation of research. Srecko Br- Daniel Lemire, a new collaborating member lek and Christophe Reutenauer are members of of LaCIM, was awarded a grant from FQRNT the editorial board of the Hungarian journal Pure under the program “Établissement de nou- and Applied Mathematics, as well as of the per- veaux chercheurs.” Marni Mishna, whose doc- manent committee overseeing the WORDS con- toral studies were supervised by François Berg- ference. Cédric Chauve was a member of the eron, has been holding an UFA position at Si- program committee of RECOMB 2006 (Compar- mon Fraser University since 2005. Hamadou ative Genomics Workshop), and Sylvie Hamel Sardaouna, who was a student of Srecko Brlek of the program committee of CBGI 2005 (In- and John Mullins and defended his thesis in ternational Conference on Computational Biol- the summer of 2006, was offered a prestigious ogy and Genome Informatics). Alain Goupil is postdoctoral fellowship by the École Polytech- a member of the permanent committee of the nique in Paris. The authors V. Makarenkov, D. FPSAC conference (Formal Power Series and Kevorkov and P. Zentilli were awarded the “Best Algebraic Combinatorics). Gilbert Labelle and Presentation Award” at the conference of the So- Christophe Reutenauer belong to the editorial ciety for Biomolecular Screening held in Geneva board of the Annales des sciences mathématiques in September 2005.

Students, postdoctoral fellows and visitors

Annie Château continued her work as postdoc- berta). In the summer of 2005, LaCIM orga- toral fellow with Cédric Chauve. Nicola Gam- nized an 8-week session for beginning students, bino, who had a postdoctoral fellowship at Ox- in order to introduce them to mathematical re- ford, is now a postdoctoral fellow at LaCIM. search; actually, it hosted undergraduates and 2 The postdoctoral fellow Aaron Lauve joined cégep students (from the Brébeuf and Bois-de- LaCIM in September 2005 and is supervised by Boulogne cégeps). In 2005 – 2006, 3 undergradu- Christophe Reutenauer. Andrei Gagarin is con- ate students, 29 master’s students, 22 Ph.D. stu- tinuing his work as postdoctoral fellow under dents and 7 postdoctoral fellows were super- the supervision of Vladimir Makarenkov and vised by Laboratory members. collaborates with Gilbert Labelle and Pierre Ler- Gregg Musiker and Adriano Garsia (UCSD) and oux. From November 2004 to November 2005, Jeremy L. Martin (University of Kansas) vis- Vladimir Makarenkov supervised Vincent De- ited François Bergeron. Gregg Musiker delivered vloo jointly with François Major (Université de a remarkable lecture on the combinatorial as- Montréal). pects of the Weil zeta functions of elliptic curves Some researchers who were postdoctoral fel- on a ﬁnite ﬁeld. Francesco Pappalardi (Roma), lows at LaCIM have been offered academic po- Laurent Habsieger (Lyon) and Marc Conrad sitions. In particular, Sara Faridi was awarded (Luton, UK) were invited by Srecko Brlek to an UFA position at Dalhousie University, Mer- give lectures on combinatorial number theory. cedes Rosas a position at Seville, Riccardo Bi- Srecko Brlek also invited Sébastien Ferenczi and aggioli a position at Lyon, Peter McNamara a Michel Mendès France. Boris Adamczewski vis- position at Bucknell University (Pennsylvania), ited LaCIM within the framework of a cooper- Manfred Schocker a position at the University ative project with the Université de Lyon (Cen- of Wales at Swansea, and Sylvie Corteel a re- tre Jacques Cartier), of which the coordinators search position at CNRS in Versailles. Axel Pavil- were Laurent Habsieger (Lyon) and Srecko Br- let defended his thesis under the supervision of lek. Within the framework of another interna- Timothy Walsh and now holds an academic po- tional project, supported by CNRS and includ- sition at Keyano College (Fort McMurray, Al- ing LaBRI (Université Bordeaux 1) on the French

77 CENTRE DE RECHERCHES MATHÉMATIQUES side, LaCIM hosted the following Ph.D. stu- Vallée) and Julia Mixtacki (Bielefeld). Miguel dents: Pascal Ochem, Jérémie Chalopin, François Mendez (Universidad Central de Venezuela) de Vieilleville, Olivier Bernardi and Rodrigue spent a sabbatical year at LaCIM and worked Ossamy. This project will last 3 years and is co- mostly with Gilbert Labelle and Pierre Ler- ordinated by Srecko Brlek and Olivier Guibert oux. Vladimir Makarenkov invited Bruno (LaBRI). Leclerc (EHESS, Paris) and Mel Janowitz (DI- Cédric Chauve invited many researchers within MACS & Rutgers). Manfred Schocker (Oxford), the framework of yet another cooperative Jacques Sakarovitch (Paris), Gérard Jacob (Lille), project between Québec and France: Guil- Vladimir Retakh (Rutgers), Claudia Malvenuto laume Fertin (Nantes), Stéphane Vialette (LRI), (Roma), Jacob Greenstein (UC Riverside) and Christophe Paul (CNRS, LIRMM), Séverine Christophe Hohlweg (Fields Institute) visited Bérard (INRA), Guillaume Blin (Marne-la- Christophe Reutenauer.

Seminars

The LaCIM Combinatorics and Theoretical In- coordinators of the LaCIM Seminar. In 2005 – formatics Seminar plays an important role 2006, this seminar featured 32 lectures, attended in bringing together the Laboratory members. by around 25 participants each Friday. Srecko Brlek and Christophe Reutenauer are the

Workshops, special sessions and others

The fifth Words conference (Words 2005) was (UQÀM), André Lauzon (UQÀM), Geneviève organized by Srecko Brlek and Christophe Paquin (UQÀM) Reutenauer in September 2005. The reader will find a description of this 5th International Conference on Words conference in the “General Program” section September 13 – 17, 2005, LaCIM (UQÀM) of the present report. Cédric Chauve orga- Sponsors: CRM, Ministère de l’Éducation, du nized the Phylogenomics 2006 meeting in Ste- Loisir et du Sport du Québec, Faculté des Sci- Adèle (Québec), in March 2006. Alain Goupil ences de l’UQÀM, PIMS, VSIS ConfTool, Chaire was a member of the organizing commit- de Recherche du Canada en algègre, combina- tee of FPSAC’05 (Taormina, Sicily). Vladimir toire et informatique mathématique, Café Rico Makarenkov was a member of the organizing (Montréal) committee of the Douzièmes journées de la So- Organizers: Srecko Brlek (UQÀM), Cédric ciété Francophone de Classification (May 30 – June Chauve (Simon Fraser/UQÀM), Annie Lacasse 1, 2005).

Members of the Laboratory

Regular members Alain Goupil (UQTR) Combinatorics, algebra, linear representations of Srecko Brlek (UQÀM) Director groups, symmetric group. Combinatorics of words, algorithmics. Sylvie Hamel (Montréal) Robert Bédard (UQÀM) Bioinformatics and algorithms, theory of lan- Representations of finite groups, Lie theory. guages and automata, algebraic combinatorics. François Bergeron (UQÀM) Gilbert Labelle (UQÀM) Combinatorics, algebra, representations of finite Enumerative combinatorics, analysis. groups. Pierre Leroux (UQÀM) Cédric Chauve (Simon Fraser & UQÀM) Enumerative and algebraic combinatorics. Enumerative combinatorics, trees, bioinformatics. Vladimir Makarenkov (UQÀM) Computational biology, mathematical classification.

78 RESEARCH LABORATORIES

John Mullins (École Polytechnique de Mont- gebra, Hopf algebras and quantum groups, cat- réal) egory theory. Analysis of cryptographic protocols and e- Luc Bélair commerce protocols, formal semantics, secure (UQÀM) mobile code specification, operational concur- Mathematical logic, model theory. rency models Nantel Bergeron (York) Applied algebra. Christophe Reutenauer (UQÀM) Algebraic combinatorics, noncommutative alge- Pierre Bouchard (UQÀM) bra, automata theory, coding theory, free alge- Commutative algebra, algebraic geometry and bras. combinatorics. Denis Thérien (McGill) Yves Chiricota (UQÀC) Complexity theory, logic, combinatorics, proba- Computer graphics, mathematical methods in bility theory. computer graphics, combinatorics, computational geometry, symbolic computation. Timothy R.S. Walsh (UQÀM) Algorithmics, enumerative combinatorics, Sylvie Corteel (CNRS) graph theory. Enumerative and bijective combinatorics, partitions of integers and q-series. Associate members Adriano Garcia (UC San Diego) Michel Bousquet (Cégep du Vieux-Montréal) Algebraic combinatorics, symmetric functions, Enumeration of combinatorial structures, planar harmonic and co-invariant spaces, quasihar- maps and cacti, theory of species, Lagrange in- monic and quasi-invariant functions. version formulas. André Joyal (UQÀM) Pierre Lalonde (Cégep Maisonneuve) Algebraic topology, category theory. Enumerative and bijective combinatorics, alter- Jacques Labelle (UQÀM) nating sign matrices, enumeration of involutions Combinatorics, topology. with respect to various parameters, use of pfaffi- ans and determinants in enumeration. Louise Laforest (UQÀM) Data structures, combinatorics, asymptotic anal- Cédric Lamathe (UQÀM) ysis, quaternary trees. Combinatorics of tree-like structures, theory of species, indicator series of partially labeled Daniel Lemire (TELUQ) structures and asymmetric structures. Database theory, data warehousing, multidimensional databases (OLAP), data mining, time Luc Lapointe (Talca, Chili) series, collaborative filtering, information re- Algebraic combinatorics, symmetric functions, trieval. integrable systems, supersymmetries. Simon Plouffe Dominic Rochon (UQTR) Integer sequences, generalized expansions of Complex analysis, hypercomplex numbers. real numbers. Xavier G. Viennot (Bordeaux 1) Collaborating members Enumerative, algebraic and bijective combina- Marcello Aguiar (Texas A&M) torics, interactions between combinatorics, the- Algebraic combinatorics, non-commutative al- oretical informatics and theoretical physics.

Mathematical Analysis

Description

At the same time classical and central to modern was created four years ago. Currently the Lab- mathematics, analysis involves studying con- oratory has 31 regular and 7 associate mem- tinuous systems, from dynamical systems to bers working at eight different universities in solutions of partial differential equations and Québec, the USA and France. The research ar- spectra of operators. The Analysis Laboratory eas of the members of the Laboratory are the

79 CENTRE DE RECHERCHES MATHÉMATIQUES following: harmonic analysis, complex analy- theory and dynamical systems, control thesis and several complex variables, potential theory, mathematical physics, applied mathematics, ory, functional analysis, Banach algebras, mi- probability, nonlinear analysis, nonlinear differ- crolocal analysis, analysis on manifolds, non- ential equations, topological methods in differ- smooth analysis, spectral theory, partial dif- ential equations, ﬂuid dynamics and turbulence. ferential equations, geometric analysis, ergodic

News and highlights

Iosif Polterovich (member of CIRGET and awarded the CMS Excellence in Teaching Award the Mathematical Analysis Laboratory) was at the CMS Summer 2006 Meeting in Calgary. awarded the André-Aisenstadt Prize. Javad Alina Stancu (Concordia) and Octav Cornea Mashregi has just published a book enti- (Montréal) have become associate members of tled Analyse abstraite. Frédéric Gourdeau was the Laboratory.

Students, postdoctoral fellows and visitors

The Laboratory welcomed 10 postdoctoral fel- The Mathematical Analysis Laboratory also wel- lows in 2005 – 2006. Abdellatif Bourhim worked comed many researchers. G. Karadzhov (Bulgar- in operator theory at Université Laval; Emily ian Academy of Sciences) visited G. Dafni; M. Dryden, in spectral geometry at McGill; A. Ivrii, Levitin visited D. Jakobson and I. Polterovich; in geometric analysis at McGill and the CRM; S. De Bièvre (Lille) visited V. Jaksic; E. Fricain M. Merkli, in mathematical physics at McGill; (Lyon) visited P. Koosis and J. Mashreghi; Y. Last Mario Roy, in dynamical systems at Université (Hebrew University) visited V. Jaksic; A. Sosh- Laval; V. Shramchenko, in analysis at Concor- nikov (UC Davis) visited V. Jaksic; Ariel Blanco dia and the CRM. Chadi Nour worked at the visited T. Ransford; Zengjian Lou (Shantou) vis- Université de Montréal under the supervision of ited the Laboratory from January 12 to Febru- R. Stern; Changzhong Zhu, at the Université de ary 11, 2006; E.S. Zeron visited P. Gauthier; A. Montréal under the supervision of P. Gauthier; Komech visited A. Shnirelman; R. Schubert vis- Sara Derivière, at the Université de Sherbrooke ited D. Jakobson, I. Polterovich and J. Toth; A. under the supervision of Tomasz Kaczynski; and Strohmaier visited D. Jakobson; L. Parnovski Biao Wu, at Carleton University under the su- visited D. Jakobson and I. Polterovich; R. Shvy- pervision of D. Dawson. Also, in 2005 – 2006, dkoi and Y. Gliklikh visited Shnirelman; S. 8 undergraduate students, 35 master’s students Zelditch visited J. Toth and V. Jaksic; A. Marino and 31 Ph.D. students were supervised by Labo- and C. Saccon (Pisa) visited M. Frigon. ratory members.

