Annualreport 2006 2007

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AnnualReport 2006 2007

AnnualReport 2006 2007 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 crm.math.ca/docs/docRap_an.shtml. c Centre de recherches mathématiques Université de Montréal, 2008 ISBN 978-2-921120-45-6 CENTRE DE RECHERCHES MATHÉMATIQUES

Presenting the Annual Report 2006 – 2007 5 A fecund year at the CRM ...... 6

Thematic Program 8 Thematic Semesters of the Year 2006 – 2007: Combinatorial Optimization and Recent Ad- vances in Combinatorics ...... 9 Aisenstadt Chairholders in 2006 – 2007: Noga Alon, Paul Seymour, and Richard Stanley . . 9 Activities Held During the Two Thematic Semesters ...... 14

General Program 24 CRM activities ...... 25 Colloquium Series ...... 35

Multidisciplinary and Industrial Program 38 Activities of the Multidisciplinary and Industrial Program ...... 39

CRM Prizes 44 CRM – Fields – PIMS Prize 2007 and CAP – CRM Prize 2007 awarded to Joel S. Feldman . . 45 André-Aisenstadt Prize 2007 awarded jointly to Alexander E. Holroyd and Gregory G. Smith 46 CRM – SSC Prize 2007 awarded to Dr. Richard Cook ...... 47

The CRM Outreach Program 48 The Mathematics of Escher’s Print Gallery Bart de Smit, Universiteit Leiden ...... 49 Les limites logiques et mathématiques Jean-Paul Delahaye, Université Lille 1 ...... 50 Euler, la vie, l’univers, l’optimisation Francis Clarke, Université Lyon 1 ...... 50

CRM Partnerships 52 CRM Partners ...... 53 Joint Initiatives ...... 56

Mathematical Education 60 Institut des sciences mathématiques (ISM) ...... 61 Other joint initiatives ...... 63

Research Laboratories 65 Applied Mathematics ...... 66 CICMA...... 69 CIRGET ...... 71 LaCIM ...... 73 Mathematical Analysis ...... 75 Mathematical Physics ...... 78 PhysNum ...... 82 Statistics ...... 84 INTRIQ ...... 87

Publications 88 Recent Titles ...... 89 Previous Titles ...... 89 CRM Preprints ...... 92

Scientiﬁc Personnel 94 CRM Members in 2006 – 2007 ...... 95 Postdoctoral Fellows ...... 97 Long-term Visitors ...... 97 Short-term Visitors ...... 98

Governance and Scientiﬁc Guidance 100 Bureau de direction ...... 101

3 CENTRE DE RECHERCHES MATHÉMATIQUES

Scientiﬁc Advisory Committee ...... 101

CRM Administrative and Support Staff 104 The Director’s Ofﬁce ...... 105 Administration ...... 105 Scientiﬁc Activities ...... 105 Computer Services ...... 105 Publications ...... 105 Communications ...... 105

Mandate of the CRM 106

4 Presenting the Annual Report 2006 – 2007 CENTRE DE RECHERCHES MATHÉMATIQUES

A fecund year at the CRM

n 2006 – 2007, the CRM thematic program was conceived in a new spirit: the two thematic semesters Icovered two complementary aspects of the same theme, one more applied and the other closer to pure mathematics. The general theme of the year 2006 – 2007 was combinatorics. Since the last ten years have highlighted the impact and depth of combinatorics through the latest developments in mathematics (several of the recent Fields medallists were awarded the Fields medal for research closely related to combinatorics), the CRM was bound to devote a whole year to this subject, given its role in the international network of mathematical institutes. The first thematic semester was more applied and dealt with combinatorial optimization, while the second one, on recent advances in combinatorics, was closer to algebraic geometry and dealt with algebraic, enumerative, and geometric combinatorics. The second semester covered a very broad spectrum of mathematics, from the interaction between combinatorics and statistical mechanics to the Gromov – Witten invariants in tropical, real and complex geometries. It was a pleasure for the CRM to organize the semester on recent advances in combinatorics, since Canada has a strong group of mathematicians working in combinatorics and the semester was coor- dinated by the LaCIM laboratory, based at UQÀM. I wish to thank François Bergeron (UQÀM), Mark Haiman (Berkeley), and many other mathematicians from Canada and abroad, for having organized the schools, workshops, and lectures of this semester. I am grateful to all the LaCIM members for their participation in this world-class event. I would like to thank also Slava Kharlamov (Strasbourg) and Rahul Pandharipande (Princeton), who accepted my invitation to conclude this semester by organizing a workhop on real, complex and tropical enumerative geometry; to my knowledge, this was the first workshop ever to be held on this topic. The thematic semester on recent advances in combinatorics also included the beautiful lectures by the Aisenstadt Chairholder, Richard Stanley, a professor at MIT and one of the foremost researchers in enumerative and algebraic combinatorics. The first thematic semester, on combinatorial optimization, was also of a very high calibre. Under the direction of Vašek Chvátal (Concordia) and a strong Canadian team including Odile Marcotte, and with the collaboration of Michel Goemans from MIT, the semester included workshops on a broad spectrum of combinatorial optimization, namely: approximation algorithms, network design, hybrid methods, data mining and mathematical programming, and polyhedral computation. The NATO Advanced Study Institute held in Montréal in 2006 (supported through the NATO Science for Peace and Security Programme in Brussels) was also devoted to combinatorial optimization; it was organized by Vašek Chvátal and Najiba Sbihi, from the École Mohammadia d’Ingénieurs in Rabat, Morocco. The thematic semester on combinatorial optimization also featured two series of outstanding lectures by the two Aisenstadt Chairholders, Noga Alon (Tel Aviv) and Paul Seymour (Princeton). One of the hallmarks of the thematic year on combinatorics was the emphasis placed on advanced schools, the NATO Advanced Study Institute on one hand, and the four schools of the semester on recent advances in combinatorics on the other hand. The latter were organized by LaCIM members, who always put a justified emphasis on the training of graduate students and postdoctoral fellows. In July 2006, the CRM also hosted a short thematic program on geometric group theory, organized and sponsored by the CIRGET laboratory (based at UQÀM). The organizers of this short thematic program were Mladen Bestvina (Utah), Steven Boyer (UQÀM), Tadeusz Januszkiewicz (Ohio), Michah Sageev (Technion) and Daniel T. Wise (McGill). The CRM general program for the year 2006 – 2007 was also of the highest calibre and included, among other events, the Conference on 3-manifold topology in Honour of Peter Shalen’s 60th birthday, the Conference on Combinatorial Optimization in Honour of Vašek Chvátal’s 60th birthday, the Workshop on Singularities in PDE and the Calculus of Variations organized by Stan Alama (McMaster), Lia Bronsard (McMaster), and Peter Sternberg (Indiana), the Gilles Fournier Memorial Conference on Classical and Computational Topological Methods, the 10th International Workshop on Differential Equations, Number Theory, Data Analysis Methods and Geometry, held in Havana (Cuba), a beautiful conference honouring John McKay (“Groups and Symmetries: From the Neolithic Scots to John McKay”), organized jointly with Concordia University, and the Workshop on the Ge- ometry of Holomorphic and Algebraic Curves in Complex Algebraic Varieties, organized by Steven Lu (UQÀM). Let us mention also that the CRM supported CanaDAM 2007, the First Canadian Dis-

6 PRESENTINGTHE ANNUAL REPORT 2006 – 2007 crete and Algorithmic Mathematics Conference, which took place in Banff in May 2007. The second CanaDAM conference will take place at the CRM in May 2009. In 2006 – 2007, the multidisciplinary and industrial program included, among other events, the XXIIIrd International Biometrics Conference, the 41st Actuarial Research Conference, the 4th RECOMB Comparative Genomics Satellite Workshop, the NBER/NSF Time Series Conference 2006, and the DIRO – CRM – ncm2 public lecture by Ralph E. Gomory entitled “Thoughts about integer programming.” Dr. Gomory is President Emeritus of the Alfred P. Sloan Foundation and was IBM Senior Vice President for Science and Technology from 1986 to 1989. The “Grandes Conférences du CRM,” geared towards a general audience, were given by three outstanding lecturers in 2006 – 2007: Bart de Smit (Leiden), Jean-Paul Delahaye (Lille), and Francis Clarke (Lyon). I wish to convey my heartfelt thanks to the organizers of those lectures, Christiane Rousseau and Yvan Saint-Aubin, both professors of mathematics at the Université de Montréal. The Accromαth magazine continues to feature prominently among the mathematical magazines catering to the needs of a general audience. The 5000 copies of Accromαth are distributed in all parts of the world and Accromαth has become a focus point for all those with an interest in mathematics in the French-speaking countries. The CRM and ISM regularly receive testimonies from high school principals and high school and college teachers who praise the contents and format of the magazine. The reader may consult the site www.accromath.ca for further information. Each year the CRM awards four prizes. In 2006 – 2007, the CRM – Fields – PIMS Prize and the CAP – CRM Prize were both awarded to Joel Feldman, from the University of British Columbia. Gregory Smith (Queen’s University) and Alexander Holroyd (University of British Columbia) were awarded jointly the André-Aisenstadt Prize, and Richard Cook (University of Waterloo) was awarded the CRM – SSC Prize. Congratulations to all! The year 2006 – 2007 saw the design of the new CRM statutes; as a result, the CRM will become a genuine multi-university institution in 2008. The new statutes give the universities participating in the CRM the impact and decision making power that they deserve; they also give the highest priority to the concerns of researchers coming from all walks of science. The numerous activities organized by the CRM are made possible through the ﬁnancial contributions of the CRM partners and sponsors. It is with great pleasure that on behalf of CRM members and my own, I gratefully acknowledge the contributions of NSERC, FQRNT and our academic partners (Université de Montréal, UQÀM, McGill University, Concordia University, Université Laval, Univer- sity of Ottawa and Université de Sherbrooke). I am also grateful to the National Science Foundation, which supports our thematic and general programs, to NATO, which ﬁnances an Advanced Study Institute in Montréal each year, to the Institut des sciences mathématiques, and to MITACS, the ncm2 and GERAD, a research centre that organized joint workshops with the CRM. The list of these partners and sponsors is a testimony to the crucial role played by the CRM in mathematical research, at the Canadian and international levels.

François Lalonde

7 Thematic Program THEMATIC PROGRAM

he core of each year’s scientific program at the CRM is its thematic program. As explained in Tthe presentation of this annual report, in 2006 – 2007, the thematic program consisted of two semesters covering two complementary aspects of combinatorics. The topic of the first semester (June – December 2006) was combinatorial optimization, and that of the second semester was recent advances in combinatorics. The CRM is very grateful to the National Science Foundation for providing generous financial support to the young American mathematicians who attended the activities of the two thematic semesters. The CRM is also grateful to MITACS for providing financial support for one of the workshops of the Thematic Semester on Combinatorial Optimization. The reports are presented in the language in which they were submitted.

Thematic Semesters of the Year 2006 – 2007: Combinatorial Optimization and Recent Advances in Combinatorics

Combinatorial optimization has grown tremen- Fields medal for research closely related to com- dously in the past few decades, because of its nu- binatorics), the CRM was bound to devote a the- merous applications to real-life problems arising matic semester to recent advances in combina- in transportation and telecommunications plan- torics, especially advances in algebraic, enumer- ning, scheduling, industrial engineering, and ative, and geometric combinatorics. This the- many other fields. It has links to both pure matic semester, from January to June 2007, cov- mathematics and operations research, and in- ered a very broad spectrum of mathematics, deed the GERAD and CIRRELT centres, which from the interaction between combinatorics and specialize in operations research, have collabo- statistical mechanics to the Gromov – Witten in- rated with the CRM within the framework of variants in tropical, real, and complex geome- the thematic semester, either through financial tries. It featured 6 workshops, four schools, contributions or through the participation of and a series of lectures by an André-Aisenstadt their members to the workshops of the semester. Chairholder. François Bergeron (UQÀM), Srecko The thematic semester on combinatorial opti- Brlek (UQÀM), Pierre Leroux (UQÀM), and mization featured a NATO Summer School, five Christophe Reutenauer (UQÀM) were the main workshops, and series of lectures by two André- organizers of the thematic semester on re- Aisenstadt Chairholders. Its organizing commit- cent advances in combinatorics; Marcelo Aguiar tee consisted of David Avis (McGill), David (Texas A&M), Mireille Bousquet-Mélou (Bor- Bremner (New Brunswick), Vašek Chvátal (Con- deaux 1), Nantel Bergeron (York), Sara Faridi cordia), Bill Cunningham (Waterloo), Michel (Dalhousie), Anthony Geramita (Queen’s), An- Goemans (MIT), Pierre Hansen (HÉC Montréal), thony J. Guttmann (Melbourne), Mark Haiman Odile Marcotte (GERAD and UQÀM), Tom Mc- (Berkeley), Slava Kharlamov (IRMA, Strasbourg Cormick (UBC), and Adrian Vetta (McGill). 1), Allen Knutson (UC San Diego), Rahul Pand- Since the last ten years have highlighted the haripande (Princeton), Bruce Sagan (Michigan impact and depth of combinatorics through the State), Alan Sokal (New York), Ravi Vakil (Stan- latest developments in mathematics (several of ford), and Stephanie van Willigenburg (UBC) the recent Fields medallists were awarded the were also members of the organizing committee. Aisenstadt Chairholders in 2006 – 2007: Noga Alon, Paul Seymour, and Richard Stanley

The two André-Aisenstadt Chairs for the the- and probabilistic combinatorics, Paul Seymour matic semester on combinatorial optimization one of the foremost experts in graph theory were Noga Alon, from Tel Aviv University, and matroid theory, and Richard Stanley one of and Paul Seymour, from Princeton University. the foremost experts in enumerative and alge- The André-Aisenstadt Chair for the thematic braic combinatorics. The lectures given by each semester on recent advances in combinatorics of these world-renowned mathematicians pro- was Richard Stanley, from the Massachusetts vided a broad view of his ﬁeld; for this reason, Institute of Technology. Noga Alon is one of in the texts that follow, we focus on the contents the foremost experts in the world in extremal of the lectures to give the ﬂavour of each of those

9 CENTRE DE RECHERCHES MATHÉMATIQUES three areas of combinatorics (probabilistic com- inequality (which is a fundamental tool in func- binatorics, graph theory, and enumerative and tional analysis) implies that v(SDP)/v(IP) is algebraic combinatorics, respectively). bounded by a constant (Grothendieck’s constant), whose precise value is not known but√ is com- Noga Alon prised between π/2 and π/2 ln(1 + 2). They The first two lectures by Noga Alon dealt with also describe rounding techniques that can be approximation results for combinatorial opti- used to transform an optimal solution of SDP mization problems. The topic of the first lecture into a feasible (integral) solution of IP whose was the approximation of a quantity known as value is not too far from v(SDP). By using these the cut-norm of a matrix. Given a real matrix techniques and the relationship between v(IP) and kAkC (kAkC ≤ v(IP) ≤ 4kAkC), Alon and A = (aij)i∈R,j∈S, the cut-norm kAkC of A is defined as the maximum absolute value of a sub- Naor designed an efficient deterministic algo- matrix sum, i.e., rithm for approximating the cut-norm. They also designed efficient randomized algorithms pro- max aij . ducing approximate solutions, but with better I⊂R ∑ J⊂S i∈I j∈J approximation ratios. In his second lecture, Noga Alon considered Finding sets I and J for which the maximum edge-deletion problems. These are a special type is achieved is a difficult combinatorial problem. of graph modification problems, which have ap- Indeed, unless the most important question in plications in numerical linear algebra and the complexity theory (“Is P equal to NP?”) has an physical mapping of DNA. Let G be an undi- affirmative answer, it is impossible to compute rected graph, consisting of a finite set of vertices efficiently sets I and J such that and a finite collection of pairs of vertices (called

a ≥ ρkAk , edges). A graph property is monotone if the re- ∑ ij C i∈I moval of a vertex or an edge from a graph G j∈J preserves the property. For instance, the prop- for any ρ greater than 16/17. erty of being triangle-free is monotone. Note that Thus one is led to consider a related opti- the obvious algorithm for verifying that G is triangle-free or transforming G into a triangle- mization problem, formulated as the following 3 integer program (called IP): free graph takes time proportional to n , since it enumerates all subsets of three vertices. Noga maximize ∑ aijxiyj Alon, Asaf Shapira and Benny Sudakov have i∈R O( 2) j∈S given an n algorithm for the latter problem, not only for the property of being triangle-free ∈ {− } ∈ {− } subject to xi 1, 1 , yj 1, 1 for all i, j. but for any monotone property. The optimal value of IP will be denoted by v(IP). More precisely, for any graph G and any 0 The program IP being difficult to solve, one is monotone property P, let EP (G) denote the led to replace the constraint “xi ∈ {−1, 1}” by smallest number of edges that must be deleted “xi is an m-dimensional vector of unit norm,” from G to transform it into a graph satisfying P. and the constraint “yj ∈ {−1, 1}” by “yj is an m- Alon, Shapira and Sudakov have shown that for dimensional vector of unit norm.” In order to ex- any fixed e > 0 and any monotone property P, tend the definition of the objective function, one there is an O(n2) deterministic algorithm that, then replaces the product xiyj by the scalar prod- given a graph G on n vertices, computes a real 0 2 uct xi · yj. The resulting optimization problem is number r satisfying |r − EP (G)/n | ≤ e. Such equivalent to a semidefinite program, denoted an algorithm was not even known for the prop- by SDP and whose optimal value is denoted by erty of being triangle-free. Alon and his coau- v(SDP). thors have also proved that if all bipartite graphs The relaxation SDP is useful in two ways. satisfy P, then it is NP-hard to approximate 0 2 −δ First, a near-optimal solution of SDP (i.e., a so- EP (G)/n to within an additive error of n for lution of value greater than v(SDP) − e) can be any fixed δ > 0. This is also a startling result, computed in time that is polynomial in the input since prior to their article it was not even known 0 length and log(1/e). Second, v(SDP) provides that computing EP (G) precisely was NP-hard, an upper bound for v(IP) since SDP is a relax- even when P is the property of being triangle- ation of IP and IP is a maximization problem. In free! a beautiful article, Noga Alon and Assaf Naor The topic of Noga Alon’s third lecture was show that the matrix version of Grothendieck’s graph property testing, a topic related to the