Seminars

The members of the Mathematical Analysis Lab- which featured 22 talks in 2005 – 2006. At the oratory organize several seminars at four main Université de Montréal, Christiane Rousseau or- locations. At Université Laval, Javad Mashreghi ganizes a Seminar in Nonlinear Analysis and and Jérémie Rostand organize an Analysis Sem- Dynamical Systems that featured 20 talks in inar, which featured 13 talks in 2005 – 2006, and 2005 – 2006. Finally, at the Université de Sher- Javad Mashreghi organizes an Analysis Work- brooke, Madjid Allili, Virginie Charette, François shop, which also featured 13 talks. Galia Dafni Dubeau and Tomasz Kaczynski organize a Sem- (Concordia) and Ivo Klemes (McGill) organize inar in Computational Geometry and Topology jointly the McGill/Concordia Analysis Seminar, that featured 19 talks in 2005 – 2006.

Workshops, special sessions and others

In 2005 – 2006, members of the Mathematical “Probability and Mathematical Physics,” a Analysis Laboratory organized three meetings Conference Celebrating the 65th Birthday of whose descriptions may be found in the “Gen- Stanislav Molchanov eral Program” section of this report. June 27 – July 1, 2005, CRM

80 RESEARCH LABORATORIES

Organizers: Don Dawson (Carleton & McGill), Colloquium on Potential Theory — 74e congrès Vojkan Jaksic (McGill), Boris Vainberg (UNC de l’Acfas May 15 – 19, 2006, McGill University Charlotte) Sponsors: Consulat général de France à Mont- réal, CRM, Mathematical Analysis Laboratory, Analysis Day, 2006 May 1st, 2006, CRM Orga- FQRNT, Ofﬁce of the McGill Vice-Principal (Re- nizer: Dmitry Jakobson search & International Relations) Organizer: Ko- hur Gowrisankaran (McGill)

Members of the Laboratory

Regular members Kohur Gowrisankaran (McGill) Potential theory. Dmitry Jakobson (McGill) Director Pure mathematics, global analysis, spectral ge- Vojkan Jaksic (McGill) ometry, quantum chaos, harmonic analysis, Quantum statistical mechanics, random eigenvalues and eigenfunctions. Schrödinger operators. Line Baribeau (Laval) Tomasz Kaczynski (Sherbrooke) Complex and functional analysis, Banach alge- Topological methods, Conley index, applica- bras, holomorphic iterations, discrete groups. tions to dynamical systems. Abraham Boyarsky (Concordia) Ivo Klemes (McGill) Dynamical systems. Harmonic analysis, trigonometric series. Francis H. Clarke (Lyon 1) Alexey Kokotov (Concordia) Nonlinear and dynamic analysis, control theory, Spectral geometry of Riemann surfaces, hyper- calculus of variations. bolic partial differential equations. Galia Dafni (Concordia) Paul Koosis (McGill) Harmonic analysis, partial differential equa- Harmonic analysis. tions, several complex variables. Javad Mashreghi (Laval) Donald A. Dawson (Carleton & McGill) Complex analysis, harmonic analysis, Hardy Probability, stochastic processes. spaces. S. W. Drury (McGill) Yiannis N. Petridis (CUNY Lehman College) Harmonic analysis, matrix theory. Automorphic forms and their spectral theory, analytic number theory, spectral and scattering Richard Duncan (Montréal) theory of manifolds. Ergodic theory, martingale theory, probability theory in Banach spaces. Iosif Polterovich (Montréal) Geometric applications of spectral analysis. Richard Fournier (Dawson College) Probability, stochastic processes. Thomas J. Ransford (Laval) Complex and harmonic analysis, functional Marlène Frigon (Montréal) analysis and theory of operators, spectral anal- Nonlinear analysis, differential equations, ﬁxed ysis, potential theory. point theory, critical point theory, multivalent analysis. Dominic Rochon (UQTR) Complex analysis, hypercomplex numbers. Paul M. Gauthier (Montréal) Complex analysis, holomorphy, harmonicity, an- Jérémie Rostand (Laval) alytic approximation. Complex analysis, experimental mathematics. Pawel Gora (Concordia) Christiane Rousseau (Montréal) Ergodic theory, dynamical systems, fractal ge- Dynamical systems, bifurcations, qualitative ometry. theory, polynomial systems, analytic invariants, integrable systems. Frédéric Gourdeau (Laval) Banach algebras, cohomology, amenability, func- Dana Schlomiuk (Montréal) tional analysis. Global analysis, dynamical systems, singulari-

81 CENTRE DE RECHERCHES MATHÉMATIQUES ties, bifurcations, algebraic curves, primary inte- Pengfei Guan (McGill) gral. Partial differential equations, geometric analysis, several complex variables. Alexander Shnirelman (Concordia) Applications of geometric analysis to ﬂuids and John Harnad (Concordia) “weak” solutions of the Euler and Navier – Mathematical physics, classical and quantum Stokes equations. physics, geometrical methods, integrable systems, group theoretical methods, random ma- Ron J. Stern (Concordia) trices, isomonodromic deformations, isospectral Functional analysis and theory of operators, lin- ﬂows. ear and nonlinear systems, non-smooth analysis, stability, optimal control. Niky Kamran (McGill) Geometric approach to partial differential equa- John A. Toth (McGill) tions. Spectral theory, semi-classical analysis, microlocal analysis, Hamiltonian mechanics. Dmitry Korotkin (Concordia) Integrable systems, isomonodromic deforma- Samuel Zaidman (Montréal) tions, classical and quantum gravity, Frobenius Functional analysis and differential equations in varieties. abstract spaces, pseudo-differential operators Nilima Nigam (McGill) Applied analysis, numerical methods in electro- Associate members magnetism. Octav Cornea (Montréal) Alina Stancu (Concordia) Algebraic topology, dynamical systems. Geometric analysis.

Mathematical Physics

Description

The mathematical physics group is one of the tems; the spectral theory of random matrices; oldest and most active at the CRM. It consists percolation phenomena; conformal field theory; of fourteen regular members, all full-time fac- quantum statistical mechanics; spectral and scat- ulty at five Quebec Universities, and fourteen as- tering theory of random Schrödinger opera- sociate members. The Laboratory also includes tors; quasi-crystals; relativity; spectral transform eight research associates and postdoctoral fel- methods; asymptotics of eigenstates; founda- lows, and lab members supervise or cosupervise tional questions in quantization; coherent states; the thesis work of fifty-one master’s and doc- wavelets; supersymmetry; the symmetry analy- toral students. The group hosts many visiting sis of PDE’s and difference equations; represen- researchers and carries out research in many of tation theory of Lie groups and quantum groups; the most active areas of mathematical physics: and the mathematical structure of classical and coherent nonlinear systems in fluids, optics and quantum field theories. plasmas; classical and quantum integrable sys-

News and highlights

There was a substantial reorganization of the 14 are regular (i.e., voting) members and 14 are Laboratory membership this year. Five mem- associate members. The addition of four new bers who were concurrently associated with members of international distinction, who have other CRM laboratories chose to demote their also been regular visitors at the CRM for a num- PhysMath membership status to Associate, and ber of years, and are engaged in ongoing collab- four new external associate members were orations with our regular members, adds a fur- added: Bertrand Eynard (CEA, Saclay), Alexan- ther international dimension to our group. der Its (IUPU Indianapolis), Robert Conte (CEA, In September 2005, a Doctorate Honoris Causa Saclay) and Jean-Pierre Gazeau (Paris 7). This was conferred upon Jiri Patera for his contribu- raised our membership to a total of 28, of whom tions to the application of Lie theoretic methods

82 RESEARCH LABORATORIES in physics and the mathematical theory of qua- John Harnad was also asked to organize, sicrystals. In October 2006, a similar distinction jointly with Jinho Baik (Michigan), the ses- will be conferred upon Pavel Winternitz. John sion on random matrices at this year’s In- Harnad was awarded the 2006 CAP – CRM Prize ternational Congress of Mathematical Physics in Theoretical and Mathematical Physics at the (ICMP), which took place in Rio de Janeiro annual Congress of the Canadian Association of in August 2006. The ICMP occurs every three Physicists (CAP), which took place at Brock Uni- years. Amongst our student successes, Vasil- versity in June 2006. This award is given annu- isa Schramchenko, who completed her Ph.D. at ally jointly by the CAP and the CRM, “in recog- Concordia in 2005 under the direction of Dmitry nition of exceptional achievements in theoreti- Koroktin, won the CMS Prize for the best doc- cal and mathematical physics.” Harnad is the toral thesis in mathematics in Canada, as well third recipient of the award amongst the mem- as the Governor General’s gold medal for the bers of the CRM PhysMath Lab — the previous best doctoral thesis in all subjects at Concordia. winners being Pavel Winternitz (2002) and Jiri She was awarded an Alexander Von Humboldt Patera (2004). The selection committee is cho- Fellowship, which she has held this past year at sen jointly by the CAP and the CRM, and con- the Max Planck Institute in Bonn, and an EPSRC sists of physicists and mathematicians from both postdoctoral research fellowship, which she will Canada and the United States. It was chaired this be holding throughout the coming year at the year by David Brydges (UBC), who was Presi- Mathematical Institute in Oxford. She was also dent of the International Mathematical Physics offered an E.U. Marie Curie fellowship, which Union last year. she had to decline because of the two postdoctoral awards that she had already accepted.

Students, postdoctoral researchers and visitors

The following researchers are postdoctoral fel- dents and 24 Ph.D. students were supervised by lows or research associates who worked this Laboratory members. year under the supervision of one or more of The following is a list of researchers who visited the regular members of the PhysMath Lab (the the Laboratory in 2005 – 2006 (their afﬁliation names of the supervisors are listed within paren- and the name of their host are indicated within theses): Hakan Ciftci (R. Hall), Michael Germain parentheses): Leonid Chekhov (Steklov Mathe- (J. Patera), Andrew McIntyre (D. Korotkin), Man matical Institute, D. Korotkin), S. Rukolajne (St. Yue Mo (J. Hurtubise, M. Bertola), Gabor Pusztai Petersburg, D. Korotkin), Vladimir Dorodnitsyn (J. Harnad), Libor Snobl (M. Grundland, P. Win- (Russian Academy of Sciences, P. Winternitz), ternitz), Ismet Yurdesen (M. Grundland, P. Win- A. Kokotov (D. Korotkin), Anatoliy Klimyk ternitz), Armen Atoyan (research associate, J. Pa- (Prague, J. Patera), Decio Levi (Roma Tre, P. Win- tera). Amongst our current postdoctoral fellows, ternitz), P. Zograf (Steklov Institute, Korotkin), Man Yue Mo has been awarded a new postdoc- V. Enolskii (Kiev, J. Harnad), Vojkan Zakrzewski toral research position at the University of Bris- (Durham, M. Grundland), Roman Smirnov (Dal- tol for 2006 – 2007. Former postdoctoral fellows housie, P. Winternitz), O. Sanchez (Havana, S.T. and students moving to new research and teach- Ali), Zora Thomova (SUNY Syracuse, P. Win- ing positions include: Jorgen Rasmussen, who ternitz), Rutwig Campoamor-Stursberg (Com- started a two-year appointment in September plutense, P. Winternitz), Stephan De Bièvre 2005 as Research Fellow at the University of Mel- (Lille, Y. Saint-Aubin), Alexander Strasburger bourne; Igor Loutsenko, who began a position (Agricultural University, Warsaw, M. Grund- as Marie Curie Research Fellow at the Oxford land), Paul Wiegmann (Chicago, J. Harnad), F. Center for Industrial and Applied Mathematics Bagarello (Palermo, S.T. Ali), Javier Negro (Val- (OCIAM); Libor Snobl, who is now assistant pro- ladolid, V. Hussin), Willy Hereman (Colorado fessor in the Department of Physics, Czech Tech- School of Mines, M. Grundland). nical University. In 2005 – 2006, 27 master’s stu-

83 CENTRE DE RECHERCHES MATHÉMATIQUES

Seminars

The usual weekly seminar series in Mathemati- addition, a new Working Seminar on Random Ma- cal Physics took place at the CRM every Tuesday trices, Isomonodromic Deformations and Riemann – afternoon, throughout both terms, with active Hilbert Problems was launched. It takes place participation by members, visitors, postdoctoral every Thursday at Concordia, again with ac- fellows and students. Approximately half the tive participation of many Laboratory members, talks were given by visiting invited speakers. In postdoctoral fellows, students and visitors.