10 THEMATIC PROGRAM graph modification problems we have just de- comparatively little attention from graph theo- scribed. The study of combinatorial property rists investigating the structure of graphs. The testing was first motivated by issues arising in second meaning, “G does not contain H as an program checking. A graph G with n vertices induced subgraph”, has received much more at- is said to be e-far from satisfying the property tention. For instance, Berge graphs are the graphs P if the number of edge insertions or deletions that do not contain any odd hole or antihole as needed to transform G into a graph satisfying an induced subgraph (where a hole is a cycle P is at least en2. A graph property P is testable with at least four vertices and an antihole is the if there exists a randomized algorithm making complement of a hole). In 1961, Claude Berge at most q(e) edge queries that can distinguish posed the Strong Perfect Graph Conjecture, that is, with high probability between graphs satisfy- the conjecture that a graph G is Berge if and only ing P and graphs that are e-far from satisfying if G is perfect, i.e., the chromatic number of any P. Note that q(e) does not depend upon n or induced subgraph H of G is equal to the clique the size of the input. In his third lecture, Noga number of H. In 2002, Paul Seymour and his Alon surveyed the main results on graph prop- collaborators (Maria Chudnovsky, Neil Robert- erty testing, especially the recent ones, and out- son, and Robin Thomas) announced a proof of lined the relationship between these results and the Strong Perfect Graph Conjecture, an achieve- Szemerédi’s regularity lemma. ment that is comparable to the proof of the four- colour theorem! Biography The third meaning of the phrase “G does not contain H” is that G does not contain H as a mi- Noga Alon is a Baumritter Professor of Mathe- nor. We say that H is a minor of G if H is ob- matics and Computer Science at Tel Aviv Uni- tained from G by deleting edges or vertices or versity in Israel. He received his Ph.D. in Math- contracting edges (contracting the edge {u, v} ematics at the Hebrew University of Jerusalem amounts to identifying the vertices u and v). Mi- in 1983 and held visiting positions in various nor containment is often encountered in topo- research institutes including MIT, The Institute logical graph theory, because it is closely related for Advanced Study in Princeton, IBM Almaden to topological containment. The best-known ex- Research Center, Bell Laboratories, Bellcore and ample in this regard is the strong version of Ku- Microsoft Research. He serves on the editorial ratowski’s theorem given by Klaus Wagner: a boards of more than a dozen international tech- graph G is planar if and only if it does not con- nical journals and has given invited lectures at tain K (the complete graph on five vertices) or many conferences, including plenary addresses 5 K (the complete bipartite graph with three ver- at the 1996 European Congress of Mathematics 3,3 tices in each part) as a minor. Another example and the 2002 International Congress of Mathe- is Tutte’s conjecture (1966), a generalization of maticians, and an invited lecture at the 1990 In- the four-colour theorem: the edges of any cubic ternational Congress of Mathematicians. He has 2-connected graph not containing the Petersen published one book and more than three hun- graph as a minor can be coloured with three dred research articles, mostly in combinatorics colours. Tutte’s conjecture was proved by Paul and theoretical computer science. He has been Seymour and Neil Robertson in 1997. a member of the Israel National Academy of Sci- ences since 1997 and received the Erd˝osprize in Given a notion of graph containment and a 1989, the Feher prize in 1991, the George Pólya fixed graph H, one may ask the following ques- Prize in 2000, the Bruno Memorial Award in tion: how does one construct explicitly all the 2001, the Landau Prize in 2005 and the Gödel graphs not containing H? After giving exam- Prize in 2005. ples of such constructions, Paul Seymour argued that the phrase “explicit construction” still lacks Paul Seymour a clear definition, as shown by the example of claw-free graphs. The graph G is claw-free if for In his first lecture, geared towards a broad audi- any v, the set of neighbours of v does not contain ence, Paul Seymour gave an overview of some of three pairwise nonadjacent vertices. Here is an the most important structure theorems in graph obvious way of constructing a claw-free graph: theory. Paul Seymour beginned his lecture by re- given a claw-free graph G and a subset X not minding the audience that given two graphs G containing three pairwise nonadjacent vertices, and H, the phrase “G does not contain H” may add a vertex to G whose set of neighbours is X. have several meanings. The first meaning, “G The resulting graph is claw-free. This inductive does not contain H as a subgraph”, has received definition yields a polynomial-time algorithm,

11 CENTRE DE RECHERCHES MATHÉMATIQUES but has the drawback that one has to “guess” Finally, the formulation of the Caccetta – the set X of neighbours of the new vertex. Maria Häggkvist conjecture can be slightly modified Chudnovsky and Paul Seymour recently proved to include the minimum in-degree; for instance, a deep structure theorem for claw-free graphs, does every simple digraph whose minimum and a likely by-product of this theorem is an out-degree and minimum in-degree are at least explicit construction for claw-free graphs that n/3 contain a directed triangle? This special case avoids such “guesses”. Paul Seymour concluded would be implied by the following conjecture his first lecture by raising the possibility that one (Seymour’s Second Neighbourhood Conjecture): any could use mathematical logic to give a precise simple digraph has a vertex v whose second meaning to the phrase “explicit construction”. neighbourhood is at least as large as its first In his second lecture, Paul Seymour turned neighbourhood. The second (resp. first) neigh- to the algorithmic aspect of induced graph con- bourhood of v is the set of vertices u such that tainment. Let F be a fixed family of graphs, there is a shortest path of length 2 (resp. 1) be- and for any graph G and any subset U of ver- tween v and u. tices of G, let G[U] denote the subgraph induced by U. Consider the following problem: given a Biography graph G and a subset S of vertices of G, does Paul Seymour is Professor of Mathematics at G have an induced subgraph G[U] belonging Princeton University. After obtaining a D.Phil. to F and such that U contains S? Most prob- from the University of Oxford, he held positions lems of this sort seem to be NP-complete. Maria at the Universities of Oxford and Waterloo and Chudnovsky and Paul Seymour, however, gave at the Ohio State University. He was a Member a polynomial-time algorithm to solve the above of Technical Staff and a Senior Scientist at Bell- problem when F is the family of trees and S a core from 1984 to 1996 and has been a Profes- set of three vertices. They called this special case sor at Princeton University since 1996. He has the “three-in-a-tree” problem, because it consists published more than 150 research articles and of deciding whether a graph G has an induced is Editor-in-Chief for the Journal of Graph Theory tree containing three specified vertices. The algo- (jointly with Carsten Thomassen). He is also ed- rithm of Chudnovsky and Seymour can be used itor for Combinatorica and the Journal of Combina- to decide whether or not a graph G contains torial Theory, Series B. He was awarded the most an induced subgraph isomorphic to a theta, i.e., prestigious prize in combinatorial optimization, a subgraph consisting of three vertex-disjoint the D.R. Fulkerson Prize, in 1979, 1994 and 2006 paths between the vertices a and b. (jointly with Neil Robertson and Robin Thomas The topic of Paul Seymour’s third lecture in 1994 and jointly with Neil Robertson in 2006). was the Caccetta – Häggkvist conjecture. In 1978, He was also awarded the Ostrowski Prize in Caccetta and Häggkvist made the conjecture 2004 and the George Pólya Prize in 1983 and that every simple digraph (i.e., a digraph with 2004 (jointly with Neil Robertson in 2004). no loop or digon) with n vertices and minimum Paul Seymour has made fundamental contri- out-degree at least equal to r contains a directed butions to the study of regular matroids, to ma- cycle of length at most dn/re. Many special cases troid theory in general, to graph colourings (es- of this conjecture are known to be true; in partic- pecially Hadwiger’s conjecture), and to graph ular, Jian Shen proved in 2003 that the Caccetta – √ minors. His work on graph minors is pub- Häggkvist conjecture holds if r is at most n/2. lished in a series of more than twenty articles in The case where r is equal to n/3 (among others) the Journal of Combinatorial Theory, Series B, and seems to be difficult, and researchers have tried in particular the twentieth article contains the to determine the smallest constant c such that G proof of a celebrated conjecture of Klaus Wag- contains a directed triangle if its minimum out- ner (1970) asserting that “for every infinite set of degree is at least cn. The best result so far, due √ finite graphs, one of its members is isomorphic to Jian Shen, is that c is at most 3 − 7 (it is to a minor of another.” conjectured that c is equal to 1/3). In a similar vein, Seymour, de Graaf, and Schrijver proposed Richard Stanley to determine the smallest constant β such that G contains a directed triangle if its minimum out- In his first lecture Richard Stanley surveyed degree and its minimum in-degree are at least the theory of increasing and decreasing sub- βn. They proved that β is at most 0.3487; Jian sequences of permutations. A permutation of Shen used their work and one of his previous re- the set {1, 2, 3, . . . , n} can be represented by the sults to show that β is at most 0.3477. word (or sequence) w = a1a2a3 ... an, where ai

12 THEMATIC PROGRAM is the image of i under the permutation. An in- quences, the maximum length of an alternating creasing subsequence of this permutation is a sub- subsequence of the permutation w is denoted by sequence ai1 ai2 ... aik satisfying ai1 < ai2 < ··· < as(w). In this lecture, Richard Stanley discussed aik ; for instance, 367 is an increasing subsequence recent work on the distribution of as(w) and on of the permutation 4326571. A decreasing subse- the enumeration of various classes of alternat- quence is defined in a similar fashion. Increasing ing permutations (such as those that are invo- subsequences have a nice interpretation in terms lutions). In his third lecture, he surveyed some of the one-person card game patience sorting, and classical and recent results concerning the group through that game, they have connections with GL(n, q) and Mat(n, q), the space of all n × n ma- airplane boarding times and disk scheduling, re- trices over the field Fq. His lecture addressed the spectively. following questions: how many orbits are there In his lecture, Richard Stanley presented in the action of GL(n, q) on Mat(n, q) by conju- the famous RSK algorithm (named after Robin- gation, and what is the cardinality of GL(n, q) ∩ son, Schensted and Knuth) for computing a H, where GL(n, q) is regarded as a subset of bijection between the set of permutations of Mat(n, q) and H is a hyperplane in Mat(n, q)? {1, 2, 3, . . . , n} and ordered pairs of standard Young tableaux of shape λ ` n. He discussed Biography the relation of the RSK algorithm to a theorem Richard Stanley is the Norman Levinson Pro- of Erd˝osand Szekeres and a fundamental re- fessor of Applied Mathematics at the Mas- sult of Schensted, from which one can derive a sachusetts Institute of Technology. He received formula for the number of permutations of the his Ph.D. from Harvard University in 1971 and set {1, 2, 3, . . . , pq} (where p ≤ q) for which the has held several visiting positions, in particu- maximum length of an increasing subsequence lar positions at Harvard University in 2000 – (denoted by is(w)) equals p and the maximum 2001 and at the Institut Mittag-Leffler (Swe- length of a decreasing subsequence equals q. It den) in 2005. Among other awards, he was turns out that the entire limiting distribution of awarded the SIAM George Pólya Prize in 1975, is(w) as n → ∞, determined by Baik, Deift, and a Guggenheim Fellowship in 1983 – 1984, the Johansson in 1999, is the (suitably scaled) Tracy – American Mathematical Society 2001 Leroy P. Widom distribution, which first arose as the dis- Steele Prize for Mathematical Exposition, and tribution of the largest eigenvalue of a random the Rolf Schock Prize in Mathematics in 2003. Hermitian matrix. In 2007, he received an Honorary Doctorate in In the last part of his talk, Richard Stanley Mathematics from the University of Waterloo considered complete matchings instead of per- and an Honorary Professorship from Nankai mutations. A complete matching M on the set University. He is a Fellow of the American {1,2,3,...,2n} is a partition of this set into n Academy of Arts and Sciences and a Member of two-element blocks. In the case of matchings, the National Academy of Sciences. Richard Stan- one should consider crossings and nestings in- ley has supervised more than 45 doctoral stu- stead of permutations. A crossing of M is a pair dents and has given many prestigious invited {ij, kl} of blocks satisfying i < k < j < l, and talks; in particular he was Erd˝osLecturer at the a nesting of M a pair {ij, kl} of blocks satisfy- Hebrew University (Jerusalem) in 1999 and Ple- ing i < k < l < j. Finally, let f (i, j) denote n nary Speaker at the International Congress of the number of matchings for which the maxi- Mathematicians in Madrid (2006). mum number of mutually crossing pairs equals i and the maximum number of mutually nest- Aisenstadt Chair ing pairs equals j. A key theorem states that this function is symmetric, i.e., fn(i, j) = fn(j, i); the The Aisenstadt Chair was endowed by Mont- proof of this theorem relies on the notion of os- réal philanthropist Dr. André Aisenstadt. Under cillating tableau and an “oscillating” analogue of its auspices, one or more distinguished mathe- Schensted’s theorem. maticians are invited each year for a period of After his first lecture, much enjoyed by the at least one week, ideally one or two months. audience, Richard Stanley gave two further lec- During their stay the lecturers present a se- tures that were more technical. The topic of the ries of lectures on a specialized topic. They second lecture was alternating permutations. A are also invited to prepare a monograph (see permutation w = a1a2a3 ... an of {1, 2, 3, . . . , n} the chapter on publications in the present re- is alternating if a1 > a2 < a3 > a4 < ··· holds. By port for a list of these monographs). At the re- analogy with increasing and decreasing subse- quest of Dr. Aisenstadt, the first lecture given

13 CENTRE DE RECHERCHES MATHÉMATIQUES by an Aisenstadt Chairholder should be acces- David P. Ruelle, Robert Bryant, Blaine Law- sible to a wide audience. Previous holders of the son, Yves Meyer, Ioannis Karatzas, László Babai, Aisenstadt Chair are: Marc Kac, Eduardo Zaran- Eﬁm I. Zelmanov, Peter Hall, David Cox, Frans tonello, Robert Hermann, Marcos Moshinsky, Oort, Joel S. Feldman, Roman Jackiw, Duong H. Sybren de Groot, Donald Knuth, Jacques-Louis Phong, Michael S. Waterman, Arthur T. Win- Lions, R. Tyrrell Rockafellar, Yuval Ne’eman, free, Edward Frenkel, Laurent Lafforgue, George Gian-Carlo Rota, Laurent Schwartz, Gérard De- Lusztig, László Lovász, Endre Szemerédi, Pe- breu, Philip Holmes, Ronald Graham, Robert ter Sarnak, Shing-Tung Yau, Thomas Yizhao Langlands, Yuri Manin, Jerrold Marsden, Dan Hou, Andrew J. Majda, Manjul Bhargava, K. Voiculescu, James Arthur, Eugene B. Dynkin, Soundararajan, and Terence Tao. Activities Held During the Two Thematic Semesters

SMS – NATO ASI 2006 Summer School polyhedra, Sbihi on the mathematics of supply Combinatorial Optimization: Methods and chain management, and Koshevoy on discrete Applications convexity. June 19 – 30, 2006, Université de Montréal Three of the School speakers were re- Sponsored by NATO, the CRM, ISM and the searchers from the University of Bonn work- Département de mathématiques et de ing on computer chip design: Rautenbach, who statistique de l’Université de Montréal spoke during the first week, and Vygen and Held (replacing Bernhard Korte), who spoke Organizers: Vašek Chvátal (Concordia), Najiba during the second week. The design of com- Sbihi (École Mohammadia d’Ingénieurs, Mo- puter chips is one of the nicest applications of rocco) combinatorial optimization (if not the nicest). In- Speakers: Gérard Cornuéjols (Carnegie Mel- deed, many of the classical topics of combina- lon), Sanjeeb Dash (IBM T.J. Watson Research torial optimization (minimum cost flows, mul- Center), Friedrich Eisenbrand (Max-Planck- ticommodity flows, shortest paths, Steiner trees Institut für Informatik), Lisa K. Fleischer (IBM and so on) occur as subproblems of the VLSI T.J. Watson Research Center), Michel X. Goe- placement and routing problem; to solve the lat- mans (MIT), Yuri Kochetov (Russian Academy ter, one must also solve more general problems of Sciences), Stephan Held (Bonn), Gleb Ko- and design algorithms fast enough to deal with shevoy (Russian Academy of Sciences), Shmuel current and future orders of magnitude (e.g., one Onn (Technion), Dieter Rautenbach (Bonn), Na- billion transistors). Vygen gave a series of lec- jiba Sbihi (École Mohammadia d’Ingénieurs, tures on this topic, state-of-the-art algorithms for Morocco), Jens Vygen (Bonn) the problems in VLSI layout. Held lectured on Number of participants: 12 speakers and 55 ways to minimize the cycle time of logic chips students and young researchers and microprocessors, once the placement and In 2006, the NATO ASI Summer School routing problem has been solved, and Rauten- brought together outstanding researchers and bach lectured on algorithms that improve the students from NATO and partner countries. Be- timing of a chip or other aspects of chip design cause of its very broad range of applications, (such as placement or power consumption). combinatorial optimization is a disparate field, During the second week, there were four se- and the series of lectures given by the speak- ries of lectures apart from those of Held and Vy- ers reflected the whole range of the subject. Dur- gen. Kochetov spoke about discrete models and ing the first week, Eisenbrand spoke about his local search methods for facility location prob- favorite problems in integer programming: esti- lems; Cornuéjols about recent developments in mating the integrality gap for the cutting stock mixed integer programming (including branch- problem, recognizing a Hilbert basis in polyno- ing rules, preprocessing and heuristics); Goe- mial time, and finding a linear (incremental) al- mans about approximation algorithms (includ- gorithm for integer programming in fixed di- ing local search methods, integral characteriza- mension. Onn gave a series of lectures on convex tions, the embedding of finite metric spaces and combinatorial optimization and convex integer various rounding schemes for linear, convex or programming, including applications to pack- semidefinite programming); and Fleischer about ing, partitioning and clustering problems and generalized congestion games, including a dis- multiway transportation problems. Dash spoke cussion of the “price of anarchy”. Overall, the on mixed integer rounding cuts and cyclic group lectures of the Summer School provided all the

14 THEMATIC PROGRAM participants with a broad view of almost all re- for variants of the Steiner Tree Problem or cent developments in combinatorial optimiza- other network design problems. Two lectures tion. (by Arora and Krauthgamer) dealt with the design of approximation algorithms in specific Workshop settings, and the remaining lectures with ap- Approximation Algorithms proximation algorithms for problems in the fol- June 12 – 14, 2006, CRM lowing areas: graph homomorphisms (Rabani), Organizers: Joseph Cheriyan (Waterloo), Michel graph connectivity (Boyd, Vetta), welfare max- Goemans (MIT) imization (Feige, Vondrak), inventory control Speakers: Matthew Andrews (Bell Labs), San- (Shmoys), submodular set functions (Chekuri), jeev Arora (Princeton), Sylvia Boyd (Ottawa), routing (Andrews, Shepherd), cycle packing Moses Charikar (Princeton), Chandra Chekuri (Salavatipour), lattices (Khot), machine schedul- (Illinois at Urbana-Champaign), Uriel Feige (Mi- ing (Garg), clustering (Williamson), feedback arc crosoft Research), Lisa Fleischer (IBM T.J. Wat- sets (Jain), and game theory (Charikar, Schulz). son Research Center), Naveen Garg (Indian In- Generally speaking, the workshop was very stitute of Technology), Michel Goemans (MIT), lively. Many of the foremost experts on approx- Anupam Gupta (Carnegie Mellon), Kamal Jain imation algorithms were present in the audi- (Microsoft Research), Subhash Khot (Georgia ence, the lectures were very well prepared, and Tech), Jochen Könemann (Waterloo), Guy Ko- the participants did not hesitate to ask questions rtsarz (Rutgers), Robert Krauthgamer (IBM Al- when they did not understand the speakers’ as- maden Research Center), Lap Chi Lau (Toronto), sertions! Yuval Rabani (Technion), R. Ravi (Carnegie Mel- Workshop lon), Mohammad R. Salavatipour (Alberta), An- Network Design: Optimization and dreas S. Schulz (MIT), Bruce Shepherd (Bell Algorithmic Game Theory Labs), David B. Shmoys (Cornell), Adrian Vetta August 14 – 16, 2006, CRM (McGill), Jan Vondrak (Microsoft Research), David Williamson (Cornell) Organizers: Shie Mannor (McGill), Adrian Vetta Number of participants: 70 (McGill) The topic of the first workshop of the com- Speakers: Elliot Anshelevich (Rensselaer), Mo- binatorial optimization semester was “approx- hammad Taghi Hajiaghayi (Carnegie Mellon), imation algorithms.” Many combinatorial opti- Jason Hartline (Microsoft Research), Nicole Im- mization problems, such as the famous Travel- morlica (Microsoft Research), Kamal Jain (Mi- ing Salesman Problem and various network de- crosoft Research), Ramesh Johari (Stanford), sign problems, are NP-hard, which means that Jochen Könemann (Waterloo), Kate Larson (Wa- it is unlikely that one will find a polynomial- terloo), Yishay Mansour (Tel Aviv), Peter Mar- time algorithm to solve them. One must then bach (Toronto), Sean Meyn (Illinois at Urbana- look for efficient approximation algorithms, that Champaign), Vahab Mirrokni (Microsoft Re- is, polynomial-time algorithms providing solu- search), Seffi Naor (Technion), Tim Roughgar- tions whose value is relatively close to the opti- den (Stanford), Andreas Schulz (MIT), Nahum mal value. Finding and proving an upper bound Shimkin (Technion), Gordon Wilfong (Bell Labs) on the difference between the approximate value Number of participants: 63 and the optimal value is often a challenge, This workshop brought together academic requiring the use of sophisticated techniques and industrial researchers from mathematics, from combinatorics and mathematical program- computer science, engineering and economics. ming. One important problem for which approx- Its goal was to discuss the fundamental mathe- imation algorithms have been proposed is the matical issues affecting network design and ap- Steiner Tree Problem, for which Michel Goemans plications. Highlights included: theoretical stud- and David Williamson gave an approximation ies on the evolution of networks such as the In- algorithm in a famous 1994 article: given an ternet; algorithmic approaches for efficient rout- undirected graph G, a weight for each edge of ing under restrictive network protocols; mech- G, and a subset R of vertices of G, find a subtree anism designs and algorithms for online auc- of G that includes all the vertices in R and is of tions; a mathematical model explaining that dra- minimum total weight. matic price change is an inherent characteristic Among the 25 lecturers of the workshop, of dynamic spot electricity markets; investiga- 7 lecturers (Fleischer, Goemans, Gupta, Köne- tions into game theoretic considerations such as mann, Kortsatz, Lau, Ravi) presented algorithms