Workshops, special sessions and others

Short Program on Random Matrices, Random the tenth anniversary of the series. The scale of Processes and Integrable Systems the next event will be much larger. June 20 – July 8, 2005, CRM Advanced course by Peter Zograf, a visitor to Organized with CIRGET the Laboratory Organizers: John Harnad (Concordia), Jacques January 2006 – April 2006 Hurtubise (McGill) A special series of lectures was given by Pe- This was a major event among the CRM scien- ter Zograf of the Steklov Mathematical Insti- tific activities of the year. It was organized by tute (Moscow). It was entitled Selected Topics in two of the PhysMath Lab members, John Har- Mathematical Physics: Graphs, Moduli and Quan- nad and Jacques Hurtubise, with active partici- tum Field Theory. The aim of this series was to pation by several more of its members (Dmitry survey some of the most striking applications of Korotkin, Marco Bertola), postdoctoral fellows combinatorics to algebraic geometry, which go (Man Yue Mo, Gabor Pusztai, Ismet Yurde- back to the pioneering work of Witten, Kontse- sen) and Ph.D. students (Julia Klochko, Ferenc vich, Okounkov and others. Balogh). A description of this workshop may be found in the “General Program” section of this Mini-lecture series by Stephan De Bièvre May report. 2006 – June 2006 Stephan De Bièvre (Lille) visited the CRM at the 9th International Workshop on Wavelets, Dif- invitation of A. Granville, V. Jaksic and Y. Saint- ferential Equations and Differential Geometric Aubin. He gave a series of five lectures on Unruh Methods radiation, using a pedagogical approach that al- February 20 – 24, 2006, Havana (Cuba) lowed graduate students to understand both the This is an annual event, organized jointly by S.T. principal mathematical difficulties of the subject Ali and members of the Department of Physics and their physical consequences. The lectures of the University of Havana. This year’s event were attended by mathematics and physics stu- was a relatively modest one, but gave the oppor- dents from McGill and the Université de Mont- tunity to prepare the next workshop, which will réal. take place in February 2007 and will represent

Members of the Laboratory

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

84 RESEARCH LABORATORIES

Véronique Hussin (Montréal) Bertrand Eynard (CEA Saclay) Group theory, Lie algebras and applications in Matrix models, integrable systems, string theory, physics, supersymmetries in classical and quan- relationship between matrix models, integrabil- tum mechanics. ity and algebraic geometry. Dmitry Korotkin (Concordia) Jean-Pierre Gazeau (Paris 7) Integrable systems, isomonodromic deforma- Coherent states, wavelets, relativistic quantum tions, classical and quantum gravity, Frobenius frames, symmetry groups for beta-lattices. varieties. Alexander Its (IUPU Indianapolis) Jean LeTourneux (Montréal) Soliton theory, integrable systems, special func- Symmetry properties of systems, special functions, mathematical physics. tions. Dmitry Jakobson (McGill) Pierre Mathieu (Laval) Pure mathematics, global analysis, spectral ge- Conformal field theory, classical and quantum ometry, quantum chaos, harmonic analysis, integrable systems, affine Lie algebras. eigenvalues and eigenfunctions. Jiri Patera (Montréal) Vojkan Jaksic (McGill) Applications of group theory, quasi-crystals, Lie Mathematical physics, quantum statistical me- algebras. chanics, random Schrödinger operators. Yvan Saint-Aubin (Montréal) Niky Kamran (McGill) Conformal field theory, statistical mechanics, 2- Geometric approach to partial differential equa- dimensional phase transition model. tions. Luc Vinet (Montréal) François Lalonde (Montréal) Symmetry properties of systems, special func- Symplectic topology and geometry, global anal- tions. ysis on manifolds, infinite dimensional transformation groups. Pavel Winternitz (Montréal) Methods of group theory in physics, nonlinear Decio Levi (Roma Tre) phenomena, symmetries of difference equations, Symmetries of differential and difference equa- superintegrability. tions, integrable nonlinear equations on the lattice and reductive perturbation theory on the lattice. Associate members Alexander Shnirelman (Concordia) Robert Conte (CEA Saclay) Applications of geometrical analysis to fluids Integrable and partially integrable systems, and “weak” solutions of the Euler and Navier – Painlevé analysis, exact solutions, finite differ- Stokes equations. ence equations. John A. Toth (McGill) Chris Cummins (Concordia) Microlocal analysis, partial differential equa- Group theory, modular functions, moonshine. tions. Stéphane Durand (Cégep Édouard-Montpetit) Carolyne M. Van Vliet (Miami) Classical and quantum physics, mathemati- Non-equilibrium statistical mechanics, fluctua- cal physics, symmetries, parasupersymmetries, tions and stochastic processes, quantum trans- fractional supersymmetries, KdV equations, port in condensed matter, electronic behavior in quantum mechanics, relativity. submicron quantum devices.

PhysNum

Description

Many activities of the PhysNum Laboratory take tory but it has extensive collaborations with re- place at the CRM itself; thus PhysNum increases search groups in neuroimaging, in Montréal and the visibility of the CRM in the ﬁeld of applied elsewhere: the Regroupement Neuroimagerie mathematics. PhysNum is not a large labora- Québec (under the guidance of Yves Joanette

85 CENTRE DE RECHERCHES MATHÉMATIQUES and Julien Doyon), the GRENE (directed by • fractal and multifractal analysis (materials Franco Lepore, from the Department of Psy- analysis, angiogenesis, turbulent signals); chology of the Université de Montréal), and the • the probabilistic approach for solving inverse quantitative imaging group of INSERM (Unité problems (maximum entropy inference, inde- 494) in Paris, directed by Habib Benali. Phys- pendence graphs). Num uses most of its financial resources to sup- These tools are used in several clinical and cog- port students who carry out their research at nitive subfields. The aforementioned research the CRM. The joint projects between PhysNum groups, which study applications to neurology, and the groups just mentioned are all related to are interested in developing a better methodol- mathematical imaging, especially in the medical ogy for their problems and are considering long- field, and encompass the following themes: term collaborations with the PhysNum team. • analysis and modeling using wavelets (ther- modynamic formalism, graphical models);

The evolution of PhysNum

In the last two years, PhysNum has increased Second, the work of some researchers now its interactions with other research centres, some takes place in close proximity to the labora- of which are close to the CRM (CRIUGM1, tories where the researchers concerned with CERNEC2, CRSN3 and MNI4), and some are applications and their equipment are located. abroad (the U-678 laboratory of INSERM in Thus PhysNum includes a team working on the France). Generally speaking, by focusing on methodology of brain imaging (MIC), which is biomedical applications, the PhysNum members part of the CRM but is located at the CRIUGM, have set themselves more precise research goals. a geriatrics research centre in Montréal. In the Two consequences follow from this situation. short and medium term, some PhysNum re- First, PhysNum is now a laboratory that car- searchers will collaborate with a CERNEC team ries out “targeted research,” which means that and the team of neuroscientists at the Sainte- it is deﬁned more by its application domain Justine Hospital. Experience has shown that the than by a speciﬁc area of mathematics. Its re- inclusion of CRM members into these research search themes span a large array of domains, for centres was needed in order to “merge” the instance dynamical models, statistics, Bayesian point of view of the mathematician and that of models, and wavelet analysis. the neuroscientist. The CRM, however, always initiates these collaborations and plays a pivotal role in the partnerships.

News and highlights

One of the highlights of the year 2005 – 2006 was by the PhysNum team. Here are some of these the visit of Habib Benali, who spent 10 months at projects. the CRM and the CRIUGM. Habib Benali is the Bayesian inference and entropy inference in director of the Unité U-678 of INSERM (Paris). MEG/EEG and optics imaging (J.-M. Lina, F. His visit strengthened the local collaborations Lesage, H. Benali, B. Goulard) (between the CRIUGM and the CRM, for in- This theme includes the following subthemes: stance) and the international ones, since he is one study of various methods for analyzing time se- of the main instigators of a joint laboratory be- ries, applications to fusion of IRMf and EEG tween INSERM and the Université de Montréal, data, sources location in optical imaging. The where the CRM will play an important role. research work will be carried out in collabora- Several research projects were started in 2005 – tion with the Functional Neuroimaging Unit of 2006, including projects in optics, thermoa- the Centre de Recherche de l’Institut Universi- coustics and magnetoencephalography, corre- taire de Gériatrie de Montréal (CRIUGM). The sponding to diverse brain imaging technologies. researcher N. Saadhenji takes part in the acqui- Within the last 18 months, these technologies be- sition of optical imaging data and develops tools came available in Québec for the ﬁrst time, and for analyzing the data. shortly thereafter some mathematical problems related to these technologies were addressed

86 RESEARCH LABORATORIES

Circular tomography and reconstruction of dynamical systems and the reaction-diffusion thermoacoustic sources (J.-M. Lina, F. Lesage) equation. The evolution of functional connectiv- Photoacoustic imaging is being developed as a ity can be monitored through repeated examina- molecular neuroimaging method for small ani- tions, and these observations will lead to models mals, because of the interesting properties of the of functional brain reorganization. resulting images. CRIUGM has acquired pho- Fractal analysis and porous media (F. Nekka) toacoustic equipement, and image reconstruc- New information and measurement technolo- tion and denoising techniques must be designed gies enable one to measure signals of an exceed- in order to optimize the quality of the data. ingly complex nature. For example, the design We propose to develop an image reconstruction of synthetic polymers has been revolutionized technique based on curvelets, a wavelet basis by the recent achievements in high-resolution, adapted to the one-dimensional structures con- broad-mass-range spectrometry. Wave propaga- tained in images. tion and scattering through porous media and Analysis of metabolic activities in IRMf (H. Be- highly ramified materials give rise to (spatial) nali, J.-M. Lina) signals that can be considered as defined on frac- The mathematical modeling of the neurolog- tal systems. A central concern when processing ical, physiological and biochemical processes such complex data is to use tools that extract underlying the activity of the brain enables the maximum information with the least de- one to describe mechanisms through which generacy. The autocorrelating process, expressed metabolism adapts to stimulation. In this way through the autocorrelation function (ACF), is a one can explain the correlations between elec- classical mathematical method widely used in trical, metabolic and hemodynamic phenomena. engineering and applied sciences to reorganize Recent work in the cognitive sciences demon- intrinsic similarities hidden in a structure. On strates the close link between the local field po- the other hand, fractal methods enable one to tentials and the IRMf signal (BOLD). Thus math- quantify efficiently complex information based ematical modeling plays an ever more impor- on existing similarities. The inadequacy of tra- tant role in the interpretation of the BOLD signal ditional methods and the known limitations of and its relationships with the activation of neu- popular fractal methods led F. Nekka to com- ron populations. One must design parametrized bine both approaches in order to create more models, different from the convolution models, powerful and less degenerate methods. F. Nekka that take into account the constraints of phys- and her research group have achieved much iological modeling (i.e., nonlinear differential progress in this endeavour and the application equations), in order to estimate quantitative pa- of complexity analysis to polymers and porous rameters from metabolic activities (neuron acti- media. The latter application has been prompted vation and neuron population location, for in- by her pharmaceutical research interests because stance). these media are widely used as vehicles for drug delivery. Analysis of functional connectivity networks (H. Benali) Phase synchrony and entropic measures in This project consists in proposing macroscopic EEG of epileptic patients (J.-M. Lina) models for the functional brain network. The This project deals with the study of the intracra- functional connectivity models that we have de- nial EEG signal in epileptic patients. We propose veloped only provide an instantaneous snap- to characterize and detect the intercritical peaks shot of the interactions between functional ar- using two approaches that will be merged even- eas; therefore, they yield litte information on tually. The first approach consists in measuring the dynamical aspects of the networks consid- the synchrony variations in the instantaneous ered. Thanks to the detection models in IRMF, phase of the signal. It is already known that this the sources location models in MEG/EEG, and measure is one of the predictors of some types the oriented Markov graphical statistical mod- of acute epileptic fits. The second approach con- els (also known as causal Markov models), it is sists in measuring order indices (Holder) in indi- becoming possible to study the dynamical and vidual signals or synchronized electrode pairs. functional relationships between populations of We will combine these measures with the syn- activated neurons. From a mathematical point chrony measure by using complex and analytic of view, understanding the emergence of a co- filters to obtain a discrete wavelet representa- hesive functional area through synchronized os- tion. These new techniques will be tested on real cillators is a very general problem, involving

87 CENTRE DE RECHERCHES MATHÉMATIQUES signals, in collaboration with J. Gotman and F. tute (McGill). We are considering applying these Dubeau from the Montreal Neurological Insti- techniques to the case of Alzheimer patients.

Students

In 2005 – 2006, 5 master’s students and 5 Ph.D. 11 and the Université de Montréal. He worked students were supervised by PhysNum mem- mostly at the CRM and defended his thesis in bers. One of the doctoral students, J. Daunizeau, September 2005. presented a thesis jointly at the Université Paris

Workshops, special sessions and others

The two workshops listed below were organized Organizers: Habib Benali (CHU Pitié-Salpê- by PhysNum. The reader may ﬁnd their descrip- trière), François Lalonde (Montréal) tions in the “Multidisciplinary and iNdustrial Program” section of this report. Members of the Laboratory

Workshop on Mathematics in Brain Imaging Regular members and its Applications to Cognitive and Clinical Neurosciences Jean-Marc Lina (ÉTS) Director October 17 – 18, 2005, Institut universitaire de Wavelets, statistical modeling and brain imag- gériatrie de Montréal ing, machine learning. Organizers: Habib Benali (CHU Pitié-Salpê- Alain Arnéodo (CNRS) trière), Julien Doyon (Montréal), Jean-Marc Lina Fractals and wavelets. (ÉTS) Habib Benali (CHU Pitié-Salpêtrière) Workshop Quantitative analysis in brain imaging, medical Current Issues in Functional Imaging with Op- imaging and multimodal systems. tical Devices May 11 – 12, 2006, CRM Line Garnero (Hôpital de la Salpêtrière) Organizers: Habib Benali (CHU Pitié-Salpê- Magnetoencephalography. trière), Frédéric Lesage (École Polytechnique de Bernard Goulard (Montréal) Montréal), Jean-Marc Lina (ÉTS) Brain imaging. Moreover, PhysNum members were involved in Frédéric Lesage (École Polytechnique de Mont- a workshop organized to foster collaborations réal) between them and other CRM mathematicians. Conformal theory, integrable systems, inverse In particular, PhysNum wants to persuade these problems, optical imaging. mathematicians to contribute to the brain imaging project. The description of this workshop Fahima Nekka (Montréal) may be found in the same section as the other Fractal analysis, porous systems, wavelets. two. Associate Member Workshop Between Specialists of Brain and Spine Imaging and Mathematicians Interested Keith J. Worsley (McGill) in the Questions Arising from Imaging Statistics of brain mapping, geometry of random May 23, 2006, CRM images in medicine and astrophysics.

Statistics

Description

Statistics is central to many endeavours in so- found everywhere in science. Recently, statistics ciety. Whether it be through surveys from sam- has undergone a revolution in its techniques and pling, clinical trials to study various biomedical approaches. This revolution has been driven by treatments or experimental designs in agricul- the need to analyze very large data sets and data ture or industry, statistical methodology can be with more complex structure, and by the ad-

88 RESEARCH LABORATORIES vent of powerful computers. For example, statis- new Pan-Canadian program in the analysis of tical methodology is now addressing problems complex data organized by the three Canadian whose structure is very complex, such as the mathematics institutes. The Laboratory consists analysis of brain images or genome data, and of the leaders of the Québec school of statistics, new methodology is developed for large data who work on topics such as statistical learning sets. Data mining is one of the tools used. One and neuronal networks, survey sampling, anal- of the aims of the Laboratory is to structure the ysis of functional data, statistical analysis of im- Québec statistical community so that it take part ages, dependence structures, Bayesian analysis, in this revolution at a time of an important re- analysis of time series and ﬁnancial data, and re- newal of the academic personnel. This structure sampling methods. allows the Québec community to beneﬁt from a

News and highlights

The year 2005 – 2006 was an excellent one for Laboratory statutes were adopted, and for the the Laboratory members. The Tier 1 Canada first time, the director of the Laboratory was Research Chair in Statistical Machine Learning, elected. In 2005 – 2006, Éric Marchand, who is a held by Yoshua Bengio, was changed into a Tier statistician and chairs the Departement of Math- 2 Chair in June 2005. Moreover, Yoshua Bengio ematics of the Université de Sherbrooke, asked has just been awarded an NSERC – CGI Indus- the Laboratory for its support in developing trial Research Chair on High-Dimensional Data the field of statistics within his department. The Mining for E-Finance. These developments are a Laboratory granted some financial support to testimony to the excellence of Yoshua Bengio’s the Department. Since the Université de Sher- work. Jean-François Quessy, assistant professor brooke is now contributing to the CRM, the at UQTR, received the Pierre-Robillard Award Laboratory will increase its support, especially (rewarding the best thesis in statistics) at the An- through the partial financing of the Statistics nual Meeting of the Statistical Society of Canada Seminar held at the Université de Sherbrooke. (SSC) in May 2006. His advisors were Christian The Laboratory members continued to be highly Genest and Bruno Rémillard. On the other hand, visible in 2005 – 2006. Here are some of the most Christian Genest, president of the Association prestigious lectures that they gave. Keith Wors- des statisticiennes et statisticiens du Québec, has ley was a plenary speaker at the European Meet- been President-elect of the SSC since last July, an ing of Statisticians held in Oslo. He was also an in- honour that matches his great leadership. vited speaker at the following conferences: Inter- Belkacem Abdous has just started a three-year face 2006, 38th Symposium on the interface of statis- term as a member of the NSERC Grant Selec- tics, computing science, and applications, and the tion Committee for statistics. Last June, Chris- Pacific Northwest Statistics Meeting. In June 2005, tian Léger became the Secretary for the SSC he gave the Gold Medal Address at the Annual Meetings. In this position he will supervise the Meeting of the SSC; the SSC Gold Medal is the scientific and logistical planning of the annual most prestigious Canadian prize for research in meetings. The termination of the NSERC Re- statistics. Jim Ramsay was invited to speak at the allocations Exercise has important implications International Meeting of the Psychometric Society in for the financing of the CRM and that of the the Netherlands. At the conference of the Inter- NPCDS (National Program on Complex Data national Association of Statistical Computing held Structures), which is vital for statisticians. Chris- in Cyprus, he was an invited speaker for a se- tian Léger, who is President of the NPCDS Gov- ries of four sessions on the theme “Statistics for erning Board, also belongs to a Liaison Com- Functional Data.” mittee with NSERC whose goal is to suggest Finally, although the competition for FQRNT avenues for continued financing of these pro- funds remained fierce in 2005 – 2006, a team con- grams. David Wolfson and Yogendra Chaubey sisting of Laboratory members and headed by are devoting most of their efforts to developing Keith Worsley obtained a FQRNT team grant. their respective departments, which they have The other members of the team are Masoud been chairing since June 2005. Asgharian, Lawrence Joseph, Brenda MacGib- The Statistics Laboratory had its first official bon, Jim Ramsay, Russ Steele, Alain Vandal and meeting in September 2005; this meeting coin- David Wolfson. Indeed, in the mathematical sci- cided with the two lectures of Brad Efron. The ences, grants were awarded to two teams only,

89 CENTRE DE RECHERCHES MATHÉMATIQUES one in mathematics and one in statistics. Jim NPCDS in order to organize a workshop on the Ramsay, along with a team of engineering pro- modeling of climate, in collaboration with math- fessors from Queen’s, also obtained ﬁnancing ematicians and statisticians from the University from MITACS for a new project on the estima- of Alberta, the University of British Columbia tion of the parameters of systems of differential and Agro-Canada. In due course, this workshop equations. Moreover, he obtained ﬁnancing from should lead to a MITACS project.

Students, postdoctoral fellows and visitors

Laboratory members are very much involved Hooker, who was supervised by Jim Ramsay as in the training of HQP. Indeed, within their re- a postdoctoral fellow, has just accepted a tenure- spective departments, statisticians are usually track position at Cornell University. The Labo- among those who train the largest number of ratory hosted several visitors during the year. students. As mentioned above, the former stu- Altogether, in 2005 – 2006, 5 undergraduate student Jean-François Quessy received the Pierre- dents, 90 master’s students, 56 Ph.D. students Robillard Award. The students and postdoctoral and 8 postdoctoral fellows were supervised by fellows trained by Laboratory members are of- Laboratory members. fered high-proﬁle positions. For instance, Giles

Seminars

On a weekly basis, the scientiﬁc life of the the end of the “General Program” section of this Laboratory revolves around two seminars, the report. Finally, in September 2005, the Statistics Colloque CRM – ISM – GERAD de statistique in Laboratory was honored by the visit of Professor Montréal and the Statistics Seminar at Univer- Bradley Efron (Stanford), who gave two lectures, sité Laval in Québec City. In 2005 – 2006, the lat- including a Grande conférence du rcm2. His two ter seminar featured 20 lectures. The lectures of lectures were attended by more than 100 and 150 the Colloque CRM – ISM – GERAD are listed at participants, respectively.

Workshops, special sessions and others

In 2005 – 2006, the main scientific activity of the Organizers: Masoud Asgharian (McGill), Thierry Laboratory was a three-day workshop on sur- Duchesne (Laval), Brenda MacGibbon (UQÀM) vival analysis. Two other activities were orga- Capture 2006: A Scientific Meeting and a Work- nized by Laboratory members: a workshop on shop on Capture – Recapture Models capture – recapture models and a school on statistical and machine learning. The reader will May 1 – 5, 2006, Université Laval Organizers find the descriptions of the two workshops in the : Gilles Gauthier (Laval), Louis-Paul “General Program” section of this report, and Rivest (Laval) the description of the School in the “Multidisci- NPCDS/MITACS Spring School on Statistical plinary and Industrial Program” section. and Machine Learning: Topics at the Interface Workshop on Survival Analysis May 23 – 27, 2006, CRM November 4 – 6, 2005, CRM Sponsored by MITACS Organizers: Yoshua Bengio (Montréal), Hugh A. Chipman (Acadia), Russell Steele (McGill)

Members of the Laboratory

Regular members Belkacem Abdous (Laval) Biostatistics, health research methodology, con- Christian Léger (Montréal) Director struction and validation of measuring tools in Resampling methods, adaptive estimation, the health sector. model selection, robustness, applications in data mining. Jean-François Angers (Montréal) Decision theory, Bayesian statistics, robustness

90 RESEARCH LABORATORIES with respect to prior information, function esti- Nadia Ghazzali (Laval) mation. Multidimensional data analysis, neural networks and genetic algorithms, applications in Masoud Asgharian (McGill) astrophysics and biostatistics. Survival analysis, changepoint problems, simu- lated annealing and its variants, optimization. Brenda MacGibbon (UQÀM) Yoshua Bengio (Montréal) Mathematical statistics, decision theory, bio- Statistical learning algorithms, neural networks, statistics. nucleus models, probabilistic models, data min- François Perron (Montréal) ing, applications in finance and statistical lan- Decision theory, multidimensional data analysis, guage modeling. Bayesian statistics. Martin Bilodeau (Montréal) James Ramsay (McGill) Multivariate analysis, decision theory, asymp- Functional data analysis, smoothing and non- totic methods. parametric regression, curve registration. Yogendra P. Chaubey (Concordia) Bruno Rémillard (HÉC) Sampling, linear models, resampling, survival Probability theory, empirical processes, time se- analysis. ries, nonlinear filtering, applications in finance. Pierre Duchesne (Montréal) Louis-Paul Rivest (Laval) Time series, sampling, multivariate analysis. Linear models, robustness, directional data, Thierry Duchesne (Laval) sampling, applications in finance. Survival analysis, longitudinal data analysis, Roch Roy (Montréal) missing data, modeling of losses, insurance of Time series analysis, predictive methods, appli- catastrophic incidents, nonparametric inference, cations in econometrics and epidemiology. model selection, warranty. Arusharka Sen (Concordia) Charles Dugas (Montréal) Statistical inference of truncated data, nonpara- Actuarial science, finance, learning algorithms, metric function estimation. neural networks, universal approximation, survival analysis. Russell Steele (McGill) Bayesian approaches to mixing modeling, mul- Debbie J. Dupuis (HÉC) tiple imputation. Extreme values, robustness. Alain C. Vandal (McGill) René Ferland (UQÀM) Biostatistics, nonparametric survival estimation Probability, stochastic processes, applications to and graph theory, imaging, capture – recapture financial mathematics. models. Sorana Froda (UQÀM) David B. Wolfson (McGill) Nonparametric methods in function estimation, Changepoint problems, survival analysis, applications of stochastic modeling in biology Bayesian statistics, optimal design, applications and medicine. in medicine. Christian Genest (Laval) Keith J. Worsley (McGill) Multidimensional data analysis, dependence Statistics of brain mapping, geometry of random measures, nonparametric statistics, decision the- images in medicine and astrophysics. ory, applications in actuarial science, finance and psychology.

91 Publications PUBLICATIONS

HE CRM publishes monographs, lecture notes, proceedings, software, videos and research re- T ports. It has several collections. The in-house collection Les Publications CRM offers titles in both English and French. The CRM also has publishing agreements with the American Mathematical Society (AMS) and Springer. Since 1992, two collections, edited by CRM, have been published and distributed by the AMS. They are the CRM Monograph Series and the CRM Proceedings and Lecture Notes. Springer publishes the CRM Series in Mathematical Physics and the Subseries of the Springer Lecture Notes in Statistics. An asterisk preceding an author indicates that this is a monograph from an Aisenstadt Chair holder.