15 CENTRE DE RECHERCHES MATHÉMATIQUES multiple ownership, contracts, limited informa- ematical programming and researchers in con- tion, equilibria, etc. straint satisfaction programming. The goal of Overall, the workshop was very successful the workshop was to bring those two commu- in highlighting key areas of research and en- nities of researchers together in order to foster couraging cross-disciplinary work. The work- exchanges on branching rules (used in most al- shop led to the statement of many new open gorithms to solve intractable problems) and hy- problems and was the catalyst for new collab- brid methods (combining heuristic search and orations. Here is an example of the problems branch-and-bound algorithms). that were discussed. Suppose that Internet bids, Seven lecturers (Achterberg, Bacchus, say, are made over time for an object or objects. Gomes, Li, Lynce, Sakallah, Simon) gave pre- When the bid is made, the seller must make a sentations on SAT or related problems and algo- decision (accept or reject or announce an alter- rithms. The other lectures dealt with resolution native price). What is the best strategy for the search (Chvátal, Demassey, Ouyang), heuristic seller? An open question in this area is the fol- search methods (Hansen, Voss, Zhang), mixed lowing: suppose the set of bids that can be ac- integer programming (Chinneck, Linderoth, cepted has a specific structure, for instance, the Sandholm), branching strategies (Boros, Gen- accepted bids form an independent set in a given dreau, Lodi, Sandholm, Walsh), efficient search matroid M (several types of matroids have nice for Golomb rulers (Jaumard), use of heuristic applications, e.g., to selling airline seats belong- methods in exact algorithms (Hertz), methods ing to several classes). If the bids arrive in a ran- combining constraint programming and integer dom order, what is the best online algorithm for programming (Bockmayr), logic and intelligent this problem? It is conjectured that a factor e systems (Truemper), and design of difficult in- competitive algorithm exists. stances of constraint satisfaction problems (Cul- berson). Four of the lecturers (Bockmayr, Lynce, Workshop Ouyang and Zhang) applied combinatorial opti- Hybrid Methods and Branching Rules in mization to problems arising in biology; indeed, Combinatorial Optimization biology is providing more and more problems September 18 – 22, 2006, CRM that can be tackled by combinatorial optimiza- Organizer: Vašek Chvátal (Concordia) tion techniques. Speakers: Tobias Achterberg (ZIB Berlin), Each day of the workshop ended with a Fahiem Bacchus (Toronto), Alexander Bockmayr round table and the workshop fostered inter- (FU Berlin), Endre Boros (Rutgers), John Chin- actions between researchers from several com- neck (Carleton), Vašek Chvátal (Concordia), Joe munities, as well as generating much interest Culberson (Alberta), Sophie Demassey (École in the Montréal operations research community. des Mines de Nantes), Michel Gendreau (Mont- According to many of the participants, the work- réal), Carla Gomes (Cornell), Pierre Hansen shop was a tremendous success, in part be- (HÉC Montréal), Alain Hertz (Polytechnique cause it is one of the few workshops to date to Montréal), Brigitte Jaumard (Concordia), Chu have brought together experts from both areas Min Li (Picardie), Jeff Linderoth (Lehigh), An- (constraint programming and integer program- drea Lodi (Bologna), Inês Lynce (Universidade ming). Técnica de Lisboa), Ming Ouyang (Univer- Workshop sity of Medicine and Dentistry of New Jersey), Data Mining and Mathematical Karem Sakallah (Michigan), Tuomas Sandholm Programming (Carnegie Mellon), Laurent Simon (Paris-Sud), October 10 – 13, 2006, CRM Klaus Truemper (Texas at Dallas), Stefan Voss Sponsored by MITACS and the CRM (Hamburg), Toby Walsh (South Wales), Weix- iong Zhang (Washington University) Organizers: Pierre Hansen (HÉC Montréal), Number of participants: 67 Panos Pardalos (Florida) Combinatorial optimization problems, espe- Speakers: Jean-Pierre Barthélémy (ENST Bre- cially those that must be solved in practice, tend tagne), Yoshua Bengio (Montréal), Kristin Ben- to be “intractable.” As a result, diverse heuristic nett (Rensselaer), Sergiy Butenko (Texas A&M), and exact methods to solve them have been pro- Gilles Caporossi (HÉC Montréal), Emilio Car- posed by researchers belonging to several com- rizosa (Sevilla), Art Chaovalitwongse (Rut- munities. For instance, the problem Satisfiabil- gers), Khalid Chenguiti (Sherbrooke), Pando G. ity or SAT (the archetypal NP-complete prob- Georgiev (Cincinnati), Mario Guarracino (ICAR- lem) has been studied by researchers in math-

16 THEMATIC PROGRAM

CNR), Peter L. Hammer (Rutgers), Pierre Legen- ematicians from different horizons who apply dre (Montréal), Vladimir Makarenkov (UQÀM), data mining techniques to many kinds of prob- Musa Mammadov (Ballarat), Olvi L. Mangasa- lems. rian (Wisconsin – Madison), Boris Mirkin (Birk- beck College, University of London), Nenad Workshop Mladenovic (Brunel University), Fionn Murtagh Polyhedral Computation (Royal Holloway, University of London), Car- October 17 – 20, 2006, CRM los Oliveira (Oklahoma State), Panos Parda- Sponsored by GERAD los (Florida), Jiming Peng (McMaster), Dolores Organizers: David Avis (McGill), David Brem- Romero Morales (Oxford), Onur Seref (Florida), ner (New Brunswick), Antoine Deza (McMaster) Steve Smale (Toyota Technological Institute, Speakers: Charles Audet (Polytechnique Mont- Chicago) réal), Roberto Bagnara (Parma), Endre Boros Number of participants: 84 (Rutgers), René Brandenberg (TU München), The goal of the new and active field of data Jesús De Loera (UC Davis), Antoine Deza mining is to find interesting, useful or profitable (McMaster), Mathieu Dutour Sikiric (Rud- information in very large databases. The main her Boskovic Institute), Khaled Elbassioni tasks of data mining, i.e., discrimination, clus- (Max-Planck-Institut für Informatik), Matthias tering and relation finding, have already been Franz (Siemens AG), Komei Fukuda (ETH explored in other fields, but the challenge re- Zürich), Vladimir Gurvich (Rutgers), Alexander sides in the huge size of the problems considered Hulpke (Colorado State), Hiroshi Imai (Tokyo), nowadays. Thus it is necessary to revise and Masakazu Kojima (Tokyo Institute of Technol- streamline traditional methods and to devise ogy), Jean-François Maurras (Aix-Marseille 2), new ones. Mathematical programming plays a Brendan D. McKay (Australian National Uni- key role in this endeavor, since it leads to rigor- versity), Pablo A. Parrilo (MIT), Gerhard Reinelt ous formulations of the problems considered in (Heidelberg), Günter Rote (FU Berlin), Achill data mining and provides powerful mathemati- Schürmann (Magdeburg), Tamon Stephen (Si- cal tools for solving them. mon Fraser), Thorsten Theobald (TU Berlin), Most of the 24 workshop lectures were one- Frank Vallentin (Centrum voor Wiskunde en In- hour lectures on a wide variety of topics and formatica) applications, including machine learning (Ben- Number of participants: 39 gio, Bennett, Guarracino), clustering (Mirkin, The Workshop on Polyhedral Computation Pardalos, Butenko, Georgiev, Murtagh, Peng, consisted mainly of 40-minute talks by the in- Barthélémy), network optimization (Oliveira), vited speakers. They came from various fields: functional data analysis (Chenguiti), sup- polyhedral combinatorics, computational alge- port vector machines (Mangasarian, Romero bra, lattice theory, semi-definite programming Morales, Seref), classification (Carrizosa, Mam- and applications of polyhedral computation. madov), and applications to biology and neu- The goal of the workshop was to explore the roscience (Legendre, Makarenkov, Chaovalit- use of symmetry and algebra to allow the ex- wongse). Gilles Caporossi spoke about data min- tension of current computational methods to ing techniques and the discovery of relations be- large scale symmetric polyhedra. All partici- tween graph invariants, and Nenad Mladenovic pants were mathematicians who actively de- about the solution of large p-median problems. sign, implement or use computer software in Professor Steve Smale, a Fields medallist, their work, and many of the principal authors gave a fascinating lecture on patterns in data, of such software were present at the workshop. showing how it is possible to “learn” the homol- For example, Mathieu Dutour spoke on vertex ogy of a submanifold when data arises from a enumeration under symmetry, and reported on probability distribution whose support is on or work where he used codes developed by six peo- near a submanifold of Euclidean space. The par- ple in the audience. ticipants of the workshop also had the honour The participants were able to get a sam- of attending one of the last lectures of Profes- ple of the wide variety of mathematical prob- sor Peter L. Hammer, one of the pillars of oper- lems for which their software is now used, its ations research, who died in December of 2006. current limitations, and ideas for future exten- Professor Hammer gave a wonderful lecture on sions. The talks were very well prepared, so that the logical analysis of data and its applications to participants outside of the speaker’s area could medicine. Overall, the workshop was a resound- understand the contributions to the theme of ing success, in that it brought together math- the workshop, i.e., polyhedral computation. The

17 CENTRE DE RECHERCHES MATHÉMATIQUES workshop included an open problems session tween participants, each surely offering the indi- on the first day and various free discussion peri- viduals new insights into their own questions. ods throughout the four days. The workshop is thought to be the first ever on the topic of poly- School hedral computation, and a follow-up meeting is Statistical Mechanics and Combinatorics planned for 2008 in Europe. February 12 – 16, 2007, Val-Morin Organizers: Mireille Bousquet-Mélou (Bor- Workshop deaux 1), Anthony J. Guttmann (Melbourne), Algebraic Combinatorics meets Inverse Pierre Leroux (UQÀM), Alan Sokal (New York) Systems Speakers: Mireille Bousquet-Mélou (Bordeaux January 19 – 21, 2007, CRM 1), Anthony J. Guttmann (Melbourne), Gilbert Labelle (UQÀM), Alan Sokal (New York), Xavier Organizers: François Bergeron (UQÀM), Kia Viennot (Bordeaux 1) Dalili (Dalhousie), Sara Faridi (Dalhousie), Number of participants: 45 Aaron Lauve (UQÀM) The goal of this mini-course was to introduce Speakers: Roberta Basili (Perugia), Nantel Ber- the basic methods of enumerative combinatorics geron (York), Anthony V. Geramita (Queen’s), and the concepts of statistical mechanics that un- Anthony Iarrobino (Northeastern), Rosa C. Orel- derlie the interactions between these two areas. lana (Dartmouth), Mercedes H. Rosas (Sevilla), The school was intended for graduate students, Yong Su Shin (Sungshin Women’s University), postdocs and researchers wishing to be intro- Gregory G. Smith (Queen’s), Hugh Thomas duced to these questions. It was held in the Lau- (New Brunswick), Jerzy Weyman (Northeast- rentians region, at the Far Hills Inn (Val-Morin, ern), Alexander Yong (Minnesota) Québec). Here is the plan of the lectures. Note Number of participants: 38 that each lecturer spoke for 3.75 hours in total. The focus of this workshop, a continuation • Mireille Bousquet-Mélou spoke on “Asymp- of a sequence of successful such workshops held totics in combinatorics and statistical mechan- in Kingston (2004), Ottawa (2005), and Toronto ics.” (2006), is to unite two research communities • Tony Guttmann gave an “An introduction to whose interests are overlapping with increas- statistical mechanics for combinatorialists.” ing regularity. Each year has brought new con- • Gilbert Labelle spoke on “Combinatorial nections and this year continued this trend. On species, labelled and unlabelled enumeration the first day we heard about research from both and Mayer graph weights.” communities on nilpotent matrices, while the • Alan Sokal spoke on “Tutte polynomials and second day saw quivers applied to questions rel- statistical mechanics.” evant to each community. • Xavier Viennot spoke on “Enumerative com- As this sequence of workshops is an attempt binatorics and physics.” to get two communities with different languages and different interests to talk to one another, the Workshop tone and spirit has been (by necessity) friendly, Combinatorial Problems Raised by patient, and cooperative. This year was no ex- Statistical Mechanics ception; it is hard to count the number of times February 19 – 23, 2007, CRM during a lecture when a question from the audience evolved into an impromptu mini-school Organizers: Mireille Bousquet-Mélou (Bor- within the mini-workshop (given by the speaker deaux 1), Anthony J. Guttmann (Melbourne), or other audience members), before a gradual re- Pierre Leroux (UQÀM), Alan Sokal (New York) turn to the speaker’s intended lecture. Speakers: Abdelmalek Abdesselam (Paris 13), Though we toil apart, the unity of mathe- Roger E. Behrend (Cardiff), Olivier Bernardi matics is ever present. The impact of workshops (CRM, Barcelona), Mireille Bousquet-Mélou such as this one, which remind us of this fact and (Bordeaux 1), Mihai Ciucu (Georgia Tech), Sylvie encourage us to acquire new languages, cannot Corteel (LRI, Paris-Sud), Johannes de Gier (Mel- be overstated. In measuring its success, one can bourne), Philippe Di Francesco (CEA Saclay), return to the anecdotes outlined above, or the Eric Fusy (INRIA Rocquencourt), Anthony J. concluding one below. As an organizer, I payed Guttmann (Melbourne), Christian Krattenthaler attention to the “non-lecture” interactions of the (Wien), Gilbert Labelle (UQÀM), Pierre Mathieu participants as well. On numerous occasions, I (Laval), Marni Mishna (Simon Fraser), Soichi witnessed new acquaintances being formed be- Okada (Nagoya), Andrew Rechnitzer (UBC),

18 THEMATIC PROGRAM

Gordon Slade (UBC), Alan Sokal (New York), problème des tours de Hanoï et des carrés ma- Chris E. Soteros (Saskatchewan), E.J. Janse van giques ; il permet de calculer certains d’entre Rensburg (York), Xavier Viennot (Bordeaux 1), eux, notamment celui qu’on retrouve dans la David G. Wagner (Waterloo), Stu Whittington gravure Melencolia de Dürer, et c’est un exemple (Toronto), Doron Zeilberger (Rutgers) typique de suite automatique à la Cobham. Il Number of participants: 72 est donc lié aux séries algébriques en caractéris- This workshop featured 24 expository and tique p. specialized talks on combinatorial problems Le mot de Prouhet-Thue-Morse permet, par raised by statistical mechanics, as well as poster un codage obtenu de diverses façons par Braun- presentations by Juan Alvarez (Saskatchewan), holtz, Thue et Morse-Hedlund, de construire un Arvind Ayyer (Rutgers), Patrick Desrosiers mot infini sans carré. Cette construction est une (Montréal), Gary Iliev (Toronto), Ming-Shr Lin étape cruciale dans la démonstration, par Adjan, (Caltech), and David Ridout (Laval). Among the que le problème de Burnside pour les groupes de topics covered by the workshop let us mention torsion a une solution négative. Jean Berstel pré- the following: enumerative problems related to senta son théorème sur les morphismes préser- the classical models of statistical mechanics, self- vant les mots sans carré, lequel permet de sim- avoiding walks, tilings, asymmetric exclusion plifier de nombreuses constructions. Il présenta processes, alternating sign matrices, plane parti- aussi avec brio et clarté les travaux de Croche- tions, multiple partitions, polymers and copoly- more caractérisant algorithmiquement les mor- mers, Mayer’s theory and graph weights, Potts phismes sans carré et les mots sans carré, ainsi model on graphs and Feynman diagrams. que la factorisation de Crochemore d’un mot. Il The workshop took place in a cordial and in- donna aussi la preuve complète de son lemme tense atmosphere and gave rise to numerous in- des trois carrés. Ce lemme permet de borner par teractions between the participants; these inter- 2n le nombre de carrés distincts dans un mot actions should lead to new research ideas and de longueur n, et par n log n le nombre d’occur- collaborations. rences de carrés de mots primitifs. Jean Berstel a School conclu son cours par les notions de motif et de carré abélien et par un survol des résultats de Combinatorics on Words Dekking, redémontrés par Currie et Visentin. March 5 – 9, 2007, CRM Le cours de Christophe Reutenauer portait Organizers: Srecko Brlek (UQÀM), Christophe sur les mots de Christoffel. Il a d’abord présenté Reutenauer (UQÀM), Bruce Sagan (Michigan leur définition par discrétisation de segments State) finis, à la Borel-Laubie, Berstel, et Osborne- Speakers: Jean Berstel (Marne-la-Vallée), Zieschang. Il a ensuite présenté leur définition Christophe Reutenauer (UQÀM) (équivalente à la précédente) par graphe de Number of participants: 48 Cayley d’un groupe à la Christoffel, et il a in- Chacun des deux conférenciers (Jean Berstel troduit les morphismes de Christoffel, lesquels et Christophe Reutenauer) a donné dix heures préservent les classes de conjugaison des mots de cours. Le professeur Berstel est un spécia- de Christoffel et forment un monoïde. Chris- liste mondialement reconnu en combinatoire des tophe Reutenauer a aussi présenté le théorème mots et poursuit des recherches sur ce sujet de- de Mignosi-Séébold et Wen-Wen, qui donne des puis trente ans. Son cours était intitulé « Répéti- générateurs de ce monoïde et montre que ce sont tions dans les mots » et un de ses thèmes prin- les automorphismes positifs du groupe libre à cipaux était le fameux mot infini de Prouhet- deux générateurs F2. Il a montré que les mots Thue-Morse, introduit par ces trois mathéma- de Christoffel pouvaient être construits par pa- ticiens (indépendamment et pour des raisons lindromisation, à la de Luca, et que l’arbre de très différentes) en 1851, 1912 et 1921, respecti- Christoffel (dû à Berstel et de Luca) permet vement. Prouhet voulait résoudre un problème d’engendrer tous ces mots ; l’arbre de Stern- d’arithmétique (appelé plus tard problème de Brocot, qui en est un cas particulier, est lié aux Tarry et Escott), Thue introduisit ce mot pour des suites de Farey. Finalement, Christophe Reute- raisons esthétiques et pour considérer des pro- nauer a montré que les conjugués des mots de blèmes difficiles, et Morse l’introduisit à cause Christoffel sont précisément les éléments primi- de sa relation avec les systèmes dynamiques. tifs positifs de F2, parlé de la relation entre frac- Le mot de Prouhet-Thue-Morse est un mot sans tions continues et mots de Christoffel, et pré- chevauchement, c’est-à-dire sans facteur de la senté de manière originale la théorie de Markoff forme uvuvu. Il est aussi utilisé dans l’étude du des approximations des réels et des formes qua-