Recent Titles

The following list of Recent Titles contains books American Mathematical Society that appeared in 2004 – 2005 or that will be pub- CRM Proceedings & Lecture Notes lished soon. Vestislav Apostolov, Andrew Dancer, Nigel Hitchin & McKenzie Wang (eds.), Perspectives in Comparison, Generalized and Special Geometry, American Mathematical Society vol. 40, 2006. CRM Monograph Series Pavel Winternitz, David Gomez-Ullate, Arieh Iserles, Decio Levi, Peter J. Olver, Reinout Quis- Olga Kharlampovich & Alexei Myasnikov, Alge- pel & Piergiulio Tempesta (eds.), Group Theory braic Geometry for a Free Group (to appear). and Numerical Analysis, vol. 39, 2005. Victor Guillemin & Reyer Sjamaar Convexity Properties of Hamiltonian Group Actions, vol. 26, Springer 2005. CRM Series in Mathematical Physics *Andrew J. Majda, Rafail V. Abramov & Mar- Marc Thiriet, Biology and Mechanics of Blood Flows cus J. Grote, Information Theory and Stochastics for (to appear) Multiscale Nonlinear Systems, vol. 25, 2005. Dana Schlomiuk, Andrei A. Bolibrukh, Sergei Les Publications CRM Yakovenko, Vadim Kaloshin & Alexandru Buium, On Finiteness in Differential Equations and Laurent Guieu & Claude Roger, L’Algèbre et le Diophantine Geometry, vol. 24, 2005. Groupe de Virasoro (to appear)

Previous Titles

American Mathematical Society *George Lusztig, Hecke Algebras with Unequal Pa- CRM Monograph Series rameters, vol. 18, 2003. Michael Barr, Acyclic Models, vol. 17, 2002. Prakash Panangaden & Franck van Breugel (eds.), Mathematical Techniques for Analyzing Con- *Joel Feldman, Horst Knörrer & Eugene current and Probabilistic Systems, vol. 23, 2004. Trubowitz, Fermionic Functional Integrals and the Renormalization Group, vol. 16, 2002. Montserrat Alsina & Pilar Bayer, Quaternion Or- ders, Quadratic Forms, and Shimura Curves, vol. 22, Jose I. Burgos, The Regulators of Beilinson and 2004. Borel, vol. 15, 2002. Andrei Tyurin, Quantization, Classical and Quan- Eyal Z. Goren, Lectures on Hilbert Modular Vari- tum Field Theory and Theta Functions, vol. 21, eties and Modular Forms, vol. 14, 2002. 2003. Michael Baake & Robert V. Moody (eds.), Direc- Joel Feldman, Horst Knörrer & Eugene tions in Mathematical Quasicrystals, vol. 13, 2000. Trubowitz, Riemann Surfaces of Inﬁnite Genus, Masayoshi Miyanishi, Open Algebraic Surfaces, vol. 20, 2003. vol. 12, 2001. *Laurent Lafforgue, Chirurgie des grassmanni- ennes, vol. 19, 2003.

93 CENTRE DE RECHERCHES MATHÉMATIQUES

Spencer J. Bloch, Higher Regulators, Algebraic John Harnad & Alexander R. Its (eds.), Isomon- K-Theory, and Zeta Functions of Elliptic Curves, odromic Deformations and Applications in Physics, vol. 11, 2000. vol. 31, 2002 James D. Lewis, A Survey of the Hodge Conjecture, John McKay & Abdellah Sebbar (eds.), Proceed- 2e édition, vol. 10, 1999 (with an appendix by ings on Moonshine and Related Topics, vol. 30, 2001. B. Brent Gordon). Alan Coley, Decio Levi, Robert Milson, Colin *Yves Meyer, Wavelets, Vibrations and Scaling, Rogers & Pavel Winternitz (eds.), Bäcklund and vol. 9, 1997. Darboux Transformations, vol. 29, 2001. *Ioannis Karatzas, Lectures on Mathematics of Fi- John C. Taylor (ed.), Topics in Probability and Lie nance, vol. 8, 1996. Groups: Boundary Theory, vol. 28, 2001. John Milton, Dynamics of Small Neural Popula- Israel M. Sigal & Catherine Sulem (eds.), Nonlin- tions, vol. 7, 1996. ear Dynamics and Renormalization Group, vol. 27, *Eugene B. Dynkin, An Introduction to Branching 2001. Measure-Valued Processes, vol. 6, 1994. John Harnad, Gert Sabidussi & Pavel Winternitz Andrew M. Bruckner, Differentiation of Real Func- (eds.), Integrable Systems: From Classical to Quan- tions, vol. 5, 1994. tum, vol. 26, 2000. *David Ruelle, Dynamical Zeta Functions for Piece- Decio Levi & Orlando Ragnisco (eds.), SIDE wise Monotone Maps of the Interval, vol. 4, 1994. III — Symmetry and Integrability of Difference Equations, vol. 25, 2000. V. Kumar Murty, Introduction to Abelian Varieties, vol. 3, 1993. B. Brent Gordon, James D. Lewis, Stefan Müller- Stach, Shuji Saito & Noriko Yui (eds.), The Arith- Maximilian Ya. Antimirov, Andrei A. Kolyshkin metic and Geometry of Algebraic Cycles, vol. 24, & Rémi Vaillancourt, Applied Integral Transforms, 2000. vol. 2, 1993. Pierre Hansen & Odile Marcotte (eds.), Graph *Dan V. Voiculescu, Kenneth J. Dykema & Colouring and Applications, vol. 23, 1999. Alexandru Nica, Free Random Variables, vol. 1, 1992. Jan Felipe van Diejen & Luc Vinet (eds.), Al- gebraic Methods and q-Special Functions, vol. 22, 1999. Michel Fortin (ed.), Plates and Shells, vol. 21, 1999. American Mathematical Society Katie Coughlin (ed.), Semi-Analytic Methods for CRM Proceedings & Lecture Notes the Navier – Stokes Equations, vol. 20, 1999. Rajiv Gupta & Kenneth S. Williams (eds.), Num- Jacques Hurtubise & Eyal Markman (eds.), Alge- ber Theory, vol. 19, 1999. braic Structures and Moduli Spaces, vol. 38, 2004. Serge Dubuc & Gilles Deslauriers (eds.), Spline Piergiulio Tempesta, Pavel Winternitz, John Har- Functions and the Theory of Wavelets, vol. 18, 1999 nad, Willard Miller Jr., Georgo Pogosyan & Miguel A. Rodriguez (eds.), Superintegrability in Olga Kharlampovich (ed.), Summer School in Classical and Quantum Systems, vol. 37, 2004. Group Theory in Banff, 1996, vol. 17, 1998. Hershy Kisilevsky & Eyal Z. Goren(eds.), Num- Alain Vincent (ed.), Numerical Methods in Fluid ber Theory, vol. 36, 2004. Mechanics, vol.16, 1998. H. E. A. Eddy Campbell & David L. Wehlau François Lalonde (ed.), Geometry, Topology and (eds.), Invariant Theory in All Characteristics, Dynamics, vol. 15, 1998. vol. 35, 2004. John Harnad & Alex Kasman (eds.), The Bispec- Pavel Winternitz, John Harnad, C.S. Lam & Jiˇrí tral Problem, vol. 14, 1998. Patera (eds.), Symmetry in Physics, vol. 34, 2004. Michel Delfour (ed.), Boundaries, Interfaces and André D. Bandrauk, Michel C. Delfour & Claude Transitions, vol. 13, 1998. Le Bris (eds.), Quantum Control: Mathematical and Peter G. Greiner, Victor Ivrii, Luis A. Seco & Numerical Challenges, vol. 33, 2003. Catherine Sulem (eds.), Partial Differential Equa- Vadim B. Kuznetsov (ed.), The Kowalevski Prop- tions and their Applications, vol. 12, 1997. erty, vol. 32, 2002.

94 PUBLICATIONS

Luc Vinet (ed.), Advances in Mathematical Sci- Springer ences: CRM’s 25 Years, vol. 11, 1997. CRM Subseries of the Lecture Notes in Donald E. Knuth, Stable Marriage and Its Relation Statistics to Other Combinatorial Problems, vol. 10, 1996. Marc Moore (ed.), Spatial Statistics: Methodologi- Decio Levi, Luc Vinet & Pavel Winternitz (eds.), cal Aspects and Applications, 2001. Symmetries and Integrability of Difference Equa- tions, vol. 9, 1995. S. Ejaz Ahmed & Nancy Reid (eds.), Empirical Bayes and Likelihood Inference, 2001. Joel S. Feldman, Richard Froese & Lon M. Rosen (eds.), Mathematical Quantum Theory II: CRM Publications Schrödinger Operator, vol. 8, 1995. Joel S. Feldman, Richard Froese & Lon M. Rosen Luc Lapointe, Ge Mo-Lin, Yvan Saint-Aubin & (eds.), Mathematical Quantum Theory I: Field The- Luc Vinet, Proceedings of the Canada-China Meet- ory and Many-Body Theory, vol. 7, 1994. ing on Theoretical Physics, 2003. Guido Mislin (ed.), The Hilton Symposium 1993, Armel Mercier, Fonctions de plusieurs variables : vol. 6, 1994. Différentiation, 2002. Donald A. Dawson (ed.), Measure-Valued Pro- Nadia El-Mabrouk, Thomas Lengauer & David cesses, Stochastic Partial Differential Equations and Sankoff (eds.), Currents in Computational Molecu- Interacting Systems, vol. 5, 1994. lar Biology, 2001. Hershy Kisilevsky & M. Ram Murty (eds.), Ellip- James G. Huard & Kenneth S. Williams (eds.), tic Curves and Related Topics, vol. 4, 1994. The Collected Papers of Sarvadaman Chowla Vol- Andrei L. Smirnov & Rémi Vaillancourt (eds.), ume I 1925-1935; Volume II 1936-1961; Vol- Asymptotic Methods in Mechanics, vol. 3, 1993. ume III 1962-1986, 2000. Philip D. Loewen, Optimal Control via Nonsmooth Michael Barr & Charles Wells, Category Theory for Analysis, vol. 2, 1993. Computing Science, 1999. M. Ram Murty (ed.), Theta Functions, vol. 1, 1993. Maximilian Ya. Antimirov, Andrei A. Kolyshkin & Rémi Vaillancourt, Mathematical Models for Eddy Current Testing, 1998. Xavier Fernique, Fonctions aléatoires gaussiennes, vecteurs aléatoires gaussiens, 1997. Faqir Khanna & Luc Vinet (eds.), Field Theory, In- tegrable Systems and Symmetries, 1997. Springer Paul Koosis, Leçons sur le théorème de Beurling et CRM Series in Mathematical Physics Malliavin, 1996. David W. Rand, Concorder Version Three, 1996 David Sénéchal, André-Marie Tremblay & (software and user guide). Claude Bourbonnais, Theoretical Methods for Strongly Correlated Electrons, 2003. Jacques Gauvin, Theory of Nonconvex Program- ming, 1994. *Roman Jackiw, Lectures on Fluid Dynamics, 2002. Decio Levi, Curtis R. Menyuk & Pavel Win- Yvan Saint-Aubin & Luc Vinet (eds.), Theoretical ternitz (eds.), Self-Similarity in Stimulated Raman Physics at the End of the Twentieth Century, 2001. Scattering, 1994. Yvan Saint-Aubin & Luc Vinet (eds.), Algebraic Rémi Vaillancourt, Compléments de mathématiques Methods in Physics, 2000. pour ingénieurs, 1993. Jan Felipe van Diejen & Luc Vinet (eds.), Robert P. Langlands & Dinakar Ramakrishnan Calogero – Moser – Sutherland Models, 1999. (eds.), The Zeta Functions of Picard Modular Sur- Robert Conte (ed.), The Painlevé Property, 1999. faces, 1992. Richard MacKenzie, Manu B. Paranjape & Woj- Florin N. Diacu, Singularities of the N-Body Prob- ciech J. M. Zakrzewski (eds.), Solitons, 1999. lem, 1992. Luc Vinet & Gordon Semenoff (eds.), Particles Jacques Gauvin, Théorie de la programmation and Fields, 1998. mathématique non convexe, 1992.