19 CENTRE DE RECHERCHES MATHÉMATIQUES dratiques, en utilisant les mots de Christoffel et siques étaient le sujet des exposés d’Alexandre la condition de Markoff. Dans toutes les preuves Blondin-Massé, Lubomira Balkova, Anna Frid, qu’il a données, le conférencier a privilégié les Petr Ambroz et Julien Cassaigne. Xavier Proven- approches tirées de la géométrie discrète. çal a parlé de pavages du plan par des polyomi- nos, et finalement, Aviezri Fraenkel a appliqué la Workshop combinatoire des mots à un problème de théorie Recent Progress in Combinatorics on des jeux. Words School March 12 – 16, 2007, CRM Combinatorial Hopf Algebras and Organizers: Srecko Brlek (UQÀM), Christophe Macdonald Polynomials Reutenauer (UQÀM), Bruce Sagan (Michigan April 30 – May 4, 2007, CRM State) Organizers: Marcelo Aguiar (Texas A&M), Speakers: Petr Ambroz (Czech TU), Pierre François Bergeron (UQÀM), Nantel Bergeron Arnoux (Aix-Marseille 2), Lubomira Balkova (York), Mark Haiman (Berkeley), Stephanie van (Czech TU), Jean Berstel (Marne-la-Vallée), Willigenburg (UBC) Valérie Berthé (Montpellier 2), Alexandre Speakers: Marcelo Aguiar (Texas A&M), Blondin-Massé (UQÀM), Julien Cassaigne (Aix- François Bergeron (UQÀM), Mark Haiman Marseille 2), Sébastien Ferenczi (Aix-Marseille (Berkeley) 2), Aviezri Fraenkel (Weizmann Institute), Anna Number of participants: 68 Frid (Sobolev Institute, Novosibirsk), Amy Glen (Adelaide), Arye Juhasz (Technion), Aldo de The goal of this mini-course was to intro- Luca (Federico II, Naples), Alexei G. Mias- duce the basic methods of Hopf algebras and nikov (McGill), Gregg Musiker (UC San Diego), their interactions with algebraic combinatorics. Dominique Perrin (Marne-la-Vallée), Xavier The topics presented were: combinatorial Hopf algebras, symmetric and quasisymmetric func- Provençal (UQÀM), Denis E. Serbin (McGill), tions, Macdonald polynomials and ties with Benjamin Steinberg (Carleton), Laurent Vuillon group representation theory. Marcelo Aguiar (Chambéry) and François Bergeron each gave lectures last- Number of participants: 65 ing five hours in total, and Mark Haiman gave Chaque journée de l’atelier consistait de lectures lasting seven and a half hours. Marcelo deux séances, et chaque séance de deux expo- Aguiar spoke on tensor categories, the theory sés d’une heure. Cette formule a été appréciée of species, and graded Hopf algebras. François des participants, ainsi que l’a exprimé le doyen Bergeron spoke on symmetric functions, the rep- des participants, Aviezri Fraenkel, dans un dis- resentation theory of finite groups, invariant the- cours improvisé à la fin de l’atelier ; les parti- ory, coinvariant spaces, harmonic polynomials, cipants ont disposé de suffisamment de temps and diagonal coinvariant spaces. Mark Haiman pour des échanges informels. La plupart des par- spoke on the Weyl character formula, algebraic ticipants de l’école sur la combinatoire des mots representations of GL(n), Macdonald polynomi- tenue la semaine précédente participèrent égale- als, Lascoux – Leclerc – Thibon polynomials, and ment à l’atelier ; vingt autres participants se joi- combinatorial models for Macdonald polynomi- gnirent à eux pour l’atelier. als. Handwritten lecture notes are available on L’exposé d’ouverture fut donné par Jean the following web site: karin.math.yorku.ca/ Berstel, qui parla de mots sturmiens et de leur ñantel/HopfAndMacdonald/index.html. généralisation aux arbres. Les mots sturmiens et leurs variantes sont apparus aussi dans les expo- Workshop sés de Valérie Berthé, Amy Glen, Pierre Arnoux, Combinatorial Hopf Algebras and Sébastien Ferenczi, Aldo de Luca et Laurent Macdonald Polynomials Vuillon. La théorie des groupes, examinée du May 7 – 11, 2007, CRM point de vue des techniques de la combinatoire des mots, a été illustrée par les exposés d’Alexei Organizers: Marcelo Aguiar (Texas A&M), Miasnikov, Denis Serbin et Arie Juhasz. Les en- François Bergeron (UQÀM), Nantel Bergeron sembles de mots ont été illustrés par les exposés (York), Mark Haiman (Berkeley), Stephanie van de Gregg Musiker (fonctions zêta des langages Willigenburg (UBC) et des courbes), Benjamin Steinberg (topologie Speakers: Sami Assaf (UC Berkeley), Louis J. pro-finie du monoïde libre) et Dominique Per- Billera (Cornell), Emmanuel Briand (Sevilla), rin (codes synchronisants). Les mots infinis clas- Adriano M. Garsia (UC San Diego), Iain Gor-

20 THEMATIC PROGRAM don (Edinburgh), Jim Haglund (Pennsylvania), Speakers: Ezra N. Miller (Minnesota), Gregory Florent Hivert (Rouen), Friedrich Knop (Rut- G. Smith (Queen’s), Monica Vazirani (UC Davis) gers), Thomas Lam (Harvard), Luc Lapointe Number of participants: 56 (Talca), Alain Lascoux (Marne-la-Vallée), Cris- The goal of this mini-course was to introduce tian Lenart (SUNY Albany), Nicholas Loehr some of the basic methods of algebraic geometry (College of William and Mary), Peter Mc- for which there is a natural interaction with alge- Namara (Bucknell), Jennifer Morse (Drexel), braic combinatorics, as well as tools of algebraic Jean-Christophe Novelli (Marne-la-Vallée), Rosa combinatorics that are of special interest for al- Orellana (Dartmouth), Frédéric Patras (Nice), gebraic geometry. Experimental aspects, involv- T. Kyle Petersen (Michigan), Kevin Purbhoo ing computer algebra, were also covered in these (UBC), Pavlo Pylyavskyy (MIT), Jeffrey Remmel introductory lectures. Monica Vazirani spoke on (UC San Diego), Mercedes Rosas (Sevilla), Anne affine Hecke algebras and their representation Schilling (UC Davis), Mark Shimozono (Vir- theory, and on combinatorics of Sn, slbn and crys- ginia Tech), Jean-Yves Thibon (Marne-la-Vallée), tals. Ezra Miller spoke on toric ideals, binomial Monica Vazirani (UC Davis), Gregory S. War- primary decomposition, D-modules, hyperge- rington (Wake Forest) ometric systems and Euler – Koszul homology. Number of participants: 102 Gregory Smith spoke on polytopes and their The goal of this workshop was to take stock associated toric varieties, f -vectors and Hilbert of ongoing work and of the many rich problems functions, and Minkowski sums and defining that still need to be addressed in two areas nat- equations for toric varieties. urally linked through the combinatorics behind the study of Macdonald polynomials. Recently Workshop one has seen a marked interest in the study of Algebraic Geometry and Algebraic graded Hopf algebras, in part because of their fundamental interactions with algebraic combi- Combinatorics natorics, but also because of their importance May 28 – June 1, 2007, CRM for theoretical physics. In particular, it has re- Organizers: François Bergeron (UQÀM), Sara cently been made apparent that Hopf algebras Faridi (Dalhousie), Anthony V. Geramita play a crucial role in the study of renormaliza- (Queen’s), Allen Knutson (UC Berkeley), Ravi tions in quantum electrodynamics. On the other Vakil (Stanford) hand, in the realm of symmetric and quasisym- Speakers: Arkady Berenstein (Oregon), Em- metric functions, Hopf algebras also appear to manuel Briand (Sevilla), Anders Buch (Rut- play a significant role, with surprising reper- gers), Mahir Can (Western Ontario), Mark cussions in representation theory, algebraic ge- Haiman (UC Berkeley), Valerie Hower (Geor- ometry, mathematical physics, and the combi- gia), Asia Matthews (San Francisco State), Laura natorics of Macdonald polynomials. From an- Matusevich (Texas A&M), Leonardo Mihal- other perspective, there has been a lot of recent cea (Duke), Ezra N. Miller (Minnesota), Di- developments regarding combinatorial models ane Maclagan (Rutgers), Ahad Rahimi (Duis- for Macdonald polynomials and their link to di- burg – Essen), Richard Rimanyi (UNC Chapel agonal coinvariant spaces. Many important ad- Hill), Joe Rusinko (Georgia), Gregory Smith vances in these subjects were presented for the (Queen’s), Hugh Thomas (New Brunswick), first time at this workshop, and several collabo- Lauren Williams (Harvard), Alexander Yong rative projects resulted from it. Slides of presen- (Minnesota), Paul Zinn-Justin (Paris-Sud) tations and handwritten notes are available at Number of participants: 81 the following address: karin.math.yorku.ca/ This workshop included expository talks as ñantel/HopfAndMacdonald/index.html. well as presentations on current research on interactions between algebraic combinatorics, al- School gebraic geometry and group representation the- Algebraic Geometry and Algebraic ory, with an emphasis on the study of sub- Combinatorics jects such as the cohomology of Schubert vari- May 21 – 25, 2007, CRM eties, Hilbert schemes, Gromov – Witten invariants, group invariant theory, coinvariant spaces Organizers : François Bergeron (UQÀM), Sara and their diagonal analogs, and various ties be- Faridi (Dalhousie), Anthony V. Geramita tween these topics and symmetric functions and (Queen’s), Allen Knutson (UC Berkeley), Ravi Schubert polynomials. A special mention should Vakil (Stanford) be made of the new combinatorial model for

21 CENTRE DE RECHERCHES MATHÉMATIQUES

Macdonald polynomials, proposed by Haglund, studying Welschinger invariants by means of Haiman and Loehr, and their relationship with symplectic field theory. Among the other talks the Lascoux – Leclerc – Thibon polynomials. of the first week let us mention Berkovich’s talk on a bridge between tropical varieties and Workshop Berkovich non-Archimedian spaces; Itenberg’s Real, Tropical, and Complex Enumerative and Brugallé’s talks on formulas of the Ca- Geometry poraso – Harris type for Welschinger invariants June 11 – 22, 2007, CRM in the projective plane and the projective 3- space, respectively; Payne’s talk on functoriality Organizers: Viatcheslav Kharlamov (Strasbourg in tropical geometry; Markwig’s talk on applica- 1) and Rahul Pandharipande (Princeton) tions of tropical intersection theory to the proof Speakers: Vladimir Berkovich (Weizmann Insti- of Kontsevich recursive formulas; and Parker’s tute), Erwan Brugallé (Paris 6), Jim Bryan (UBC), talk introducing a new enhanced tropical geom- Carel Faber (Johns Hopkins), Kenji Fukaya (Ky- etry. But the most sensational talks were those oto), Andreas Gathmann (TU Kaiserslautern), by J. Solomon, who discovered completely new Ilia Itenberg (Strasbourg 1), Hannah Mark- recursive formulas combining Welschinger in- wig (IMA, Minnesota), Davish Maulik (Prince- variants with Gromov – Witten invariants. These ton), Rahul Pandharipande (Princeton), Brett formulas lead to a new kind of PDE, related to Parker (MIT), Sam Payne (Stanford), Sergey WDVV equations; the algebraic interpretation of Shadrin (Zürich), Jake Solomon (IAS, Princeton), these formulas is an intriguing and challenging Frank Sottile (Texas A&M), Bernd Sturmfels (UC question. Berkeley), Johannes Walcher (IAS, Princeton), The main topic of the second week was the Jean-Yves Welschinger (ENS Lyon), Ilia Zharkov study of complex enumerative questions. The (Harvard), Aleksey Zinger (Stony Brook) lectures were given by C. Faber, J. Bryan, and Number of participants: 45 R. Pandharipande. Faber gave an exposition of The workshop was devoted to new devel- his work with Aluffi on a more or less complete opments in enumerative geometry, in particu- description of the degree of the orbit of a plane lar, to developments related to the recent emer- curve (in the projective space of plane curves). gence of tropical geometry and a breakthrough Faber and Aluffi used classical methods to in some enumerative problems over the reals; it achieve this. Bryan gave three lectures on mod- also included recent ideas such as string/gauge ern questions. The first two lectures concerned dualities. All the topics discussed point to new Donaldson – Thomas theory and the crepant res- directions in enumerative geometry. The afore- olution conjecture for quotient stacks. From the mentioned fields are developing very quickly, work presented by Bryan came closed formu- and one of the purposes of the workshop was las for box counting in new geometries (extend- to bring together the people working in these ing the classical MacMahon function). The third different, but closely related, directions. We ex- lecture by Bryan concerned again the crepant pect that the workshop will stimulate progress resolution conjecture and Hurwitz – Hodge inte- in these areas. To familiarize the participants grals. Pandharipande’s lectures started with the with the important developments of the field, algebraic foundations of the virtual cycle and five series of introductory lectures were orga- then moved to threefold theories: the GW/DT nized in addition to the advanced talks. These correspondence and then a new theory of stable lectures were given by Jim Bryan, Carel Faber, pairs for threefolds (developed with R. Thomas). Andreas Gathmann, Rahul Pandharipande, and Among other complex geometry lectures, let us Jean-Yves Welschinger. mention those by Zinger, Maulik and Shadrin. The main topic of the first week was the Zinger spoke about computing virtual contribu- study of the tropical and real enumerative ge- tions by deforming sections, and Maulik spoke ometries. Four lectures on tropical geometry about the connections between GW theory and were given by A. Gathmann and four lectures Noether – Lefschetz loci for K3 surfaces. Shadrin on real (symplectic) enumerative geometry by explained Givethals theory of semi-simple quan- J.-Y. Welschinger. Not only did both lecturers tum cohomology, with new applications to r- succeed in providing a thorough introduction spin curves. Finally, there were a few computa- to their respective subjects, but they also pre- tional talks by Sturmfels and Sottile during the sented new techniques and results. Gathmann second week. presented a new tropical intersection theory, and All of the participants agree that the work- Welschinger a new method of computing and shop was very successful and instructive.

22 THEMATIC PROGRAM

Past Thematic Programs The Centre de recherches mathématiques has organized thematic activities every year since 1993. From 1987 to 1992, the CRM organized various types of activities, including special semesters, con- centration periods and thematic activities. Here is a list of the main activities organized by the CRM since 1987.

2005 – 2006 Analysis in Number Theory 1994 – 1995 Geometry and Topology 2004 – 2005 The Mathematics of Stochastic and 1993 – 1994 Dynamical Systems and Applica- Multiscale Modeling tions 2003 – 2004 Geometric and Spectral Analysis 1992 Probability and Stochastic Control (special 2002 – 2003 Mathematics in Computer Science semester) 2001 – 2002 Groups and Geometry 1991 – 1992 Automorphic Forms in Number 2000 – 2001 Mathematical Methods in Biology Theory and Medicine 1991 Operator Algebras (special semester) 1999 – 2000 Mathematical Physics 1990 Nonlinear PDEs and Applications (con- 1998 – 1999 Number Theory and Arithmetic Ge- centration period) ometry 1988 Shimura Varieties (special semester) 1997 – 1998 Statistics 1987 Quantum Field Theory (special semester) 1996 – 1997 Combinatorics and Group Theory 1987 – 1988 Fractals: Theory and Application 1995 – 1996 Applied and Numerical Analysis 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, allow- ing projects to be considered as they arise. The reports are presented in the language in which they were submitted. CRM activities

Conference on 3-manifold Topology in five lectures delivered by recent PhDs and the Honour of Peter Shalen’s 60th Birthday large number of students and young mathemati- June 12 – 15, 2006, CRM cians who attended the workshop reflected the Sponsored by CIRGET robust health of the subject. Organizers: Steven Boyer (UQÀM), Richard Conference on Combinatorial Canary (Michigan), Marc Culler (Illinois at Optimization in Honour of Vašek Chicago), Nathan Dunfield (Caltech), Benson Chvátal’s 60th Birthday Farb (Chicago) June 16 – 17, 2006, CRM Speakers: Ian Agol (Illinois at Chicago), Sponsored by CRM and GERAD Cameron Gordon (UT Austin), Alex Lubotzky Organizers: David Avis (McGill), Gena Hahn (Hebrew University), Dan Margalit (Utah), Yair (Montréal), Bruce Reed (McGill) Minsky (Yale), Maryam Mirzakhani (Prince- Speakers: David Avis (McGill), Xiaomin Chen ton), John Morgan (Columbia), Lenhard Ng (Rutgers), Jarmila Chvátalová (Champlain Col- (Stanford), Peter Ozsvath (Columbia), Jake Ras- lege Saint-Lambert), Sanjeeb Dash (IBM Watson mussen (Princeton), Michah Sageev (Technion), Research Center), Chinh Hoang (Wilfrid Lau- Peter Storm (Stanford) rier), Bahman Kalantari (Rutgers), Jean-François Number of participants: 70 Maurras (Aix-Marseille 2), Ming Ouyang (Uni- A conference in honour of Peter Shalen, versity of Medicine and Dentistry of New Jer- whose work has been a major force in bringing sey), Hui-Yu Wang (Rutgers) many different aspects of mathematics to bear Number of participants: 21 on the study of 3-manifolds, and in expanding Le colloque en l’honneur de Vašek Chvá- the influence of 3-manifold topology into other tal à l’occasion de ses 60 ans a réuni quelques- areas, was held at the CRM on July 12 – 15, 2006. uns de ses proches collaborateurs, de ses anciens The subject of 3-manifold topology has a long étudiants et de ses amis mathématiques. Vašek history of deep and interesting interactions with Chvátal est un des chercheurs les plus impor- other parts of mathematics. The complexity of tants et les plus influents en optimisation com- these connections has increased with time, as the binatoire, et il a joué un rôle crucial dans l’or- subject developed, and has exploded in recent ganisation du semestre thématique en optimisa- years. The coincidence of this explosion with the tion combinatoire tenu au CRM en 2006. Le pré- recent solution of several of the major outstand- sent colloque a été marqué entre autres par une ing problems in the area made this a good time conférence de Xiaomin Chen sur le théorème for a reflection on its relationship to the rest of de Sylvester-Chvátal et des problèmes connexes, mathematics. une conférence de Chinh Hoang sur les graphes The conference brought together a var- parfaitement ordonnables et une conférence de ied group of leading researchers whose work David Avis sur une heuristique pour le pro- demonstrates deep connections between 3- blème du transversal. manifold topology and other areas of mathemat- Sanjeeb Dash a donné une conférence sur les ics. The areas covered by the lectures included: plans de coupure pour les problèmes de pro- geometrization of 3-manifolds; virtual proper- grammation en nombres entiers mixte. Ming ties of 3-manifolds; combinatorial group the- Ouyang et Hui-Yu Wang ont donné une confé- ory and coarse geometric properties of groups; rence sur le jeu « Master Mind » et Bahman Ka- properties of random 3-manifolds and asymp- lantari une conférence sur la mise à l’échelle de totic properties of hyperbolic surfaces; Floer matrices et un algorithme de Chvátal en pro- homology, Khovanov – Rozansky homology; 3- grammation linéaire. Finalement, Jean-François manifold invariants arising from contact struc- Maurras a donné une conférence sur les preuves tures; character varieties; and Dehn surgery. The

25 CENTRE DE RECHERCHES MATHÉMATIQUES que certaines inégalités définissent des facettes. with polynomial growth). Finally, Mike Davis Les participants ont eu assez de temps libre pour gave a mini-course on “L2-Betti numbers,” an échanger des idées et travailler entre les sessions older and more analytic topic whose presence is de conférences. increasingly felt in the theory of infinite groups. These courses were a great success. In addi- Mini-courses and Conference on tion to a substantial student presence, there were Geometric Group Theory a fair number of seasoned mathematicians from July 3 – 14, 2006, CRM neighboring fields who were interested in learn- Sponsored by CIRGET ing more about geometric group theory. Their Organizers: Mladen Bestvina (Utah), Steven numerous informed questions heightened the Boyer (UQÀM), Tadeusz Januszkiewicz (Ohio level of communication for all participants dur- State), Michah Sageev (Technion), Daniel T. Wise ing the mini-courses. (McGill) During the second week, there were approx- Mini-Course Lecturers: Mike Davis (Ohio imately thirty advanced research lectures on a State), Chris Hruska (Chicago), Graham Niblo wide variety of topics within geometric group (Southampton), Michah Sageev (Technion), theory. The organizers included a number of Jacek Swiatkowski (Wroclaw), Kevin Whyte (Illi- shorter contributed talks by additional partici- nois at Chicago) pants; many of these talks built upon the mini- Speakers: Jason Behrstock (Utah), Marc Bour- courses from the previous week. For instance, don (Nancy 1), Noel Brady (Oklahoma), Inna Bruce Kleiner spoke about the quasi-isometric Bumagin (Carleton), Ruth Charney (Brandeis), rigidity of right-angled Artin groups, building Matthew Clay (Utah), Yves de Cornulier (Penn upon both the quasi-isometric rigidity and the State), Tullia Dymarz (Chicago), Mark Feighn CAT(0) cube complexes mini-courses. Tim Hsu (Rutgers), Soren Galatius (Stanford), Tim Hsu spoke about cubulating graphs of groups, build- (San Jose State), Olga Kharlampovich (McGill), ing upon CAT(0) cube complexes and relative Bruce Kleiner (Yale), Ian Leary (Ohio State), Dan hyperbolicity. Roman Sauer spoke about measure theoretic methods in the study of L2-Betti Margalit (Utah), Eduardo Martinez (Oklahoma), 2 Jon McCammond (UC Santa Barbara), Alexei G. numbers, building upon the introduction to L - Miasnikov (McGill), Lee Mosher (Rutgers), De- Betti numbers in group theory. There were excit- nis Osin (City College of New York, CUNY), ing announcements of new results in the area, Bertrand Remy (Lyon 1), Roman Sauer (Göttin- such as Osin’s announcement of the construc- gen), Richard Scott (Santa Clara), Karen Vogt- tion of certain small-cancellation monsters (thus mann (Cornell), Bertold Wiest (Rennes 1) settling old questions from the Kovourka prob- Number of participants: 98 lem book). Mark Feighn announced a surpris- The first week of the conference was dedi- ing characterization of constructible subsets of cated to five mini-courses that were pitched at free groups. There were also many new research an introductory level and aimed at students en- directions opened: Jon McCammond outlined a tering the field. Chris Hruska gave a mini-course new approach to geometrize Artin groups to re- on “Relative Hyperbolicity,” which is a topic of solve notorious problems about their algebraic continual interest having matured during the properties. last couple of years. Graham Niblo and Michah The participants were able to spend much Sageev jointly gave a mini-course on “CAT(0) time together in the evenings and during the Cube Complexes,” a topic that is becoming in- breaks, to pursue ongoing collaborations. The creasingly central in geometric group theory and conference was a resounding success and will is rekindling in higher dimensions the monu- have a major impact on the next generation of mental impact of group actions on trees intro- researchers in the area; it introduced them to duced by Serre in the 1970s. Jacek Swiatkowski several of the most important current topics, gave a mini-course on “Simplicial Nonpositive and allowed them to interact with seasoned re- Curvature,” which is an exciting emerging area; searchers in the field. many of the student participants now embark- Mini-workshop on Computational Aspects ing on a PhD are actually planning to work of Dynamical Systems in this area. Kevin Whyte gave a mini-course July 7, 2006, Concordia University on “Quasi-isometric Rigidity,” which lies at the Sponsored by the Applied Mathematics heart of geometric group theory and has fea- Laboratory, CRM tured many striking results (beginning with Gro- mov’s virtually nilpotent classification of groups Organizer: Eusebius J. Doedel (Concordia)

26 GENERAL PROGRAM

Speakers: Bernd Krauskopf (Bristol), Hinke In this workshop were presented results of a Osinga (Bristol), Volodymyr Romanov (Concor- very high level in a remarkable range of subjects dia), Paul Tupper (McGill) in the field. The atmosphere of the workshop Number of participants: 12 was relaxed and of exceptional congeniality. Par- This mini-workshop provided an opportu- ticipants included researchers and students from nity for European and Canadian researchers in several countries in North and South America, dynamical systems to meet and work together. Europe, and Asia. The main theme of the meet- The lectures were very well presented and cov- ing was the formation of geometrical singulari- ered an interesting range of topics. The topic ties in PDE problems with a variational formu- of Hinke Osinga’s talk was “Boundary Crisis: lation. These equations typically arise in some Mind the Gaps!”; that of Paul Tupper’s talk, applications (to physics, engineering, or biology, “A Non-Existence Result for Hamiltonian Inte- for example), and their resolution requires com- grators”; that of Bernd Krauskopf, “Global Bi- bining methods from functional and harmonic furcations of the Lorenz Manifold”; and that analysis, differential geometry, and geometric of Volodymyr Romanov’s talk, “Elemental Peri- measure theory (for instance). Numerical simu- odic Orbits Associated with the Libration Points lations can also be helpful to visualize and pre- of the Homogeneous Rotating Gravitating Tri- dict the types of singularities expected in com- axial Ellipsoid.” The mini-workshop was held plex problems. The talks lasted 45 minutes each, on the occasion of a 10-day visit to Montreal which left ample time for discussions between by Bernd Krauskopf and Hinke Osinga. During participants, the fruits of which may be divulged this visit, they worked with Eusebius Doedel on in upcoming meetings! “Global Bifurcations of the Lorenz Model.” They The excellent opening talk of the conference, also met other Montreal researchers, including by David Kinderlehrer, set the high tone for Paul Tupper and Volodymyr Romanov (Euse- the week. Throughout his distinguished career, bius Doedel’s PhD student). These encounters D. Kinderlehrer has often pioneered methods are very likely to lead to further scientific con- and directions for research, and his influence tact. (through former students and postdocs) is very significant. He spoke about the problem of trans- Workshop on Singularities in PDE and the port in cells, a problem that combines modelling Calculus of Variations questions with optimization and diffusion and is July 17 – 21, 2006, CRM a real challenge for researchers in PDE. Financed by the CRM and the National Science A recurrent theme in the meeting involved Foundation the Cahn – Hilliard model for phase transitions, Organizers: Stan Alama (McMaster), Lia Bron- which is ubiquitous in the description of domain sard (McMaster), Peter Sternberg (Indiana) walls (codimension-one singularities) in many Speakers: Yaniv Almog (Louisana State), contexts. Bob Kohn has played a major role in Leonid Berlyand (Penn State), Fabrice Béthuel the development of this area, not only through (Paris 6), Rustum Choksi (Simon Fraser), his own groundbreaking research but through Manuel Del Pino (Chile), Carlos J. Garcia- his many successful former students and post- Cervera (UC Santa Barbara), Stephen Gustafson docs (who were well represented at this meet- (UBC), Radu Ignat (Paris 6), Robert Jerrard ing). His importance in the field of PDE is under- (Toronto), Shuichi Jimbo (Hokkaido), Bernd lined by his selection as plenary speaker in this Kawohl (Köln), David Kinderlehrer (Carnegie year’s ICM. At the workshop he spoke on the Mellon), Robert V. Kohn (Courant Institute, dynamics of crystal facets as a steepest descent NYU), Chun Liu (Penn State), Andrea Malchiodi problem for a non-smooth energy functional. (SISSA, Trieste), Vincent Millot (Carnegie Mel- There were many other fascinating results on lon), Alberto Montero Zárate (Toronto), Yoshi- Cahn – Hilliard-type systems. M. Del Pino spoke hisa Morita (Ryukoku), Pablo Padilla (UNAM), about the existence of multiple transition lay- Daniel Phillips (Purdue), Xiaofeng Ren (Utah ers, a talk which generated much interest as State), Maria G. Reznikoff (Georgia Tech), Sylvia the problem had been studied by many partici- Serfaty (Courant Institute, NYU), Daniel Spirn pants. M. Reznikoff presented a new approach to (Minnesota), Gabriella Tarantello (Tor Vergata), studying stochastic effects in switching between William P. Ziemer (Indiana), William K. Ziemer local minima for such problems. X. Ren gave (California State University, Long Beach) new results on how modifications to Cahn – Number of participants: 57 Hilliard (arising in other applications) can have

27 CENTRE DE RECHERCHES MATHÉMATIQUES a stabilizing effect on the stationary problem. Many fascinating talks fell outside of these Radu Ignat spoke about a related problem from broad categories, illustrating the breadth of the micromagnetism, in which nonlocal effects are field. A. Malchiodi gave a very beautiful talk introduced. R. Choksi presented striking results on singular perturbation problems with concen- (obtained with P. Sternberg) on some new non- trations along curves or surfaces. These prob- local isoperimetric problems arising from the lems are related to pattern formation in biolog- Ohna – Kawasaki model for diblock copolymers. ical systems. P. Padilla gave a very enlighten- A second major theme of the workshop was ing and entertaining closing talk on the wealth the family of Ginzburg – Landau models for su- of variational problems in nature, where pat- perconductors, superfluids, and Bose – Einstein terns may arise as optimal geometrical forms. condensates. These models involve a complex- B. Kawohl compared several variational mod- valued wave function, and the singularities els (such as Mumford – Shah) and geometrical are typically “vortices”: quantized codimension- models (such as Perona – Malik) used in image two defects in the complex phase. F. Béthuel processing. C. Liu presented results on difficult beautifully presented some very impressive re- problems of well-posedness in viscoelastic ma- sults on the dynamics and interactions of vor- terials. C. Garcia-Cervera presented numerical tex solutions, including the difficult problem and analytical results on density functional the- of “annihilation” and splitting in finite time, ory from quantum chemistry, an area which was a fundamental problem that has been open new to most participants. for some time. Dynamical results on the diffi- Several talks (including many of those men- cult Schrödinger map problem (which is con- tioned above) also addressed the analytic foun- nected to models of micromagnetism) were de- dations behind the models. R. Jerrard presented scribed by S. Gustafson. L. Berlyand discussed a new measure-theoretic approach to Monge – the role of the capacity in minimizing the Ampère functions, which doesn’t require con- Ginzburg – Landau functional with prescribed vexity assumptions and is applied to the study degrees. A. Montero Zárate presented results of isoperimetric immersions and functionals of (some of which were obtained with S. Alama the Jacobian determinant. V. Millot discussed the and L. Bronsard) on local minimizers with vor- lifting of H1/2 maps with values in the circle, a tices in a Bose – Einstein condensate. problem related to Ginzburg – Landau function- In the setting of superconductivity there als in higher dimensions. W. Ziemer spoke (with were many new and exciting results. S. Serfaty the collaboration of his son W.K. Ziemer) about gave a sweeping overview of the vorticity of a very weak form of the Gauss – Green theorem, minimizers in increasing magnetic fields, tying which turns out to be related to methods de- the problem to the methods of div-curl systems scribed by S. Serfaty in her talk. introduced by DiPerna and Majda. S. Jimbo de- The workshop also included two poster ses- scribed a method producing solutions in nar- sions, in which seven posters were exhibited. row three-dimensional superconductors via a The posters, made by graduate students or post- dimension-reduction procedure. This talk was docs, were of very high quality and attracted nicely complemented by that of Y. Morita, who the interest of many participants. The organiz- gave a complete bifurcation analysis of the re- ers were happy to give young mathematicians duced problem in a closed loop. Y. Almog ana- a chance to show their results to a larger au- lyzed the normal/superconducting transition in dience, and to allow students and postdocs a the presence of electric currents. chance to meet one another and exchange re- There were also some very interesting results sults. The participants were chosen so as to in- on alternative models of Ginzburg – Landau clude a wide spectrum of interests in the field type. D. Phillips presented a model for high- of PDE and singular perturbation theory. One temperature superconductors with results on measure of the organizers’ success in this regard the unusual pattern of vortices observed. There is that everyone attended the talks across the were two talks on the Chern – Simons – Higgs various “groups,” although several participants functional from gauge-field theory: G. Taran- had never met before in person. The organiz- tello discussed uniqueness problems in the self- ers are grateful to the NSF for providing a gen- dual regime, while D. Spirn showed gamma- erous grant ($15,000) to support young mathe- convergence of the functional in the large- maticians coming from the United States. coupling limit. These functionals presented many new challenges and open problems for the participants.

28 GENERAL PROGRAM

MOPTA 06 tion, Roger Fletcher (Dundee), Sven Leyffer (Ar- The 6th Annual Conference on Modeling gonne National Laboratory) and Philippe Toint and Optimization: Theory and (Facultés Universitaires Notre-Dame de la Paix). Applications This prize is awarded jointly by the Mathemati- July 24 – 27, 2006, University of Waterloo cal Programming Society (MPS) and the Society Sponsored by the University of Waterloo, the for Industrial and Applied Mathematics (SIAM). Fields Institute, MITACS, the CRM, the Conference in honour of Pierre Leroux University of Waterloo Department of September 8 – 9, 2006, Université du Québec à Combinatorics and Optimization and the Montréal Department of Management Sciences Sponsored by LaCIM Organizers: Tony Vanelli (Waterloo) and Henry Organizers: Srecko Brlek (UQÀM), Christophe Wolkowicz (Waterloo), Chairs of the program Reutenauer (UQÀM), François Bergeron committee; Abdo Alfakih (Windsor), Antoine Deza (McMaster), Samir Elhedhli (Waterloo) (UQÀM) Speakers: Plenary/Invited Speakers: Thomas F. Cole- Dominique Foata (Strasbourg), Adri- man (Waterloo), Michael Ferris (UW Madison), ano Garsia (UC San Diego), Alain Goupil Charles Johnson (College of William and Mary), (UQTR), Dominique Gouyou-Beauchamps Sven Leyffer (Argonne National Laboratory), (Paris 11), André Joyal (UQÀM), Gilbert La- Zhi-Quan Luo (Minnesota), Michael Saunders belle (UQÀM), Cédric Lamathe (UQÀM), Volker (Stanford), Yinyu Ye (Stanford) Strehl (Erlangen-Nürnberg), Xavier Viennot Number of participants: 140 (Bordeaux 1), Timothy Walsh (UQÀM) This four-day conference brought together a Number of participants: 56 diverse group of people from both discrete and Le but de ces journées était d’honorer Pierre continuous optimization, working on both theo- Leroux, qui fonda le LaCIM et est l’un des cher- retical and applied aspects. The aim of the con- cheurs québécois les plus actifs en combinatoire ference was to bring together researchers from algébrique et énumérative. Les Journées Pierre both the theoretical and applied communities, Leroux, organisées quelques mois avant sa re- who would not usually have the chance to inter- traite, permirent de réunir d’anciens étudiants et act in the framework of a medium-scale event. des collaborateurs qui travaillent avec lui depuis To encourage synergy, we hosted a combina- longtemps. tion of theoretical and applied one-hour talks by Les conférences prononcées pendant ces seven distinguished invited researchers. Michael journées couvrirent de nombreux domaines Saunders opened the conference with his talk de la combinatoire. Xavier Viennot parla on matrix factorization and updating methods. d’exclusion symétrique et de tableaux de Ca- Later that day, Charles Johnson presented the talan et Adriano Garsia de produits de Krone- newly established results concerning positive, cker et de la combinatoire de certaines équations path-product, and inverse M-matrices. On the diophantiennes. André Joyal donna un exposé second day, Zhi-Quan (Tom) Luo described a sur les catégories de Möbius, la caractéristique probabilistic analysis of semidefinite relaxation d’Euler-Poincaré et l’interpolation de Newton. for binary quadratic minimization with appli- Cédric Lamathe parla d’énumération de graphes cation to wireless communication, and Michael de k-arches étiquetés et Dominique Gouyou- Ferris presented the latest techniques for solv- Beauchamps d’énumération de tableaux de ru- ing hard optimization models in parallel. On the bans. Pendant la deuxième journée, Dominique third day, Yinyu Ye introduced the semidefinite Foata donna un exposé sur les permutations programming approach to tensegrity theory and signées, les points fixes et les points pixes, et realizability of graphs, and Sven Leyffer gave an Alain Goupil un exposé sur les polynômes de overview of filter methods and discussed novel caractères et le produit de Kronecker. Volker approaches. On the fourth day, Thomas Cole- Strehl donna une conférence intitulée « Com- man spoke on his recent work on calibration and binatoire analytique – et nostalgique » et Timo- hedging of equity-linked insurance benefits un- thy Walsh une conférence intitulée « Énuméra- der a jump model. The conference also featured tion des réseaux à deux pôles fortement pla- about 80 contributed talks. naires ». Pour conclure les journées, Gilbert La- On the second day of the conference, a cel- belle parla de ses aventures mathématiques avec ebration was held to honour the recipients of Pierre Leroux. the Lagrange Prize in Continuous Optimiza-