95 CENTRE DE RECHERCHES MATHÉMATIQUES

Pierre Ferland, Claude Tricot & Axel van de *R. Tyrrell Rockafellar, La théorie des sous- Walle, Analyse fractale, 1992 (software and user gradients et ses applications à l’optimisation, fonc- guide). tions convexes et non convexes, 1979. Stéphane Baldo, Introduction à la topologie des en- *Jacques-Louis Lions, Sur quelques questions sembles fractals, 1991. d’analyse, de mécanique et de contrôle optimal, 1976. Robert Bédard, Groupes linéaires algébriques, 1991. *Donald E. Knuth, Mariage stables et leurs relations Rudolf Beran & Gilles R. Ducharme, Asymptotic avec d’autres problèmes combinatoires, 1976. Theory for Bootstrap Methods in Statistics, 1991. *Robert Hermann, Physical Aspects of Lie Group James D. Lewis, A Survey of the Hodge Conjecture, Theory, 1974. 1991. *Mark Kac, Quelques problèmes mathématiques en David W. Rand & Tatiana Patera, Concorder, 1991 physique statistique, 1974. (software and user guide). *Sybreen de Groot, La transformation de Weyl et la David W. Rand & Tatiana Patera, Le Concordeur, fonction de Wigner: une forme alternative de la mé- 1991 (software and user guide). canique quantique, 1974. Véronique Hussin (ed.), Lie Theory, Differential Equations and Representation Theory, 1990. Other Collaborations with Publishers John Harnad & Jerrold E. Marsden (eds.), Hamil- tonian Systems, Transformation Groups and Spectral Marc Moore, Sorana Froda & Christian Léger (eds.), Mathematical Statistics and Applications: Transform Methods, 1990. Festschrift for Constance van Eeden, Lecture M. Ram Murty (ed.), Automorphic Forms and An- Notes – Monograph Series, vol. 42, 2003 (a col- alytic Number Theory, 1990. laboration with the Institute of Mathematical Wendy G. McKay, JiˇríPatera & David W. Rand, Statistics). Tables of Representations of Simple Lie Algebras. Duong H. Phong, Luc Vinet & Shing-Tung Yau Volume I. Exceptional Simple Lie Algebras, 1990. (eds.), Mirror Manifolds and Geometry, AMS/IP Anthony W. Knapp, Representations of Real Re- Studies in Advanced Mathematics, vol. 10, 1998 ductive Groups, 1990. (a collaboration with the AMS and the Interna- tional Press). Wendy G. McKay, JiˇríPatera & David W. Rand, SimpLie, 1990 (software and user guide). Pierre Ferland, Claude Tricot & Axel van de Walle, Fractal Analysis User’s Guide, 1994 (a col- Francis H. Clarke, Optimization and Nonsmooth laboration with the AMS). Analysis, Montréal, 1989. Hedy Attouch, Jean-Pierre Aubin, Francis Samuel Zaidman. Une introduction à la théorie des Clarke & Ivar Ekeland (eds.), Analyse non linéaire, équations aux dérivées partielles, 1989. 1989 (a collaboration with Gauthiers-Villars). *Yuri I. Manin, Quantum Groups and Noncommu- tative Geometry, Les Publications CRM, 1988. Videos Lucien Le Cam, Notes on Asymptotic Methods in Statistical Decision Theory, 1974. Eﬁm Zelmanov, Abstract Algebra in the 20th Cen- tury, 1997. Les Presses de l’Université de Montréal Aisenstadt Chair Collection Serge Lang, Les grands courants, 1991 Robert Bédard, Brouiller les cartes, 1991. Laurent Schwartz, Semimartingales and Their Stochastic Calculus on Manifolds, 1984. Serge Lang, Les équations diophantiennes, 1991. *Yuval Ne0eman, Symétries, jauges et variétés de Laurent Schwartz, Le mouvement brownien,1990. groupe, 1979. Laurent Schwartz, Une vie de mathématicien, 1989.

CRM Preprints

Ayoub, N., An L2 inequality for real polynomials, Bertola, M., Biorthogonal polynomials for 2-matrix CRM-3216, April 2006 models with semiclassical potentials, CRM-3205, October 2005

96 PUBLICATIONS

Bertola, M., Commuting difference operators, spinor blocked unsteady channel flow, CRM-3194, August bundles and the asymptotics of pseudo-orthogonal 2005 polynomials with respect to varying complex weights, Kolyshkin, A. A., Vaillancourt, R., Volodko, I., CRM-3217, May 2006 Weakly nonlinear analysis of rapidly decelerated Bertola, M., Harnad, J., Its, A., Dual Riemann – channel flow, CRM-3198a, September 2005 Hilbert approach to biorthogonal polynomials, CRM- Kolyshkin, A. A., Vaillancourt, R., Volodko, I., 3206, 2005 Approximative method for the calculation of the Bertola, M., Mo, M. Y., Isomonodromic deformation change in impedance due to a flaw in a conducting of resonant rational connections, CRM-3189, July cylindrical Layer, CRM-3212, January 2006 2005 Krejci, P., Sorine, M., Sainte-Marie, J., Urquiza, J. Colin, F., Frigon, M., Systems of singular Poisson M., Modelling and simulation of an active fibre for equations in unbounded domains, CRM-3177, Jan- cardiac muscle, CRM-3208, January 2006 uary 2005 Madrane, A., El Boukili, A., Vaillancourt, R., A Dellacherie, S., Existence et unicité d’une solu- new overlapping unstructured grid algorithm, CRM- tion classique à un modèle abstrait de vibration de 3203, October 2005 bulles de type hyperbolique-elliptique, CRM-3200, Morimoto, A., Ashino, R., Vaillancourt, R., Mul- September 2005 tiwavelet neural network preprocessing, CRM-3213, Dellacherie, S., Lafitte, O., Solutions autosem- March 2006 blables pour l’équation de la chaleur avec coefficients Morimoto, A., Shimano, Y., Ashino, R., Vaillan- discontinus, CRM-3207, December 2005 court, R., Wavelet and block singular value image Fournier, R., Ruscheweyh, S., Salinas, L., On a denoising, CRM-3202, October 2005 question of Brézis and Korevaar concerning a class of Nguyen-Ba, T., Vaillancourt, R., Hermite – square-summable sequences, CRM-3215, April 2006 Birkhoff – Obrechkoff 3-stage 6-step ODE solver of Grundland, A. M., Huard, B., Rank-k solutions de- order 14, CRM-3214, April 2006. scribed by hyperbolic systems, CRM-3197, Septem- Pelletier, E. F., Vaillancourt, R., Modelling instru- ber 2005 ments sounds using Malvar wavelets, CRM-3191, Haddou, M., Perron, F., Nonparametric estimation August 2005 of a cdf with mixtures of cdf concentrated on small Rousseau, C., The root extraction problem, CRM- intervals, CRM-3210, January 2006 3209, January 2006 Hariton, A. J., Supersymmetric extension of inte- Saidi, A., Roy, R., Robust optimal tests for causality grable Born – Infeld equation, CRM-3199, Septem- in multivariate time series, CRM-3228, May 2006 ber 2005 Sharp, P. W., Vaillancourt, R., Error growth of some Harnad, J., Orlov, A. Y., Fermionic approach to the symplectic explicit Runge – Kutta Nyström methods evaluation of integrals of rational symmetric func- for a simulation of the gas giants, CRM-3192, Au- tions, CRM-3195, August 2005 gust 2005 Hua, X., Vaillancourt, R., Dynamics of permutable Sharp, P. W., Vaillancourt, R., Efficient order-five meromorphic functions, CRM-3190, August 2005 second-derivative explicit Runge – Kutta pairs with Hua, X., Vaillancourt, R., Prime factorization of en- interpolants, CRM-3193, August 2005 tire functions, CRM-3211, January 2006 Jourdain, Sharp, P. W., Vaillancourt, R., Explicit Pouzet B., Le Bris, C., Lelièvre, T., Otto, F., Long-time Runge – Kutta pairs for Voltera integro-differential asymptotics of a multiscale model for polymeric fluid equations, CRM-3234, May 2006 flows, CRM-3188, July 2005 Sharp, P. W., Vaillancourt, R., New Nyström pairs Kolyshkin, A. A., Vaillancourt, R., Volodko, I., for the general second-order problem, CRM-3235, Complex Ginzburg – Landau equation for suddenly May 2006

For other preprints by CRM members go to www.crm.umontreal.ca/pub/bibliographies/index_e.html.

97 Scientiﬁc Personnel SCIENTIFIC PERSONNEL

CRM Members in 2005 – 2006

N contrast with most other mathematics institutes around the world, the CRM can count on the Isolid foundation of regular, associate and invited members. Regular members are all professors at partner institutions: Montréal, Concordia, McGill, UQÀM, Laval, Sherbrooke, and Ottawa. Other members are researchers affiliated with the CRM in 2005 – 2006 as part of exchange agreements with neighbouring universities and industry or are long-term visitors from Canadian and foreign institutions. The presence at the CRM of such an active group of researchers has brought many benefits to the Centre. In particular, the CRM’s national program is greatly facilitated by having on hand a large reserve of willing organizers, who have even contributed financially to the organization of activities. The largest partnership is with the Université de Montréal, which gives the equivalent of five full- time teaching positions in release time to the CRM. Release agreements with the other Montréal area universities afford the equivalent of two more full-time positions. Facilities are also provided to researchers affiliated with junior colleges. Several members are affiliated to the CRM through industrial agreements.

Regular Members

Ali, Syed Twareque, Concordia Darmon, Henri, McGill Apostolov, Vestislav, UQÀM David, Chantal, Concordia Arminjon, Paul, Montréal De Koninck, Jean-Marie, Laval Bandrauk, André D., Sherbrooke Delfour, Michel C., Montréal Doedel, Eusebius J., Concordia Baribeau, Line, Laval Dssouli, Rachida, Concordia Bartello, Peter, McGill El-Mabrouk, Nadia, Montréal Bédard, Robert, UQÀM Fortin, André, Laval Bélair, Jacques, Montréal Fournier, Richard, Dawson College Benali, Habib, CHU Pitié-Salpêtrière Frigon, Marlène, Montréal Bengio, Yoshua, Montréal Garon, André, École Polytechnique de Montréal Bergeron, François, UQÀM Gauthier, Paul M., Montréal Bertola, Marco, Concordia Goren, Eyal Z., McGill Bourgault, Yves, Ottawa Goulard, Bernard, Montréal Bourlioux, Anne, Montréal Granville, Andrew, Montréal Boyer, Steven, UQÀM Grundland, Alfred Michel, UQTR Brassard, Gilles, Montréal Guan, Pengfei, McGill Brlek, Srecko, UQÀM Hahn, Gena, Montréal Broer, Abraham, Montréal Hall, Richard L., Concordia Brunet, Robert C., Montréal Hamel, Sylvie, Montréal Harnad, John, Concordia Bryant, David, McGill Humphries, Tony R., McGill Chauve, Cédric, UQÀM Hurtubise, Jacques, McGill Chvátal, Vašek, Concordia Hussin, Véronique, Montréal Clarke, Francis H., Lyon 1 Iovita, Adrian, Concordia Collin, Olivier, UQÀM Jakobson, Dmitry, McGill Cornea, Octavian, Montréal Jaksic, Vojkan, McGill Cs˝urös,Miklós, Montréal Joyal, André, UQÀM Cummins, Chris, Concordia Kamran, Niky, McGill Dafni, Galia, Concordia Kharlampovich, Olga, McGill

99 CENTRE DE RECHERCHES MATHÉMATIQUES

Kisilevsky, Hershy, Concordia Murty, M. Ram, Queen’s Koosis, Paul, McGill Nekka, Fahima, Montréal Korotkin, Dmitry, Concordia Nigam, Nilima, McGill Labelle, Gilbert, UQÀM Owens, Robert G., Montréal Labute, John, McGill Patera, Jiˇrí,Montréal Lalonde, François, Montréal Polterovich, Iosif, Montréal Léger, Christian, Montréal Ransford, Thomas J., Laval Leroux, Pierre, UQÀM Reutenauer, Christophe, UQÀM Lesage, Frédéric, École Polytechnique de Rosenberg, Ivo G., Montréal Montréal Rousseau, Christiane, Montréal Lessard, Sabin, Montréal Roy, Damien, Ottawa LeTourneux, Jean, Montréal Roy, Roch, Montréal Levesque, Claude, Laval Russell, Peter, McGill Lina, Jean-Marc, École de Technologie Saint-Aubin, Yvan, Montréal Supérieure Sankoff, David, Montréal Lu, Steven, UQÀM Schlomiuk, Dana, Montréal MacGibbon, Brenda, UQÀM Shnirelman, Alexander, Concordia Makarenkov, Vladimir, UQÀM Stern, Ron J., Concordia Makkai, Michael, McGill Thaine, Francisco, Concordia Marcotte, Patrice, Montréal Toth, John A., McGill Mashreghi, Javad, Laval Vinet, Luc, Montréal Maslowe, Sherwin A., McGill Walsh, Timothy R. S., UQÀM Mathieu, Pierre, Laval Winternitz, Pavel, Montréal McKay, John, Concordia Wise, Daniel T., McGill Miasnikov, Alexei G., McGill Worsley, Keith J., McGill

Associate Members

Beaulieu, Liliane, Vieux-Montréal Levi, Decio, Roma Tre Bergeron, Nantel, York Li, Jun, Montréal Conte, Robert, CEA Saclay Petridis, Yiannis N., CUNY Lehman College Durand, Stéphane, Édouard-Montpetit Shahbazian, Elisa, Lockheed Martin Gander, Martin J., Genève Valin, Pierre, Lockheed Martin Garnero, Line, CHU Pitié-Salpêtrière Van Vliet, Carolyne M., Miami Leisen, Dietmar, McGill Zolésio, Jean-Paul, INRIA Sophia-Antipolis

Invited Members

Doray, Louis G., Montréal Larose, Benoît, Champlain Regional College Duchesne, Pierre, Montréal LeBlanc, Victor G., Ottawa Dugas, Charles, Montréal

100 SCIENTIFIC PERSONNEL

Postdoctoral Fellows

Each year the CRM plays host to a great number of postdoctoral fellows. Their funding is provided by the NSERC and FQRNT postdoctoral programs, the NATO international program administered by NSERC, the CRM (usually in collaboration with the ISM), the CRM’s research laboratories, and individual research grants from CRM members. The list below includes postdoctoral fellows in residence at the CRM and those co-funded by the CRM. Some of the fellows were in residence at the CRM for only part of the year. The afﬁliation given is the institution where the doctorate was obtained.