29 CENTRE DE RECHERCHES MATHÉMATIQUES

Gilles Fournier Memorial Conference on Financed by the Number Theory Foundation, Classical and Computational Topological CICMA and the Department of mathematics Methods and statistics of Université Laval September 22 – 24, 2006, Université de Organizers: Claude Levesque (Laval), Jean- Sherbrooke Marie De Koninck (Laval) Sponsored by the CRM, the Mathematical Distinguished plenary speaker: Jean-Pierre Analysis Laboratory, CRM, Bishop’s University Serre (Collège de France) and the Faculty of Sciences of the Université de Plenary speakers: Chris Cummins (Concor- Sherbrooke dia), Henri Darmon (McGill), Eyal Goren Organizers: Madjid Allili (Bishop’s), Tomasz (McGill), Farshid Hajir (UMass Amherst), Her- Kaczynski (Sherbrooke) shy Kisilevsky (Concordia), Manfred Kolster Speakers: Jean-Marc Belley (Sherbrooke), (McMaster), John Labute (McGill), John McKay Hichem Ben-El-Mechaiekh (Brock), Octav (Concordia), Carl Pomerance (Dartmouth Col- Cornea (Montréal), David Corriveau (Sher- lege), Francisco Thaine (Concordia) brooke), Jean-Noël Corvellec (Perpignan), Ketty Invited speakers: Andreas Bender (KIAS), El- de Rezende (Estadual de Campinas), Sara De- liot Benjamin (Maine), David Bradley (Maine), rivière (Sherbrooke), Marlène Frigon (Mont- Hugo Chapdelaine (McGill), John Culli- réal), Patrizio Frosini (Bologna), Massimo Furi nan (Bard College), Mairead Greene (UMass (Firenze), Lech Gòrniewicz (Nicolaus Coperni- Amherst), Kiran Kedlaya (MIT), Dominic Klyve cus), Jan Jaworowski (Indiana), Robert Kotiuga (Dartmouth College), Andrew Knightly (Maine), (Boston), Jean-Philippe Lessard (Georgia Tech), Emmanuel Letellier (Concordia), Roger Oyono Mario Martelli (Claremont McKenna College), (Waterloo), Paul Pollack (Dartmouth College), Marian Mrozek (Jagellon University), Piotr Andrew Sills (Rutgers), Chip Snyder (Maine), Oprocha (AGH-UST), Andrzej Szymczak (Geor- Nicolas Thériault (Fields), Erik Tou (Dartmouth gia Tech), Anik Trahan (Collège de Sherbrooke), College) Marcin Zelawski (Jagellon University), Natalia Number of participants: 45 Zelazna (Jagellon University) In 1998 number theorists at Université Laval Number of participants: 34 and the University of Maine founded the This conference brought together many re- Québec – Maine Conference on Number Theory searchers working on topological methods in a and Related Topics. Since then it has been held variety of problems ranging from classical ap- annually on a weekend in early Fall (except plications to nonlinear analysis and dynamics. in 2001). The organizers invite number theo- These methods include Morse theory, the topo- rists and mathematicians in related fields from logical degree, the fixed point index, the Con- New England, Eastern Canada, and beyond to ley index, and the most recent applications of speak about their research and discuss ideas computational topology to computer science, for future work. Each year there is a change in namely, to image modelling and reconstruc- venue: odd years at the University of Maine, tion. We also commemorated Professor Gilles even years at Université Laval. Thus the 2006 Fournier by bringing up his numerous contri- conference took place at Université Laval, and butions to applications of topology. The confer- the highlight of the conference was the presence took place at Bishop’s University. Partici- ence of Jean-Pierre Serre, who is a Fields medal- pants at all stages of their careers (MSc and PhD list and one of the foremost mathematicians in students, Emeritus Professors, etc.) came from the world. His lecture was entitled “Groupes fi- Canada, the United States, Poland, France, Italy nis: choix de théorèmes.” There were 26 other and Brazil. The conference unfolded in an at- lectures, including 5 by graduate students. The mosphere of friendship that promoted interac- program of the conference may be found at the tion and discussion. Among others, the collab- address germain.umemat.maine.edu/msfiles/ oration between the research groups of Sher- numbertheory/mainequebec.html. brooke – Bishop’s, Cracow and Bologna was re- Xth International Workshop on inforced by this meeting. Differential Equations, Number Theory, Québec – Maine Conference on Number Data Analysis Methods and Geometry Theory and Related Topics February 19 – 23, 2007, Universidad de La September 30 - October 1, 2006, Université Laval Habana Sponsored by CICMA

30 GENERAL PROGRAM

Sponsored by the Faculty of Mathematics and exchanges. Simultaneously these meetings have Computation of the University of La Habana, provided opportunities for research groups from the Department of Mathematics and Statistics of Canada, Europe and Latin America to collab- Concordia University, the Institute of orate with Cuban mathematicians. This year’s Cybernetics, Mathematics and Physics of the meeting was widely attended and brought to- Academy of Sciences of Cuba, and the CRM gether some of the leading experts in the domains represented. Organizers: Syed Twareque Ali (Concordia), Reinaldo Rodriguez Ramos (La Habana), Mini-course on GARCH Volatile Processes François Lalonde (Montréal) March 12 and 14, 2007, Université de Montréal Speakers: Jean-Pierre Antoine (Université Sponsored by GERAD and the Statistics catholique de Louvain), Natig Atakishiyev Laboratory, CRM (UNAM Cuernavaca), Jorge Barrios Ginart Organizers: (La Habana), Françoise Bastin (Liège), Ste- Roch Roy (Montréal), Pierre Du- fan Berceanu (IFIN-HH), Alexander Bobenko chesne (Montréal) Speakers: (TU Berlin), Walter Carballosa (La Habana), Christian Francq (Lille 3), Jean- Felix Carbonell (McGill), Sergei Chumakov Michel Zakoïan (Lille 3) Number of participants: 30 (Guadalajara), Pierre Colmez (École Polytech- Ce mini-cours était une introduction aux nique, Palaiseau), Chantal David (Concordia), modèles GARCH et à volatilité stochastique Didier Domínguez (ICIMAF), A. Fraguela Col- utilisés dans la modélisation des séries finan- lar (Universidad Autónoma de Puebla), Nassif cières. Les modèles linéaires de séries tempo- Ghoussoub (UBC), Joanka Hernández Cabañas relles se révèlent incapables de représenter cer- (La Habana), Jarmo Hietarinta (Turku), Adrian taines propriétés caractéristiques des séries fi- Iovita (Concordia), Ángela León Mecías (La nancières (absence de corrélation entre les ren- Habana), Trueman MacHenry (York, Toronto), dements, corrélation des carrés, regroupement Manuel Mañas (Complutense), José Marin- des extrêmes, distributions leptokurtiques, ef- Antuna (La Habana), Rob Martin (Waterloo), fet de levier, etc.). Les modèles GARCH, intro- Vladimir Matveev (Bourgogne, Dijon), Lester duits par Engle en 1982, sont particulièrement Melie-García (Centro de Neurosciencias de adaptés à la prise en compte de ces proprié- Cuba), Frank W. Nijhoff (Leeds), George W. tés, ce qui explique leur fort impact dans les Patrick (Saskatchewan), Nasser Saad (Prince Ed- littératures économique, financière et économé- ward Island), Federico Sabina (UNAM), Yiannis trique. Ils reposent sur une spécification de la va- Sakellaridis (Tel Aviv), Martin Schlichenmaier riance conditionnelle du rendement. Les points (Luxembourg), Peter Schneider (Münster), Di- ci-dessous ont été abordés. eter Schuch (Frankfurt), Yuri Suris (München), José R. Talavera Hurtado (La Habana), Nelson J. 1. Conditions de stationnarité et propriétés pro- Trujillo-Barreto (Centro de Neurosciencias de babilistes du modèle GARCH standard Cuba), Pedro Valdés Sosa (Centro de Neuro- 2. Asymétries et autres spécifications de la va- sciencias de Cuba), Ronald Van Luijk (Simon riance conditionnelle Fraser), Otmar Venjakob (Heidelberg), Alexan- 3. Estimation et tests, propriétés asymptotiques der P. Veselov (Loughborough), Lilian Villarin de la méthode du quasi-maximum de vrai- Pildain (La Habana), John Willis (Cambridge), semblance, méthodes alternatives Kurt Bernardo Wolf (UNAM Cuernavaca) 4. Modèles à volatilité stochastique et modèles Number of participants: 60 ARCH à changement de régime markovien Certains de ces points ont été illustrés à partir de This was the 10th anniversary meeting of données réelles, et certains résultats récents pa- an annual series of activities that have been rus dans des articles scientifiques ont été men- organized since 1998. These meetings have fo- tionnés. cused on the areas of differential equations, sig- The 4th Montreal Scientific Computing nal processing, quantization and composite sys- Days tems. This year the scope of the meeting was April 16 – 17, 2007, CRM broadened to include number theory and inte- Sponsored by the Applied Mathematics grable systems. The main objective of the series Laboratory, CRM is to provide Cuban researchers and students with an opportunity to interact with mathemati- Organizers: Emmanuel Lorin de la Grandmai- cians and physicists from outside Cuba, in order son (Montréal), Robert G. Owens (Montréal), to foster the development of collaborations and Thomas P. Wihler (McGill)

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Lecturers: Don Estep (Colorado State), Number of participants: 56 Christoph Schwab (ETH Zürich) This conference honoured the contributions Number of participants: 86 of John McKay, a world-renowned mathemati- By holding the Montreal Scientific Comput- cian and one of the most influential Canadian ing Days, the Applied Mathematics Labora- mathematicians. Out of the 56 participants (who tory seeks to nurture its young researchers and came from all parts of the globe), 46 were in- gather researchers interested in scientific com- vitees and 18 gave one-hour talks. Yuri Manin puting. The 4th in the series of this very suc- gave two one-hour talks, and George Hart, cessful conference was held on April 16 and sculptor and mathematician, gave a workshop 17, and 86 students, postdocs and faculty mem- session on polyhedral sculpture construction. bers from Québec, Ontario, New York State and The two main conference topics, “Monstrous even such faraway countries as India, Haiti and Moonshine” and the “McKay Correspondence,” France registered for the event. Travel support are topics to which John McKay made pioneer- was offered to participants coming from outside ing contributions. The conference also included Montréal. The participants were treated to excel- lectures on finite groups, Galois theory, modu- lent graduate-level lectures on adjoint-based er- lar groups and functions, algebraic computation, ror estimators and hierarchical wavelet methods number theory, group representations, and alge- for high-dimensional problems, given by Profes- braic geometry. sors Don Estep and Christoph Schwab. The titles, abstracts and videos of the confer- The lecture notes have been posted on the ence talks may be found at the conference web- website of the conference. The organizing com- site (crm.math.ca/McKay07/index_e.shtml). A mittee selected 11 out of the abstracts submitted volume based upon the invited talks plus a num- by participants for oral presentation, and other ber of additional refereed contributions will be contributions were made in the form of posters published in the CRM Proceedings and Lecture displayed during an evening reception on April Notes; it should be available in 2008. 16. SIAM gift certificates were awarded for the best oral presentations and the best poster. Feed- Workshop on the Geometry of back from the participants at the end of the con- Holomorphic and Algebraic Curves in ference confirmed the success of the adopted for- Complex Algebraic Varieties mat and encouraged the members of the Ap- April 30 – May 4, 2007, CRM plied Mathematics Laboratory to make plans for Organizers: Xi Chen (Alberta), James D. Lewis similar events in the years to come. (Alberta), Steven Shin-Yi Lu (UQÀM), Peter Groups and Symmetries: From the Russell (McGill) Neolithic Scots to John McKay Speakers: Fedor Bogomolov (Courant Insti- Conference Honouring the Contributions tute, NYU), Karen Chandler (Illinois at Urbana- of John McKay Champaign), Jean-Pierre Demailly (Grenoble 1), April 27 – 29, 2007, CRM Gerd-Eberhard Dethloff (Bretagne Occidentale, Sponsored by CRM, Concordia University, and Brest), Hélène Esnault (Duisburg-Essen, Es- the CICMA Laboratory, CRM sen), Samuel Grushevsky (Princeton), Ryoichi Kobayashi (Nagoya), James D. Lewis (Alberta), Organizers: John Harnad (Concordia), Pavel Michael McQuillan (Glasgow), Reiko Miyaoka Winternitz (Montréal) (Kyushu), Yoichi Miyaoka (Tokyo), Terrence Speakers: Daniel Allcock (UT Austin), Philip Napier (Lehigh), Bruno de Oliveira (Miami), Boalch (ÉNS, Paris), John Conway (Prince- Gianluca Pacienza (Strasbourg), Mohan Ra- ton), Henri Darmon (McGill), Jorge Andres De- machandran (Buffalo), Ziv Ran (UC Riverside), voto (Instituto Tecnológico de Buenos Aires), Erwan Rousseau (Strasbourg 1), Min Ru (Hous- Igor V. Dolgachev (Michigan), Chongying Dong ton), Shuji Saito (Tokyo), Bernard Shiffman (UC Santa Cruz), John Duncan (Harvard), (Johns Hopkins), Jason Starr (Stony Brook), An- Noam D. Elkies (Harvard), Nora Ganter (Illi- drey Todorov (UC Santa Cruz), Yuri Tschinkel nois at Urbana-Champaign), Eyal Z. Goren (Courant Institute, NYU), Eckart Viehweg (McGill), Valery Gritsenko (Lille 1), George Hart (Duisburg-Essen, Essen), Jörg Winkelmann (Stony Brook), Nicholas M. Katz (Princeton), (Bayreuth), Pit-Mann Wong (Notre Dame), Yuri Manin (MPIM), Jack Morava (Johns Hop- Sai-Kee Yeung (Purdue), Qi Zhang (Missouri- kins), M. Ram Murty (Queen’s), Iku Nakamura Columbia), Scott Zrebiec (Johns Hopkins) (Hokkaido), Viacheslav V. Nikulin (Liverpool), Doctoral students with financial support: John Simon P. Norton (Cambridge) Baber (Johns Hopkins), Simone Diverio (La

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Sapienza & Grenoble 1), Fabrizio Donzelli (Mi- on varieties, and have helped resolve the ques- ami), Ning Hao (Stony Brook), Dano Kim tion of the nonexistence of curves of low genus (Princeton), Brian Macdonald (Johns Hopkins), in general hypersurfaces in projective space (a Scott Zrebiec (Johns Hopkins) question in the spirit of Lang’s conjectures). Qi Number of participants: 45 Zhang gave an overview of the state of the art al- The past decades have seen several ma- gebraic method in the analysis of varieties with jor breakthroughs in our understanding of the nef anticanonical bundle, first introduced by Lu structure of algebraic varieties both from the al- (2002). The important question in this regard is gebraic geometric side and the complex ana- whether varieties with nef and big anticanonical lytic side. A major intersectRion of the two sides bundle are rationally connected. has to do with certain structural conjectures of On the arithmetic side, the principal speakers Serge Lang that have catalyzed some of these ad- were Esnault, Tschinkel and Saito. Esnault pre- vances. The conjectures are natural extensions of sented her new result, i.e., a successful interpre- questions originating in hyperbolic geometry on tation of Grothendieck’s section conjecture for the role of curvature in the distribution and be- the arithmetic fundamental group of hyperbolic havior of curves and, by analogy, rational points, curves, via an arithmetic analog of connections. in algebraic varieties. This workshop brought to- Over a number field, her result shows that the gether some international experts in this area; said conjecture is in fact equivalent to the same they presented the new ideas and introduced conjecture over the projective line minus three the rapid developments to a new generation of points. Shuji Saito presented some state of the art mathematicians. The workshop was intended as techniques from Hodge theory for dealing with a small memorial to Serge Lang. Its talks rotated classical arithmetic questions, including ques- between algebraic geometry, complex geometry tions on the distribution of rational points on and related issues in arithmetic geometry. algebraic varieties. Tschinkel pampered the au- On the algebraic side, the principal speak- dience with a beautiful PowerPoint presentation ers were Viehweg, Bogomolov and Y. Miyaoka. of the general conjecture concerning the distri- Viehweg gave an overview of his results on bution of rational points on algebraic varieties. the existence and hyperbolicity of the moduli He focused most of his talk on algebraic function stacks of Calabi – Yau (resp. canonically polar- fields and varieties that are rationally connected. ized) algebraic manifolds, including a sketch of On the complex analytic side, the principal the proof and some beautiful applications to speakers were Demailly, Shiffman, Kobayashi the nonexistence of holomorphic (resp. Shimura) and Winkelmann. Demailly presented his pow- curves. He concluded with a list of open prob- erful tool of contact jet spaces, with which one lems concerning curves and hyperbolicity of expects to resolve Lang’s holomorphic and alge- moduli spaces. Bogomolov spoke on his re- braic conjectures in full. In dimension two, for cent generalizations of his famous inequality example, this was used to give the best bound of Chern numbers for the tangent bundle of a so far on the degree of generic hypersurfaces of a complex surface to the case of surfaces with projective space that ensures hyperbolicity; this nodal singularities. Miyaoka gave a new effec- bound was obtained by Erwan Rousseau and tive bound in terms of the genus and Chern well presented by him. In higher dimensions, numbers for curves in Bogomolov surfaces. a Riemann – Roch calculation gives the maximal Other talks of interest were given by Starr, growth of the alternating sum of the cohomo- Ran and Zhang. Starr presented his generaliza- logical dimensions of the sheaf of jet differen- tion of the thesis of Serge Lang, who wrote the tials. The goal is to show that the 0th cohomol- first and last work on the topic (before Starr’s ogy (i.e., the space of global jet differentials) has work). Starr’s attempt is to connect rational the same maximal growth. Although this goal simple connectedness (simple connectedness via has not been reached yet, Demailly shows how chains of rational curves) to “weak approxima- to use his powerful holomorphic Morse inequal- tion” by polynomials (algebraic interpolation). ities in order to bound the higher cohomologies. Examples and counterexamples were discussed, Demailly and his student Diverio (who was an as well as the proof, and Starr concluded his invited participant) have used these inequalities talk by a slew of natural questions. Ran gave an to obtain exact formulas. It is hoped that their overview of a general theory of deformation in techniques will be successfully applied to give the algebraic category that he is putting together; the desired maximal growth. This would imply special cases of this theory, due to Ran, are now a weakened form of Lang’s conjecture for all va- powerful tools in the study of algebraic curves rieties of general type.

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Shiffman gave a presentation of recent re- Speakers: Francis Clarke (Lyon 1), François sults, mainly due to him, on the distribution Germinet (Cergy-Pontoise), Igor Wigman of the zeros for Gaussian random holomorphic (McGill) functions and on its connection to various as- Number of participants: 30 pects of physics and mathematics (the problem This activity is the third edition of the Analy- of sphere packing, for instance). His student, sis Day organized since 2004-2005 by the Math- Scott Zrebiec, also gave a talk on this subject. ematical Analysis Laboratory. This year, the Kobayashi gave a beautiful exposition of his re- Analysis Day Conference featured three speak- sults on the Gauss map of algebraic minimal sur- ers: Igor Wigman, Francis Clarke and François faces, obtained through value distribution the- Germinet. Wigman spoke on “nodal lines for ory. This represents one of the most relevant ap- random eigenfunctions of the Laplacian on the plications of the value distribution of holomor- torus,” Clarke on the “regularity of solutions in phic curves, since the Gauss map of such a sur- the calculus of varations,” and Germinet on “sin- face is a holomorphic curve in a projective space. gle energy multiscale analysis and Anderson lo- These results are especially interesting in view of calization.” the fact that Serge Lang has paid a lot of atten- CanaDAM 2007 tion to the ramification term in Nevanlinna theory. Winkelmann presented his thesis that entire The 1st Canadian Discrete and Brody curves (that is, holomorphic curves with Algorithmic Mathematics Conference bounded derivatives) have less to do with the May 28 – 31, 2007, Banff Conference Centre arithmetic geometry of the ambient variety than Sponsored by the Department of Computing general holomorphic curves. His discussion was Science at the University of Alberta, the Fields a tour de force of transcendental arithmetic ge- Institute, CRM, PIMS, iCORE, and MITACS ometry and was an attempt to bridge the gap Executive committee: Jason Brown (Dal- between arithmetic geometry and holomorphic housie), Derek Corneil (Toronto), Chair, Pavol geometry. Hell (Simon Fraser), Ortrud Oellermann (Win- Other talks of interest included that of Min nipeg), Daniel Panario (Carleton), Bruce Reed Ru, who spoke on his solution to a conjec- (McGill) ture of Shiffman and some generalizations by Local arrangements committee: Joe Culberson Dethloff and V.T. Tran; the talk of Dethloff on his (Alberta), Ryan Hayward (Alberta), Chair, Guo- characterization with Lu of hyperbolic surfaces hui Lin (Alberta), Daniel Panario (Carleton), Mo- with log irregularity 2; the talks of Ramachan- hammad R. Salavatipour (Alberta), Lorna Stew- dran and Napier on an analytic Castelnuovo – art (Alberta) DeFranchis lemma, a characterization of mani- Plenary speakers: Valerie King (Victoria), Janos folds mapping to curves and its implications for Pach (City College of New York), Bill Pulley- the conjecture of Shafarevich concerning the uni- blank (IBM Global Services), David Sankoff (Ot- versal cover of an algebraic manifold; and the tawa), Bruce Shepherd (McGill), Vera Sós (Rényi talk of S.K. Yeung on his remarkable results, Institute), Peter Winkler (Dartmouth College), which gave an almost complete classification of Xuding Zhu (National Sun Yat-sen University) fake projective planes via an arithmetic study of Number of participants: 230 the automorphism group of the hyperbolic ball. The field of discrete mathematics has grown In conclusion, the workshop gathered some tremendously in recent years, on the theoretical of the foremost experts on the various Lang con- as well as the algorithmic side, and it has broad jectures on structures (hyperbolic or not) and applications outside of mathematics as well as curves in algebraic varieties. The comments and inside (i.e., to other fields of mathematics). The discussions were unusually fruitful and helped flagship international discrete mathematics con- chart out future directions; they also fostered ference, the SIAM Conference on Discrete Math- collaborations between researchers. ematics, is held each even year by SIAM (the So- Analysis Day 2007 ciety for Industrial and Applied Mathematics). May 2, 2007, CRM Since Canadian researchers in discrete mathe- Organized by the Mathematical Analysis matics have a strong international reputation, a Laboratory, CRM group of researchers proposed a series of conferences, to be called CanaDAM conferences, in Organizer: Dmitry Jakobson (McGill) order to complement the SIAM Conference on