Belhaj, Adil, Mohammed V Maher, Joseph, UC Santa Barbara Bourhim, Abdellatif, Mohammed V McIntyre, Andrew, SUNY Stony Brook Charollois, Pierre, Bordeaux 1 McNamara, Peter, MIT Dellacherie, Stéphane, Paris 7 Merkli, Marco, Toronto Derivière, Sara, Rouen Mo, Man Yue, Oxford Gabbouhy, Mostafa, Ibn Tofaïl Mohammadalikhani, Ramin, Toronto Gay, David T., UC Berkeley Moyers-Gonzalez, Miguel Angel, UBC Hachimori, Yoshitaka, Tokyo Nour, Chadi, Saint-Joseph à Beyrouth Helfgott, Harald Andres, Princeton Pierre, Charles, Nantes Ivrii, Alexander, Stanford Pusztai, Bélà Gabor, Szeged Jones, Nathan Conrad, UC Los Angeles Sevilla Gonzalez, David, Cantabria Kashuba, Iryna, Sao Paulo Snobl, Libor, Czech Technical Institute Lelièvre, Tony, École Nationale des ponts et Tian, Ye, Columbia chaussées Tillmann, Stephan, Melbourne Letellier, Emmanuel, Paris 6 Titcombe, Michèle Suzanne, UBC Lisi, Samuel, New York Tore, Jensen Bernt, McMaster Lorin de la Grandmaison, Emmanuel, ÉNS Urquiza, José Manuel, Paris 6 Cachan Yurdusen, Ismet, Middle East Technical Lucier, Jason Bryan, Waterloo University

Long-term Visitors

Each year the CRM hosts a large number of visitors. The majority come to the Centre to participate in scientiﬁc activities organized or co-organized by the CRM. In the year 2005-2006, 676 such participants registered in the thematic program workshops, 488 in activities of the general program and 369 in those of the industrial and multidisciplinary program. The following list only includes visitors who were in residence for at least four weeks.

Adhikari, Sukumar Das, Harish-Chandra Bhowmik, Gautami, Lille 1 Institute Blomer, Valentin, Toronto Agboola, Adebisi, UC Santa Barbara Boyko, Vyacheslav, National Academy of Areﬁjamaal, A., Meshhed Sciences of Ukraine Asatryan, Davit, National Academy of Sciences, Campoamor-Stursberg, Otto Rutwig, Armenia Complutense Balog, Antal, A. Rényi Institute Chekhov, Leonid, Steklov Mathematical Batubenge, Augustin, Witwatersrand Institute Benali, Habib, CHU Pitié-Salpêtrière Chen, Huaihui, Nanjing Normal University Bhargava, Manjul, Princeton Christopher, Colin, Plymouth

101 CENTRE DE RECHERCHES MATHÉMATIQUES

Cilleruelo, Javier, Universidad Autónoma de Levi, Decio, Roma Tre Madrid Levitin, Michael, Heriot-Watt Cojocaru, Alina Carmen, Princeton Liquet, Benoît, Pierre Mendès France Coleman, Mark David, Manchester Logan, Adam, Liverpool Colmez, Pierre, Paris 6 Luca, Florian, UNAM Croot, Ernest S., Georgia Institute of Technology Lucier, Jason Bryan, Waterloo Dasgupta, Samit, Harvard Majard, Dany, Méditerranée De Bièvre, Stephan, Université des Sciences et Mantovan, Elena, UC Berkeley Technologies de Lille Martin, Greg, UBC De Koninck, Jean-Marie, Laval Milicevic, Djordje, Princeton Deshouillers, Jean-Marc, Bordeaux Moroz, Boris, Bonn Dumortier, Freddy, Limburgs Universitair Mosaki, Élie, Lyon 1 Centrum Mukhopadhyay, Anirban, IMSc Chennai Elashvili, Alexandre, Academy of Sciences of Murty, M. Ram, Queen’s Georgia Nang, Philibert, Tsukuba Elekes, Gy˝orgy, E˝otv˝osLoránd Neisendorfer, Joseph, Rochester Enolskii, Victor, National Academy of Sciences Ng, Nathan, Ottawa of Ukraine Pappalardi, Francesco, Roma Tre Erdélyi, Tamás, Texas A&M Pasol, Vicentiu, Boston Fang, Jiannong, École Polytechnique de Lausanne Prakash, Gyan, Harish-Chandra Institute Reznikov, Andrei, Weizmann Institute Fehr, Laszlo, Research Institute for Particle and Nuclear Studies Royer, Emmanuel, Montpellier 3 Fernandez, David J., CINVESTAV Saad, Nasser, Prince Edward Island Fleischer, Isidore Sabitova, Maria, Pennsylvannia Fricain, Emmanuel, Lyon 1 Safapour, A., Meshhed Friedlander, John, Toronto Saksida, Pavle, Ljubljana Sárk˝ozy, András, E˝otv˝osLoránd Gao, Peng, Michigan Schneider, Peter, Münster Garg, Gagan, Indian Institute of Science Schubert, Roman, Bristol Green, Ben, Bristol Shen, Hui, UBC Hamilton, Mark, University of Toronto Skorobogatov, Alexei, Imperial College Hariton, Alexander J., MIT Smirnov, Roman, Dalhousie Hereman, Willy, Colorado School of Mines Solymosi, Jozsef, UBC Hida, Haruzo, UC Los Angeles Soundararajan, Kannan, Michigan Ille, Pierre, Institut de mathématiques de Strasburger, Aleksander, Bialystok Luminy Tanré, Daniel, Lille 1 Jimenez Urroz, Jorge, Universitat Politècnica de Catalunya Tao, Terence, UC Los Angeles Karadzhov, Georgi Eremiev, Bulgarian Tavassoly, M. K., Isfahan Academy of Sciences Taylor, Jonathan, Stanford Khan, Rizwan, Institute for Advanced Study Teleman, Andrei, Provence Klimyk, Anatoliy, Bogolyubov Institute Thangadurai, R., Harish-Chandra Institute Konyagin, Sergei, Moscow State Thiriet, Marc, INRIA Rocquencourt Lafaye de Micheaux, Pierre, Pierre Mendès Thomova, Zora, SUNY Syracuse France Tian, Qingchun, McGill

102 SCIENTIFIC PERSONNEL

Tilouine, Paris 13 Witte, Nicholas, Melbourne Tolar, Jiˇrí,Czech Technical University Wooley, Trevor, Michigan Tornaria, Gonzalo, Texas à Austin Yatracos, Yannis, National University of Tsemo, Aristide, ICTP Singapore Van Luijk, Ronald, UC Berkeley Zeron, Eduardo Santillan, Cinvestav-IPN Vatsal, Vinayak, UBC Zhang, Yuanli Vu, Van H., UC San Diego Zhao, Liangyi, Toronto Vulpe, Nicolae, Académie des Sciences of Zhedanov, Alexei, Donetsk Institute for Physics Moldavie and Technology Watkins, Mark, Sydney Zhu, Hongmei, York Winterhalder, Axel, Universidade Estadual do Zograf, Peter, Steklov Institute Moranhao Zolésio, Jean-Paul, INRIA Sophia-Antipolis

Short-term Visitors

The following visitors were in residence for less than four weeks.

Adler, Mark, Brandeis Kuijlaars, Arno, Katholieke Universiteit Leuven Adler, Robert, Technion Last, Yoram, Université hébraïque Artes, Joan Carles, Universitat Autònoma de Le Bris, Claude, École Nationale des ponts et Barcelona chaussées Banks, William, Missouri Lemire, Frank, Windsor Bilu, Yuri, Bordeaux 1 Lindenstrauss, Elon, Princeton Bleher, Pavel, IUPU Indianapolis Longo, Matteo, Strasbourg 1 Bodner, Mark, MIND Institute Marklof, Jens, Bristol Bourgain, Jean, Institute for Advanced Study McLaughlin, Kenneth, UNC Chapel Hill Chipman, Hugh A., Acadia Michel, Philippe, Montpellier 2 Deift, Percy, Courant Institute Milson, Robert, Dalhousie Di Francesco, Philippe, CEA Saclay Murty, V. Kumar, Toronto Dorodnitsyn, Vladimir, Keldysh Institute Okounkov, Andrei, Princeton Duke, William, UCLA Orlov, Aleksander Yu., Institute of Oceanology Ekeland, Ivar, UBC Parnovski, Leonid, University College, London Ford, Kevin, Illinois à Urbana-Champaign Rochon, Frédéric, MIT Fouque, Jean-Pierre, North Carolina State Rudnick, Zeev, Bristol Germinet, François, Cergy-Pontoise Ruzsa, Imre, Hungarian Academy of Sciences Goldston, Daniel, San Jose State Saad, Yousef, Minnesota Gowers, William Timothy, Cambridge Semenoff, Gordon, UBC Heath-Brown, Roger, Oxford Shariﬁ, Romyar, McMaster Its, Alexander, IUPU Indianapolis Siddiqi, Abul Hasan, King Fahd University of Ivanova, Natalia, Brock Petroleum & Minerals Jackiw, Roman W., MIT Sircar, Ronnie, Princeton Kazakov, Vladimir, École Normale Supérieure Soshnikov, Alexander, UC Davis Kra, Bryna, Northwestern Stark, Harold, UC San Diego Kröger, Helmut, Laval Tocon, Maribel, Ottawa

103 CENTRE DE RECHERCHES MATHÉMATIQUES

Tracy, Craig A., UC Davis Venkatesh, Akshay, MIT Tsai, Tai-Peng, UBC Widom, Harold, UC Santa Cruz Tschinkel, Yuri, Göttingen Wiegmann, Paul, Chicago Tvalavadze, Marina, Memorial University of Zabrodin, Anton, ITEP Newfoundland Zeitouni, Ofer, Minnesota Tvalavadze, Tim, Memorial University of Zhu, Ji, Michigan Newfoundland Ullmo, Emmanuel, Paris 11 Zhukavets, Natalia, Czech Technical University van Moerbeke, Pierre, Université Catholique de Zinn-Justin, Paul, Paris 11 Louvain Zuber, Jean-Bernard, Paris 6

104 Governance and Scientiﬁc Guidance CENTRE DE RECHERCHES MATHÉMATIQUES

Bureau de direction

HE Bureau de direction consists of 8 to 11 members from the Université de Montréal and 2 to 5 Tmembers from the outside. The rector of the university and the dean of the Faculté des arts et sciences are represented on the Bureau. (Note that the new CRM statutes that will come into effect in 2007, will make the Bureau de direction, an interuniversity Board. Indeed, except for vice-principal of research and the FAS dean, university partners will be represented equally in the new Bureau, which will have up to 13 members.) Its role is to adopt the policies of the Centre, to recommend the nomination and the promotion of researchers and the apointment of regular members, to advise the director on the preparation of the budget and the university on the choice of the director.

Syed Twareque Ali Véronique Hussin Concordia University Université de Montréal Yoshua Bengio Niky Kamran Université de Montréal McGill University François Bergeron François Lalonde Université du Québec à Montréal Université de Montréal Michel Delfour Javad Mashreghi Université de Montréal Université Laval Joseph Hubert, doyen Christiane Rousseau Faculté des arts et des sciences Université de Montréal Université de Montréal Jacques Turgeon Université de Montréal

Chantal David (Concordia University) Andrew Granville (Université de Montréal), Christian Léger (Université de Montréal), and Jean LeTourneux (Université de Montréal), all Deputy Directors of the CRM, were invited members.

Scientiﬁc Advisory Committee

HE Scientific Advisory Panel advises the CRM on all scientific orientations: selection, organisation Tand elaboration of the thematic programs (annual programs, semestral programs and short programs), elaboration of the general and multidisciplinary programs and all other important activities. The Scientific Advisory Panel meets at the CRM at least once a year during a weekend of October and several times a year by electronic mail. Here is a list of its members:

Jerry Bona is a Professor at itorial board of twenty-five scientific journals the Department of Mathemat- and of several academic committees and panels. ics, Statistics and Computer Sci- Jerry Bona is a co-organizer of the Mathemati- ence at the University of Illi- cians and Educational Reform Network. nois at Chicago. He received Jean-Pierre Bourguignon re- a B.Sc. degree from Washing- ceived an engineering de- ton University in Saint Louis gree from École Polytech- (1966) and a Ph.D. from Har- nique and a Ph.D. in mathe- vard University (1971). His research experience matics. A differential geome- is vast. His research interests include fluid me- ter by training, he has been chanics, partial differential equations, computa- interested by the mathemat- tional mathematics and the associated numeri- ical aspects of physical theo- cal analysis, oceanography, coastal engineering ries: Dirac operators and spins, and general rel- and mathematical economics. He is an Elected ativity. His areas of specialty are the geometrical Fellow of the American Association for the Ad- estimation of eigenvalues of Laplace – Beltrami vancement of Science and a member of the ed- operators, Kählerian geometry and, more re-

106 SCIENTIFIC PERSONNEL cently, Finslerian geometry. Jean-Pierre Bour- 1979, and Ph.D., 1981) and has held positions at guignon directs advanced research classes at Brown University and Stanford University be- CNRS. He is the Director of Institut des hautes fore joining McMaster. He is principally inter- études scientifiques (IHES) at Bures-sur-Yvette ested in linear and nonlinear partial differen- and Professor of Mathematics at École Polytech- tial equations, Hamiltonian dynamical systems, nique. From 1990 to 1992, he served as President fluid dynamics, quantum mechanics, and non- of the Société mathématique de France and from linear functional analysis. He is a member of the 1995 to 1998 of the European Mathematical Soci- editorial boards of SIAM: Mathematical Analysis ety. He is a member of several scientific advisory and the Fields Institute and a Council member committees in Europe. Since 1996, he is a mem- of the American Mathematical Society. ber of Academia Europaea and since 2002 a for- Mark Haiman is a Profes- eign associate of the Spanish Royal Academy. sor at the Department of H. E. A. (Eddy) Campbell is Mathematics of the Univer- Vice President (Academic) and sity of California, Berkeley. Pro Vice Chancellor at Memorial He received his degrees from University of Newfoundland. He the Massachusetts Institute of received his Ph.D. from the Uni- Technology in Computer Sci- versity of Toronto in 1981. He was ence and Electrical Engineer- an NSERC postdoctoral fellow at ing (B.Sc., 1979) and in Mathematics (Ph.D., the University of Western Ontario 1984). His research interests are in algebraic from 1981 to 1983 before joining Queen’s Univer- combinatorics, algebraic geometry, representa- sity in 1984. He was Head of the Department of tion theory, and lattice theory. He is a member Mathematics and Statistics at Queen’s from 1995 of the editorial board of Algebra universalis. to 2000, and Associate Dean of the Faculty of A mathematician and physicist Arts and Science at Queen’s from 2000 to 2004. by training, Francois Lalonde Eddy Campbell was also President of the Cana- holds a Doctorat d’État (1985) dian Mathematical Society from 2004 to 2006. He from the Université de Paris- is a specialist in algebraic topology and invariant Sud Orsay in the field of differ- theory and the connections between them. ential topology. His fields of in- Jean-Louis Colliot-Thélène terests include symplectic topol- is directeur de recherche ogy, Hamiltonian dynamics and at the Centre national de the study of infinite-dimensional groups of la recherche scientifique transformations. He is member of the Royal So- (CNRS) at UMR 8628 (Uni- ciety of Canada since 1997 and was a Killam versité de Paris-Sud, Orsay). Research Fellowship recipient in 2000 – 2002. He He specializes in algebraic holds the Canada Research Chair in the field of geometry and its links to Symplectic Geometry and Topology at the De- arithmetic. He obtained a Doctorat d’État (1978) partment of Mathematics and Statistics of Uni- from Paris-Orsay. He is a member of the editorial versité de Montréal. Plenary speaker at the First boards of Annales scientifiques de l’École Normale Canada – China congress in 1997, part of his Supérieure (of which he was editor-in-chief until works in collaboration with Dusa McDuff was recently), the Journal of Number Theory and the presented in her plenary address at the ICM 1998 Journal of K-Theory. Jean-Louis Colliot-Thélène in Berlin. He was an invited speaker at the ICM is one of the main organizers of the 2005 – 2006 2006 in Madrid. Thematic Program at MSRI (Berkeley). Richard Lockhart is a Professor at Walter Craig is Canada Re- the Department of Statistics and Ac- search Chair of Mathematical tuarial Science Simon Fraser Uni- Analysis and its Applications versity. He received a B.Sc. in at the Department of Math- Mathematics from the University ematics and Statistics of Mc- of British Columbia (1975) and de- Master University. He received grees in Statistics from the Univer- degrees from the University sity of California, Berkeley (M.A., of California, Berkeley (B.A., 1976, Ph.D., 1979). A former Editor of the Cana- 1977) and from the Courant Institute of Math- dian Journal of Statistics, he has also served on the ematical Sciences, New York University (M.Sc., Advisory Committee on Statistical Methods of

107 CENTRE DE RECHERCHES MATHÉMATIQUES

Statistics Canada. He was President of the Sta- Normale Supérieure in Paris. His main re- tistical Society of Canada in 199 – 1997. Much of search interests are 3-dimensional topology, hy- his work is in the area of model assessment, gen- perbolic geometry, and geometric and combina- erally in the form of goodness-of-fit. torial group theory. He is associate editor of the Mitchell Luskin is a Pro- Journal of Knot Theory and its Ramifications and fessor of Mathematics at was the geometric topology editor of the Trans- the University of Min- actions of the American Mathematical Society from nesota, a Fellow of the 1992 to 2000. Minnesota Supercomput- Steven Zelditch is a Profes- ing Institute and a mem- sor of Mathematics at Johns ber of the graduate fac- Hopkins University. He re- ulty of the Department of ceived his Ph.D. from the Uni- Aerospace Engineering and Mechanics of the versity of California, Berkeley, University of Minnesota. He holds degrees in in 1981. A past member of Mathematics from Yale University (B.Sc., 1973) the editorial board of Annales and the University of Chicago (M.Sc., 1976, Scientifiques de l’École Normale Ph.D., 1977). His research interests include nu- Supérieure, he is presently on the editorial board merical analysis, scientific computing, applied of the American Journal of Mathematics. His re- mathematics, partial differential equations, com- search centers around applications of microlo- putational materials science, and computational cal analysis to problems concerning: asymp- physics. He delivered an invited lecture at the totics of eigenfunctions/eigenvalues on Rie- International Congress of Mathematicians held mannian manifolds, statistical algebraic geom- in Beijing in 2002. He is a member of the editorial etry, problems of mathematical physics rang- boards of Dynamics and Differential Equations, the ing from quantum chaos to 2D Yang – Mills to International Journal of Computational and Numer- string/M theory. ical Analysis and Applications, Communications in Jacques Turgeon, Vice-Principal (Research), Applied Analysis, the International Journal of Dif- Université de Montréal, is ex-officio member of ferential Equations and Applications, and the Inter- the Advisory Committee. Chantal David (Con- national Journal of Pure and Applied Mathematics. cordia University), Andrew Granville (Univer- Carl Pomerance is a Professor sité de Montréal), Christian Léger (Université de at the Department of Mathe- Montréal), and Jean LeTourneux (Université de matics of Dartmouth College. Montréal), all Deputy Directors of the CRM, are From 1999 to 2003, he was a invited members of the Committee. member of the technical staff of Bell Labs-Lucent Technolo- gies. He holds degrees from Brown University (B.A., 1966) and from Harvard University (M.A., 1970, Ph.D., 1972). A number theory specialist, he has received numerous prizes and awards including the Levi L. Conant Prize of the American Math- ematical Society. He is one of the editors-in-chief of Integers: The Electronic Journal of Combinatorial Number Theory and a member of the editorial board of the Journal of Supercomputing and the AMS Undergraduate Book Series. Peter Shalen is a Professor at the Department Mathematics, Statistics and Computer Sci- ence at The University of Illi- nois at Chicago. He received his B.A. from Harvard Col- lege (1966) and his Ph.D. from Harvard University (1972). He also spent a year as an undergraduate at École

108 CRM Administrative and Support Staﬀ CENTRE DE RECHERCHES MATHÉMATIQUES

The Director’s Oﬃce

François Lalonde Andrew Granville Director Deputy Director, CRM Prizes Christian Léger Jean LeTourneux Acting Director (Fall 2005), Deputy Director Deputy Director, Publications Chantal David Deputy Director, Theme Years and Theme Semesters

Administration

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

Scientiﬁc Activities

Louis Pelletier Sakina Benhima Coordinator Project Manager (on maternity leave starting in Josée Laferrière September 2005) Assistant Josée Simard Project Manager (starting in September 2005)

Computer Services

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

Publications

André Montpetit Louise Letendre TeX Expert (half time) Technician

Communications

Suzette Paradis Mélisande Fortin-Boisvert Communications Ofﬁcer and Webmaster Annual Report Coordinator

110 Statement of Revenue and Expenditures for the Fiscal Year Ending on May 31, 2006 CENTRE DE RECHERCHES MATHÉMATIQUES ) AL 3 407

50 000 30 000 30 000 85 605 27 500 20 000 20 047 17 762 52 500 55 206 49 455 53 486

525 000 341 000 120 000 100 000 288 995

1 478 100 3 348 063

TOT

------

3 407

continued on next page ( 85 605 27 500 20 000 12 262 53 263

202 036

Other Sources

------

20 047 52 500 55 206 288 995 416 748

Partners &

Researchers

------

49 455 49 455

Funds

Endowment

------

50 000 30 000 30 000

120 000 100 000 330 000

Other

Universities ------

223 4 000

515 000 361 000 870 223

UdeM CÉDAR

------

- 1 500

455 000 456 500

Centre FQRNT

------

57 100 57 100

NPCDS NSERC-

------ear Ending on May 31, 2006 966 000 966 000

Centre NSERC-

evenue chers) (Prague) contribution REVENUE dia University grant TIA AL ACS contributions Statement of Revenue and Expenditures for the Fiscal Y REVENUE Operating grants Université de Montréal grant (Resear Université de Montréal grant (Operations) UQÀM grant McGill University grant Concor Université Laval grant University of Ottawa grant National Science Foundation grants MIT Clay Institute contribution DIMA Contributions for Colloquia (ISM & GERAD) Other contributions for workshops ISM contribution for CRM-ISM Postdoctoral fellows Matching contributions for Postdoctoral fellows Matching contributions for workshops Endowments (Aisenstadt & Bissonnette) Publications, Registration fees and other r TOT

112 STATEMENT OF REVENUEAND EXPENDITURES 1 360 1 880 AL 5 228

1 41 616 47 428 67 080 69 400 54 486 67 813 72 513 79 407 32 559 28 499 20 723 99 887

61 191 802 209 821 502 028 286 620 131 825 432 940 174 032 109 571 651 222 515 020 773 333 120 885

(329 635) 3 677 698

TOT

------

200

1 522 7 559 7 559 5 999 1 000 1 154 8 153 1 256

1 55 559 53 777 12 952 43 644 39 153 19 725 19 222

(70 687) 133 810 272 723

Other Sources

------

992

(324)

9 667 1 343 1 343

12 000 21 667 61 241

331 828 417 072

Partners &

Researchers ------

5 000 5 000 5 674

14 923 14 923 23 859 43 781

Funds

Endowment ------

9 860

30 000 54 400 19 000 48 599 34 059 81 032 68 071

(15 021) 315 021 345 021

Other

Universities ------

6 121 4 089 3 000 3 219 4 851 3 457

(2 555) 14 265 57 000 51 047 89 350 49 448

(96 590) 1 515 020 523 328 182 766 966 813

UdeM CÉDAR

------

- 455

4 234 3 395 7 381

41 991 46 680 48 251 15 000 35 486 13 214 27 676 18 500 41 500 32 559 22 500 55 059 27 510

(98 526) 151 377 215 373 555 026

Centre FQRNT

------

(74 525) 131 625 131 625

NPCDS NSERC-

------

12 3 000 2 884 1 900

(1 592) 16 1 10 937 82 252 37 761 20 443 73 667 36 000 24 000 63 000 18 996 23 712 20 363

155 589 284 947 103 503 355 469 945 637

Centre NSERC-

eport TORIES Annual r ogram 2005-2006 eceding years) chers esear chers chers - Thematic pr chers and travel chers chers esear esear esear esear esear eleases eleases . de Montréal r orkshops and schools 2005-2006 orkshops and schools (Pr orkshops and seminars isiting r isiting r isiting r isiting r otal - Thematic program otal - Laboratories otal - Other scientiﬁc expenditures EXPENDITURES Aisenstadt Chairs V CRM-ISM Postdoctoral fellows (2) W W T Course r V V W Postdoctoral fellows Students Administrative support T Univ College r Course r V Publicity (activities' posters), Bulletin, T AL EXPENDITURES SCIENTIFIC PROGRAMS - CENTRE Thematic rogram General program Industrial and multidisciplinary program National Program on Complex Data Structures (NPCDS) Postdoctoral fellows and students SCIENTIFIC PROGRAMS -RESEARCH LABORA Other scientiﬁc expenditures Personnel (Non-academic) Academic management, Advisory committee, Networking Operating and computing expenditures TOT YEAR-END BALANCE

113 Mandate of the CRM MANDATE OF THE CRM

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

115