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Discrete Mathematics. The first CanaDAM con- crete dynamical systems over graphs; covering ference was held at the Banff Conference Center arrays and applications to software testing; ap- on May 28 – 31, 2007. plications of discrete mathematics to the analysis The program committee was chaired by Bo- of algorithms; games on graphs; combinatorial jan Mohar (Simon Fraser) and all of its mem- designs; graph minors; and topological graph bers are outstanding mathematicians. It also in- theory. cluded Bill Cook (Georgia Tech), Pavol Hell (Si- One of the primary goals of the conference mon Fraser), Joan Hutchinson (Macalester Col- was to encourage the participation of Canadian lege), Nati Linial (Hebrew University), Chris- graduate students and PDFs. The three Cana- tos Papadimitriou (UC Berkeley), Pavel Pevzner dian Mathematics Institutes (Fields, CRM and (UC San Diego), Doug Stinson (Waterloo), Éva PIMS) provided $25,000 to support the graduate Tardos (Cornell), Godfried Toussaint (McGill), students and postdocs attending the conference. Herb Wilf (Pennsylvania), and Nick Wormald The graduate students were encouraged to con- (Waterloo). The plenary talks were of the high- tribute talks in order to receive financial support; est calibre. Valerie King spoke on dynamic furthermore, there was a problem session (fol- graph algorithms, Janos Pach on the “state of lowed by a reception) devoted to the presenta- the intersection,” David Sankoff on polyploidy tion of research problems appropriate for grad- and rearrangement phylogeny, Bruce Shepherd uate students. The list of these problems will on single-source network flows with side con- appear in the Discrete Mathematics journal. The straints, Vera Sós on graph limits and the sim- organizers were especially pleased that about ilarity of large graphs, and Xuding Zhu on the 80 graduate students and postdocs attended the circular choosability of graphs. Bill Pulleyblank conference. Two other institutions, iCORE and gave an entertaining lecture on the history of su- MITACS, each provided $10,000 in support of percomputing and Peter Winkler an equally en- the plenary speakers and graduate students. tertaining one on percolation, entitled “You can The organizers of CanaDAM 2007 expected do physics. . . .” that 100 participants would attend the confer- To ensure critical mass in the areas cov- ence, but as the registrations started pouring ered by the plenary speakers, each plenary lec- in, they had to replace the 120-seat room ini- ture was the focus of at least one invited min- tially booked as the main hall by a 250-seat lec- isymposium. Altogether, CanaDAM 2007 feature hall! The number of parallel sessions was tured 19 minisymposia, covering a very broad increased to five, and in the end, 230 partici- range of topics in discrete mathematics: ran- pants attended CanaDAM 2007, representing 36 domized algorithms; combinatorial geometry Canadian universities, all 10 provinces and ev- and graph drawing; linear and polyhedral opti- ery continent except Antarctica. There were 51 mization; combinatorial problems in genomics; invited minisymposia talks, 62 contributed min- graphs, matroids, colourings and flows; ex- isymposia talks and 71 contributed talks. The tremal combinatorics; problems at the interface strong Canadian and international attendance of discrete mathematics and statistical physics; of CanaDAM 2007 suggests that the CanaDAM graph colouring; graph homomorphisms; spec- conference series is already established as one of tral graph theory; discrete-time, deterministic the main international conferences on discrete graph processes and games; applications of asso- and algorithmic mathematics. ciation schemes to combinatorial problems; dis- Colloquium Series

The CRM, together with the Institut des sciences mathématiques du Québec (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 In the Fall 2006 semester, the colloquium coordinators were Marco Bertola (Concordia) and Vo- jkan Jakši´c(McGill), and in the Winter 2007 semester, Jacques Hurtubise (McGill) and Alexander Shnirelman (Concordia).

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September 8, 2006 February 2, 2007 Ken McLaughlin (UNC Chapel Hill) Applications Yvan Saint-Aubin (Montréal) Une courte histoire of an asymptotic expansion for the one-point func- du modèle d’Ising tion of random matrix theory: loop equations, parti- February 9, 2007 tion function, large deviation principles Jack Edmonds (Waterloo) Second Hamiltonian September 22, 2006 paths and Nash equilibria Elliott Lieb (Princeton) Quantum mechanics, the stability of matter, and quantum electrodynamics February 23, 2007 September 29, 2006 Philippe Di Francesco (CEA Saclay) Integrable combinatorics Joseph Kohn (Princeton) Introduction to analysis on CR manifolds March 2, 2007 October 6, 2006 Catherine Sulem (Toronto) Water waves over a Michael Aizenman (Princeton) Randomness, and varying bottom its effects on spectra March 9, 2007 October 13, 2006 Tomasz Mrowka (MIT) What do we know about Jean-Pierre Bourguignon (IHÉS) Comprendre la four-dimensional manifolds? courbure March 16, 2007 October 20, 2006 Michael Brenner (Harvard) Mathematical issues Anatole Katok (Penn State) Rigidity of orbit struc- and opportunities in self assembly ture for actions of higher-rank abelian groups: kam- theory and algebraic k-theory March 23, 2007 November 3, 2006 Ed Stredulinsky (UW Rock County) Extreme David Ruelle (IHÉS & Rutgers) Why is nonequi- heating of the sun’s atmosphere and the topology of librium statistical mechanics so hard to understand? magnetic ﬁeld lines November 10, 2006 March 30, 2007 Leszek F. Demkowicz (UT Austin) hp-adaptive ﬁ- Tamar Ziegler (Michigan) Polynomial progressions nite elements: a quest for exponential convergence in primes November 17, 2006 April 13, 2007 Paul Tupper (McGill) The trouble with molecular Stephen Kudla (Toronto) Representation densities dynamics and arithmetic geometry November 24, 2006 April 20, 2007 Jonathan Taylor (Montréal) The integral geometry of random sets Steven Kleiman (MIT) Equisingularity, multiplic- ity, and dependence December 1, 2006 Richard Taylor (Harvard) The Sato-Tate conjecture April 27, 2007 January 19, 2007 Yuri Manin (MPIM) Counting rational points and Dmitry Jakobson (McGill) Eigenfunctions: limits, rational curves: from Waring’s problem to quantum nodal sets and critical points cohomology January 26, 2007 May 4, 2007 Tadashi Tokieda (Cambridge) Turn table, tippy Jean-Pierre Demailly (Grenoble 1) New analytic tops, tapped turtles techniques in algebraic geometry

CRM – ISM – GERAD Statistics Colloquium In 2006 – 2007, the coordinators of the CRM – ISM – GERAD Statistics Colloquium were Arusharka Sen (Concordia), Pierre Duchesne (Montréal), Christian Léger (Montréal), Brenda MacGibbon (UQÀM), and Russell Steele (McGill).

September 22, 2006 October 13, 2006 Siva Athreya (ISI Bangalore) Some remarks on age Andrew Heunis (Waterloo) A problem on multiple dependent branching and super processes time-scales in perturbed stochastic differential equations October 6, 2006 Erica Moodie (McGill) Introduction to optimal dynamic treatment regimes

36 GENERAL PROGRAM

October 20, 2006 February 9, 2007 Yali Amit (Chicago) Statistical models for object Anthony Brockwell (Carnegie Mellon) Brain- recognition machine interfacing: direct mental control of a robotic October 27, 2006 arm Jean-François Quessy (UQTR) Comportement February 16, 2007 asymptotique local de tests pour l’indépendance Raphael Gottardo (UBC) A flexible and powerful Bayesian hierarchical model for ChIP-chip data November 3, 2006 February 23, 2007 Paul Gustafson (UBC) On identifiability and prior Hugh A. Chipman (Acadia) Monitoring func- information tional data mixed effects and high-dimensional clus- November 10, 2006 tering Marc Hallin (Université Libre de Bruxelles) The March 9, 2007 general dynamic factor model: selecting the number Christian Francq (Lille 3) Estimating and testing of factors GARCH processes when the parameter is on a bound- November 17, 2006 ary Sarat Dass (Michigan State) Markov models for di- March 16, 2007 rectional field and singularity extraction in finger- David O. Siegmund (Stanford) Do complex sta- print images tistical methods help in mapping and quantitative November 24, 2006 traits? Charmaine Dean (Simon Fraser) Mixed nonhomo- March 23, 2007 geneous Poisson process spline models for the analy- Aurélie Labbe (Laval) Latent class models for pedi- sis of recurrent event panel data gree data March 30, 2007 December 1, 2006 Yong Zeng (Missouri-Kansas City) Filtering with Werner Stuetzle (Washington) Estimating the marked point process observations: applications to cluster tree of a density ultra-high frequency data January 12, 2007 April 13, 2007 Jeffrey S. Rosenthal (Toronto) Les marches aléa- Kjell Doksum (UW Madison & UC Berkeley) Di- toires et les algorithmes MCMC mension reduction and tuning parameter selection in February 2, 2007 nonparametric regression Jeffrey Morris (M.D. Anderson Cancer Research April 20, 2007 Center) Bayesian wavelet-based mixed models for Brad Carlin (Minnesota) Bayesian areal wombling functional data for geographical boundary analysis

37 Multidisciplinary and Industrial Program MULTIDISCIPLINARY AND INDUSTRIAL PROGRAM

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

Activities of the Multidisciplinary and Industrial Program

XXIIIrd International Biometrics Carolina Espinosa (Heriot-Watt), Tingfing Fan Conference (Waterloo), Runhuan Feng (Waterloo), Esteban July 16-21, 2006, McGill University Flores (Instituto Tecnológico Autónomo de Méx- Organized by the National Research Council of ico), Keith Freeland (Waterloo), Edward Furman Canada (Haifa), Jinadasa Gamage (Illinois State), Denise Gómez Hernandez (City University, London), Organizer: James A. Hanley (McGill) Vincent Goulet (Laval), Wenjing Guo (Water- Number of participants: 750 loo), John B. Henry (Oregon State), Mary Hardy The International Biometrics Conference is (Waterloo), Michel Jacques (Laval), Marwa Kha- held every two years and brings together re- lafallah (City University, London), Hyun Tae searchers who measure and analyze (through Kim (Waterloo), Ohoe Kim (Towson), Johnny statistical means) biological, biomedical, envi- Siu-Hang Li (Waterloo), Lily Yunsui Li (Wa- ronmental, agricultural and ecological informa- terloo), Zhongfei Li (Waterloo), Jed Linfield tion. The 2006 conference featured 14 invited (Kaiser Permanente), Yang Liu (Waterloo), Yi sessions, 70 contributed sessions and 3 poster Lu (Simon Fraser), Natalia Lysenko (Simon sessions. The CRM contributed to this confer- Fraser), Jean-Louis Massé (International Actuar- ence by defraying some of the costs of Canadian ial Association), Jorge Munoz Perez (ING Mex- mathematicians attending the conference. ico), Claude Pichet (UQÀM), Ke Qiu (Water- loo), Sudath Ranasinghe (Connecticut), Mark 41st Actuarial Research Conference Reesor (Western Ontario), Jiandong Ren (West- August 10 – 12, 2006, CRM ern Ontario), Jean-François Renaud (Montréal), Sponsors: Research and Education Commit- Gurbakhshash Singh (Simon Fraser), Jiafeng tee of the Actuarial Foundation, American Sun (UW Madison), Ranee Thiagarajah (Illinois Academy of Actuaries, American Society of Pen- State), Matthew Till (Waterloo), Cary Chi-Liang sion Professionals & Actuaries, Canadian In- Tsai (Simon Fraser), Barry Turner (McGill), Emil- stitute of Actuaries, Casualty Actuarial Society, iano Valdez (New South Wales), Frank Xuyan Colegio Nacional de Actuarios (Mexico), Confer- Wang (Waterloo), Chengguo Weng (Waterloo), ence of Consulting Actuaries, Society of Actuar- Jun Zhou (Concordia), Xiaowen Zhou (Con- ies, Département de mathématiques et de statis- cordia), Yanyun Judy Zhu (Illinois at Urbana- tique of the Université de Montréal and CRM Champaign) Organizing committee: Louis G. Doray (Mont- Number of participants: 126 réal), Chair, Charles Dugas (Montréal), Manuel The CRM hosted the 41st Actuarial Research Morales (Montréal) Conference from August 10 to 12, 2006. This Scientific committee: Louis G. Doray (Mont- annual conference is sponsored by the Society réal), José Garrido (Concordia) of Actuaries and the Casualty Actuarial Society. Speakers: Doug Andrews (Waterloo), Jean- This year, the ARC brought together, at the Uni- François Angers (Montréal), Alexandru Asimit versité de Montréal, nearly 130 participants from (Western Ontario), Enrico Biffis (City Univer- 10 countries on 4 continents. Most of them were sity, London), Jose Blanchet (Harvard), Mathieu professors of actuarial mathematics from vari- Boudreault (HÉC Montréal), Phelim P. Boyle ous universities, while the others came from in- (Wilfrid Laurier), James Bridgeman (Connecti- dustry or public institutions. Within 10 sessions cut), Kai Chen (Waterloo), Corina Constanti- spanning two and a half days, about 60 speak- nescu (Oregon State), Steven Craighead (Tow- ers presented the results of their research on risk ers Perrin), Victor De la Pena (Columbia), Alain models, health insurance, finance, life insurance, Desgagné (UQÀM), Maikol Alejandra Diasparra mortality, pensions, option pricing, and statisti- Ramos (Carlos III de Madrid), Matthieu Du- cal models in insurance. The ARC 2006 confer- four (UQÀM), Daniel Dufresne (Melbourne), ence was followed by a 2-hour workshop spon- Tom Edwalds (Munich American Reassurance sored by the Canadian Institute of Actuaries, in Company), Karl-Theodor Eisele (Strasbourg 1),

39 CENTRE DE RECHERCHES MATHÉMATIQUES which the participants discussed a proposal for travaillent sur des sujets connexes. Par consé- a new model of actuarial education in Canada. quent, même s’ils ne se connaissaient pas avant The Conference led to the creation of the l’atelier, les échanges scientifiques sont très fruc- Montréal Seminar in Actuarial and Financial tueux et aboutissent généralement à des collabo- Mathematics. In 2006 – 2007, this new seminar rations. featured 14 talks, held in one of the three Pour ce qui est du public, la participation Montréal universities offering an actuarial pro- des étudiants a été remarquable cette année. Les gram (Université de Montréal, Concordia and inscriptions des étudiants constituaient 60% des UQÀM). The organizers of this seminar in 2006 – inscriptions. L’une des raisons en est la séance 2007 were Louis Doray and José Garrido. d’affiches, qui a attiré plusieurs étudiants mont- réalais et ontariens. De plus, les différentes uni- 4th RECOMB Comparative Genomics versités montréalaises (Université de Montréal, Satellite Workshop UQÀM, McGill et Concordia) étaient bien repré- September 24 – 26, 2006, Montréal sentées. Il est incontestable que l’organisation de Sponsored by the CRM and the Centre cet atelier à Montréal a favorisé les collabora- Robert-Cedergren, Université de Montréal tions entre les professeurs et étudiants de ces dif- Organizers: Guillaume Bourque (National Uni- férentes universités. À titre d’exemple, Nadia El- versity of Singapore), Nadia El-Mabrouk (Mont- Mabrouk a été invitée par le professeur Donal réal) Hickey de l’Université Concordia à faire partie Invited speakers: Lars Feuk (The Hospital for du comité de doctorat d’un de ses étudiants. Ma- Sick Children, Toronto), Jennifer Gardy (UBC), thieu Blanchette, de l’Université McGill, a égale- Thomas J. Hudson (Montreal General Hospital), ment accepté de co-diriger l’un des étudiants de Tao Jiang (UC Riverside), Liqing Zhang (Virginia doctorat de Nadia El-Mabrouk. Tech) NBER/NSF Time Series Conference 2006 Number of participants: 83 September 29 – 30, 2006, Montréal Le programme de cet atelier a comporté cinq Organized by the CRM and CIREQ (Centre présentations plénières de conférenciers invités interuniversitaire de recherche en économie renommés, ainsi que des présentations d’articles quantitative) scientifiques. Les conférences plénières ont été Financed in part by the National Science prononcées par Lars Feuk, Jennifer Gardy, Tho- Foundation (NSF) and the National Bureau of mas Hudson, Tao Jiang et Liqing Zhang. D’autre Economic Research (NBER) part, les articles scientifiques ont été sélection- nés par un comité de programme comprenant Organizer: Roch Roy (Montréal) une vingtaine de chercheurs en biologie, ma- Speakers: Donald Andrews (Yale), Christian thématiques et informatique du monde entier. Bontemps (Toulouse 1), Marine Carrasco (Mont- Cette année, le comité de programme a reçu réal, CIREQ, CIRANO), Kung-Sik Chan (Iowa), 34 soumissions d’articles, parmi lesquels 17 ont Miguel A. Delgado (Carlos III de Madrid), été sélectionnés ; c’était la première fois qu’au- David Dickey (North Carolina State), Fran- tant d’articles étaient soumis, et les présenta- cis X. Diebold (Pennsylvania & NBER), Rainer tions choisies furent particulièrement bonnes. Dahlhaus (Heidelberg), Jean-Marie Dufour Comme pour les ateliers précédents, les (Montréal, CIREQ and CIRANO), Robert En- comptes rendus de cet atelier ont été publiés gle (New York), David Findley (U.S. Census dans la série Lecture Notes in Bioinformatics, sous- Bureau), Nikolay Gospodinov (Concordia & série de Lecture Notes in Computer Science (pu- CIREQ), Stéphane Grégoire (CREST-INSEE), bliée par Springer). De plus, pour la première Clifford Hurvich (New York), Ivana Komunjer fois, les versions longues des articles sélection- (UC San Diego), Alexei Onatski (Columbia), nés ont été publiées dans un numéro spécial de Benedikt Pötscher (Wien), Suhasini Subba Rao la revue Journal of Computational Biology. (Bristol), Neil Shephard (Oxford), Mark Watson L’atelier a eu lieu à l’Hôtel de l’Institut de (Princeton) tourisme et d’hôtellerie du Québec. La salle était Number of participants: 128 parfaitement adaptée à un public de 80 per- Cette série de congrès sur les séries chro- sonnes. De plus, les repas du midi étaient ser- nologiques a commencé dans les années 1970 vis sur place, ce qui permettait à tous les par- sous l’impulsion d’Arnold Zellner de l’Univer- ticipants de rester ensemble pour échanger des sité de Chicago, un des chercheurs les plus émi- idées. En effet, l’un des avantages majeurs d’un nents en économétrie. L’objectif premier de ces tel atelier spécialisé est le fait que les participants congrès était d’amener les statisticiens et les éco-

40 MULTIDISCIPLINARY AND INDUSTRIAL PROGRAM nomètres qui s’intéressent aux séries chronolo- le Nigéria et le Royaume-Uni. Étant donné la giques à partager leurs expériences de recherche forte participation de la communauté montréa- afin d’améliorer la compréhension et la prévi- laise et le haut niveau des conférenciers invités, sion des phénomènes économiques. Le premier les organisateurs sont convaincus que ce congrès congrès ayant connu un grand succès, la série aura des retombées à moyen et à long terme. s’est poursuivie avec un congrès chaque année. Jusqu’au début des années 1990, George Tiao, Launch of the Transdisciplinary Institute également de l’Université de Chicago, fut le res- for Quantum Information (INTRIQ) ponsable principal de la composante statistique November 9, 2006, CRM de ces congrès. Organizer: Gilles Brassard (Montréal) En 2006, le congrès eut lieu pour la première Speakers: Charles H. Bennett (IBM Research), fois à Montréal ; c’était aussi la première fois Chip Elliott (BBN Technologies), Michele Mosca qu’il avait lieu au Canada. Le fonctionnement de (Waterloo), Barry Sanders (Calgary), John Wa- ce congrès est assez différent de celui de la plu- trous (Waterloo) part des congrès de mathématiques ou de sta- Number of participants: 30 tistique. Les conférenciers ne sont pas contac- The launch of the Transdisciplinary Insti- tés directement, mais une invitation à soumettre tute for Quantum Information (INTRIQ) took une proposition est lancée aux chercheurs poten- place at the CRM on Thursday November 9, tiellement intéressés et le comité du programme 2006. Quantum information is an emerging field choisit les conférenciers invités en se basant sur of research, at the crossroads of mathemat- les propositions soumises. En 2006, le comité du ics, physics, computer science and chemistry. It programme était composé de Russell Davidson could bring a fundamental revolution, not only (McGill), Richard Davis (Colorado State), Jean- in our way of processing information, but also in Marie Dufour (Montréal), Nour Meddahi (Mont- our way of understanding the world. Ever since réal), Roch Roy (Montréal), James Stock (Har- the fundamental work of Claude Shannon and vard & NBER) et Ruey Tsay (Chicago). Alan Turing during the first half of the 20th cen- Cent quatre propositions de conférences (un tury, information theory has been anchored in nombre record !) ont été soumises. De ces 104 a classical conception of the physical world in- propositions, 20 ont été retenues pour des pré- herited from Newton and Einstein. This concep- sentations orales et 20 pour des affiches. Comme tion has prevented scientists from exploiting the le veut la tradition de ce congrès, le comité full potential of the physical world for the pro- du programme s’est assuré d’une part que des cessing of information, since actually the world chercheurs établis et des jeunes chercheurs figu- is governed by the laws of quantum mechanics. raient au programme des présentations orales, These laws are quite different from those of clas- et d’autre part que la répartition des présenta- sical physics. For instance, quantum mechanics tions entre statisticiens et économètres était équi- teaches us that elementary particles do not be- librée. Les conférences invitées ont été réparties have like macroscopic objects such as planets en six sessions, soit deux sessions le vendredi and hockey pucks. What influence could this après-midi et quatre sessions le samedi. Les af- reality have on our way of processing infor- fiches ont été réparties en deux sessions, une ses- mation? Several laboratories have been estab- sion le vendredi après-midi et l’autre le samedi. lished worldwide to investigate this avenue of Parmi les conférenciers, Chan, Dahlhaus, research; the members of INTRIQ are among the Delgado, Dickey, Findley et Pötscher sont des pioneers of this extraordinary scientific adven- statisticiens très connus dans le domaine des sé- ture. ries chronologiques. Subba Rao est une statisti- The launch started with welcoming remarks cienne junior. Andrews, Diebold, Dufour, Engle by Gilles Brassard, who holds a CRC in Quan- et Watson sont des sommités en économétrie. tum Information Processing in the Department Engle a été le co-récipiendaire du prix Nobel of computer science and operations research of d’économie en 2003 et Andrews a été de loin the Université de Montréal and is director of l’économètre le plus prolifique des années 1990 INTRIQ, and Francois Lalonde, director of the (le Peter Hall de l’économétrie !). CRM. These remarks were followed by five talks Au total, 128 personnes se sont inscrites à ce on different aspects of quantum information: congrès : environ 60 venaient du Canada (dont Barry Sanders lectured on Implementing quan- près de 50 de la région de Montréal), environ tum information, Michele Mosca on Self-testing 50 des États-Unis, et les autres de l’Allemagne, of quantum circuits, Chip Elliott on Architectures l’Autriche, l’Espagne, la France, la Grèce, Israël, for quantum networks, John Watrous on Zero-

41 CENTRE DE RECHERCHES MATHÉMATIQUES knowledge against quantum attacks, and Charles H. 2. Acquisition MEG (Anne-Sophie Dubarry) Bennett on Privacy, publicity, and permanence of in- 3. Basic data processings and time-frequency analy- formation. The day ended with the ﬁrst plenary sis (Stephan Grimault) meeting of INTRIQ members, and a reception 4. Introduction to EEG/MEG source localization not to be forgotten soon! (Christophe Grova) Pour la partie pratique, les organisateurs ont Principles of magnetoencephalography, formé 3 groupes d’environ 10 participants cha- methods and tools for data analysis cun. Chaque participant disposait d’un ordina- November 22 – 23, 2006, CRM teur pour effectuer différents traitements sur un Organized by the Centre de recherche en enregistrement MEG-EEG. Les outils de traite- neuropsychologie et cognition (CERNEC) of the ment de signal MEG-EEG avaient été installés Université de Montréal au préalable, et un jeu de données avait été co- Organizers: Anne-Sophie Dubarry (Montréal), pié sur le serveur. Chaque utilisateur accédait Stephan Grimault (Montréal) aux outils et aux données grâce à un compte per- Speakers: Anne-Sophie Dubarry (Montréal), sonnel dans un environnement Linux. Un do- Stephan Grimault (Montréal), Christophe Grova cument décrivant les différentes étapes à suivre (Montréal), Kevin Sauvé (Montréal) pour le traitement avait été fourni aux partici- Number of participants: 36 pants et une version électronique était dispo- Les neurosciences connaissent un dévelop- nible sur le serveur. Durant cette session, les or- pement considérable quant aux outils de me- ganisateurs ont d’abord présenté oralement la sure et de visualisation de l’activité cérébrale. La démarche à suivre, puis ont suivi pas à pas tous diversité de ces outils (IRM, EEG, MEG, NIRS) les participants durant la réalisation des diffé- tient aux nombreux principes (magnétisme nu- rentes étapes. cléaire, bioélectricité, magnétisme et diffusion Thoughts about integer programming optique) qui permettent ces mesures, directes DIRO – CRM – ncm2 public lecture by ou indirectes, de l’activité neuronale. Parmi ces Ralph Gomory techniques, la magnétoencéphalographie (MEG) January 26, 2007, CRM consiste à mesurer le champ magnétique externe Sponsored by the Département d’informatique créé par l’activité du cerveau. En se dotant du et de recherche opérationnelle (DIRO) of the plus récent équipement de ce genre, le CERNEC Université de Montréal, the CRM and the ncm (centre de recherche du Département de psy- 2 chologie de l’Université de Montréal) offre aux Le vendredi 26 janvier 2007, M. Ralph E. Go- chercheurs en neurosciences un appareil unique mory a prononcé une grande conférence inti- qui complète la panoplie des outils déjà dispo- tulée Thoughts About Integer Programming, dans nibles dans les différents centres de recherche ou laquelle il a parlé des méthodes de plans de centres hospitaliers de Montréal. coupes et de leurs relations avec les « corner po- Le CRM s’est associé au CERNEC pour of- lyhedra » et les fonctions sous-additives. En se frir un atelier portant sur les aspects théoriques servant de ce cadre théorique, il a montré com- et pratiques de la MEG. Destiné principalement ment construire une nouvelle famille de coupes aux usagers des neurosciences, cet atelier a pré- utilisant l’information de plusieurs équations à senté les principes de base de la magnétoencé- la fois, contrairement aux coupes de Gomory phalographie ainsi que les outils logiciels pour classiques, qui sont basées sur une seule équa- le traitement et l’analyse des signaux ainsi me- tion. surés. La seconde partie de l’atelier, plus orien- Cette grande conférence soulignait le se- tée vers les mathématiques appliquées, concer- mestre thématique en optimisation combina- nait l’analyse de la localisation des sources d’ac- toire, organisé par le Centre de recherches ma- tivité cérébrale grâce à une approche distribuée. thématiques (CRM) ; elle soulignait aussi le 40e L’atelier était donc constitué de deux par- anniversaire du Département d’informatique et ties : une partie théorique qui dura une demi- de recherche opérationnelle (DIRO). S’associait journée et une partie pratique qui dura trois également à l’évènement le Réseau de calcul et demi-journées. La partie théorique consista de de modélisation mathématique (rcm2), auquel quatre présentations d’une heure portant sur les sont afﬁliés deux centres de réputation inter- principes de la magnétoencéphalographie et les nationale en recherche opérationnelle, le Centre méthodes d’analyse des données. Voici les titres interuniversitaire de recherche sur les réseaux et les auteurs de ces présentations. d’entreprise, la logistique et le transport (CIR- 1. MEG, What is it, what can it see (Kevin Sauvé) RELT) et le Groupe d’études et de recherche

42 MULTIDISCIPLINARY AND INDUSTRIAL PROGRAM en analyse des décisions (GERAD). Immédiate- une personne qui s’est distinguée à l’échelle in- ment avant la conférence, le prix Harold Larnder ternationale par ses réalisations dans le domaine 2006 de la Société canadienne de recherche opé- de la recherche opérationnelle. La conférence a rationnelle (SCRO) a été attribué à M. Gomory. été un franc succès et a attiré plus de 100 partici- Ce prix est décerné annuellement par la SCRO à pants.

43 CRM Prizes CRMPRIZES

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 the CRM’s Scientiﬁc Advisory Committee. 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 2007 and CAP – CRM Prize 2007 awarded to Joel S. Feldman

The CRM – Fields – PIMS Prize A detailed description of the contributions for 2007 was awarded to Pro- of Professor Feldman to mathematics may be fessor Joel S. Feldman (Uni- found in Le Bulletin du CRM (Spring 2007), at versity of British Columbia) the address crm.math.ca/rapports/bulletin/ in recognition of his excep- bulletin13-1.pdf. Finally, Joel S. Feldman was tional achievement and work also awarded the CAP – CRM Prize 2007 (see be- in mathematical physics. Pro- low for a description of this prize). fessor Feldman has risen to The CRM – Fields – PIMS Prize a position of international prominence in the world of mathematical physics, with a 30- This prize was established in 1994 as the CRM – year record of sustained output of the high- Fields prize to recognize exceptional research est calibre. He has made important contribu- in the mathematical sciences. In 2005, PIMS be- tions to quantum field theory, many-body the- came an equal partner in the awarding of the ory, Schrödinger operator theory, and the the- prize and its name was changed to the CRM – ory of infinite genus Riemann surfaces. Many of Fields – PIMS prize. A committee appointed by Professor Feldman’s recent results on quantum the three institutes chooses the recipient. The many-body systems at positive densities and on previous recipients of the prize are H.S.M. (Don- Fermi liquids and superconductivity have been ald) Coxeter (1995), George A. Elliott (1996), ranked as some of the best research in mathe- James Arthur (1997), Robert V. Moody (1998), matical physics in the last decade. Stephen A. Cook (1999), Israel Michael Sigal (2000), William T. Tutte (2001), John B. Friedlan- Professor Feldman received his B.Sc. from der (2002), John McKay (2003), Edwin Perkins the University of Toronto in 1970, and his A.M. (2003), Donald A. Dawson (2004), David Boyd and Ph.D. from Harvard University in 1971 and (2005), and Nicole Tomczak-Jaegermann (2006). 1974, respectively. He worked as a Research Fel- low at Harvard University from 1974 to 1975, The CAP – CRM Prize and was a C.L.E. Moore Instructor at the Mas- The Centre de recherches mathématiques (CRM) sachusetts Institute of Technology (MIT) from and the Canadian Association of Physicists 1975 to 1977. Since 1977, he has taught at the (CAP) created in 1995, on the occasion of the University of British Columbia, where he is cur- 50th anniversary of the CAP, a joint prize for rec- rently a full professor. Professor Feldman was an ognizing exceptional achievements in theoreti- invited speaker at the International Congress of cal and mathematical physics. The prize consists Mathematicians in Kyoto in 1990. He was a ple- of a $2,000 award and a medal. nary speaker at the XIIth International Congress The previous recipients of the prize are on Mathematical Physics in Brisbane in 1997, Werner Israel (1995), William G. Unruh (1996), and an invited speaker at the XIVth Interna- Ian Affleck (1997), J. Richard Bond (1998), tional Congress on Mathematical Physics in Lis- David J. Rowe (1999), Gordon W. Semenoff bon in 2003. He is a fellow of the Royal Society of (2000), André-Marie Tremblay (2001), Pavel Canada, and has been awarded the 1996 John L. Winternitz (2002), Matthew Choptuik (2003), Jiˇrí Synge award and the CRM Aisenstadt Chair Patera (2004), Robert C. Myers (2005), and John lectureship in 1999/2000, as well as the 2004 Harnad (2006). Jeffery-Williams Prize by the Canadian Mathe- matical Society for outstanding contributions to mathematical research.

45 CENTRE DE RECHERCHES MATHÉMATIQUES

André-Aisenstadt Prize 2007 awarded jointly to Alexander E. Holroyd and Gregory G. Smith

Alexander E. Holroyd was Dr. Smith has proposed and explored the no- educated at the University tion of Castelnuovo – Mumford regularity in the of Cambridge, where he ob- multigraded context. Their subtle approach gen- tained his Ph.D. in mathe- eralizes and extends tentative approaches of oth- matics in 2000 under the su- ers in specialized cases, and sets the stage for fu- pervision of Geoffrey Grim- ture advances. mett. Subsequently he be- Dr. Smith’s clarity as a teacher and enthusi- came a Hedrick Assistant asm as an expositor have made him a regularly Professor at UCLA, then a Postdoctoral Fellow invited speaker at conferences and workshops at the University of California at Berkeley. Since around the world. 2002 he has been at the University of British A detailed description of the contribu- Columbia, where he is now Associate Profes- tions of Gregory G. Smith may be found sor. In 2004, he was awarded the Rollo Davidson in Le Bulletin du CRM (Fall 2007), at the Prize, an annual international prize for young address crm.math.ca/rapports/bulletin/ probabilists. bulletin13-2.pdf. Dr. Holroyd is an outstanding young prob- The André-Aisenstadt Prize abilist, with broad research interests. His work is focused on discrete spatial models, includ- Created in 1991, the André-Aisenstadt Mathe- ing cellular automata, percolation, matching, matics Prize is intended to recognize and re- traffic models, and sorting networks. Despite ward research achievements in pure and ap- his youth he is already a major figure in this plied mathematics by talented young Canadian multi-disciplinary area. One of his most striking mathematicians. This prize consists of a $3,000 achievements is the determination of the exact award and a medal. The recipient is chosen by threshold for bootstrap percolation, an impor- the CRM’s advisory committee. At the time of tant example of a cellular automata. consideration, candidates must be Canadian cit- A detailed description of the contribu- izens or permanent residents of Canada, and no tions of Alexander E. Holroyd may be found more than seven years from their Ph.D. in Le Bulletin du CRM (Spring 2007), at The previous recipients of the André- the address crm.math.ca/rapports/bulletin/ Aisenstadt Prize are Niky Kamran (1992), Ian bulletin13-1.pdf. Putnam (1993), Michael Ward (1995), Nigel Gregory G. Smith Higson (1995), Adrian S. Lewis (1996), Lisa was a mathemat- Jeffrey (1997), Henri Darmon (1997), Boris ical physics un- Khesin (1998), John Toth (1999), Changfeng Gui dergraduate at (2000), Eckhard Meinrenken (2001), Jinyi Chen Queen’s Univer- (2002), Alexander Brudnyi (2003), Vinayak Vat- sity, obtaining an sal (2004), Ravi Vakil (2005), Iosif Polterovich M.A. at Brandeis (2006) and Tai-Peng Tsai (2006). University, and re- ceiving his Ph.D. in 2004 at Berkeley under the supervision of David Eisenbud. For the next three years he was a postdoctoral fellow at Barnard College of Columbia University, before returning to Canada to accept a tenure-track position at Queen’s. Dr. Smith has already made significant contributions in Algebraic Geometry and Commu- tative Algebra. His joint work with L. Chen and L.A. Borisov, in which toric Deligne – Mumford stacks are introduced and their orbifold cohomology calculated, has already been used to resolve a long-standing conjecture of Hibi on re- flexive polytopes. Along with D. Maclaghan,

46 CRMPRIZES

CRM – SSC Prize 2007 awarded to Dr. Richard Cook

Richard Cook, Professor in the Richard Cook obtained his B.Sc. in Statistics Department of Statistics and Ac- from McMaster University and his M.Math., in tuarial Science of the Univer- 1989, and Ph.D., in 1993, from the University of sity of Waterloo, is the 2007 Waterloo. He was appointed a Research Assis- winner of the CRM-SSC prize. tant Professor in Statistics in 1993 at the Univer- Dr. Cook’s work in longitudi- sity of Waterloo. He currently holds adjunct ap- nal and lifetime data analysis pointments in the Department of Health Studies has had immense impact on bio- and Gerontology of the University of Waterloo statistics, medicine and public health. Within 15 and the Faculty of Health Sciences of McMaster years of his Ph.D., Richard Cook has made out- University. In 1998, he became an Associate Pro- standing contributions to an impressive number fessor and then, in 2003, a Full Professor. He was of statistical research fields covering the design awarded a Tier I Canada Research Chair in Sta- of clinical trials, hierarchical models, robust in- tistical Methods for Health Research at the Uni- ference, and the analysis of survival, multi-state, versity of Waterloo in 2005. Professor Cook has and recurrent event data. He has made inge- served as Associate editor of the Canadian Jour- nious contributions to the analysis of multi-state nal of Statistics and Lifetime Data Analysis and as models and the joint analysis of multiple events. President of the Biostatistics Section of the SSC. His joint work with Jerry Lawless has helped set Professor Cook has also made important contri- current frameworks used in the analysis of re- butions to training by supervising four postdoc- current events, and their jointly authored book toral fellows, six doctoral students and thirteen The Statistical Analysis of Recurrent Events has Master’s students. been published in 2007. The CRM – SSC Prize Richard Cook’s work is solidly grounded in important problems in public health and clini- The SSC, founded in 1977, is dedicated to the cal trials and he has substantially raised the level promotion of excellence in statistical research of statistical expertise in the Canadian and in- and practice. The prestigious CRM – SSC Prize, ternational medical community through his im- jointly sponsored by the SSC and the Centre de portant methodological advances in these fields. recherches mathématiques (CRM), is given each He has made exceptional contributions to the year to a Canadian statistician in recognition of medical community and is a leading expert in outstanding contributions to the discipline dur- the application of statistics to rheumatology, ing the recipient’s first 15 years after earning a cardiovascular disease, oncology, clinical trials doctorate. and transfusion medicine. He has also provided Richard Cook is the ninth recipient of the great leadership through service on several med- CRM – SSC Prize. The previous winners of the ical advisory panels and medical research grant award are Christian Genest (1999), Robert J. Tib- selection committees. shirani (2000), Colleen D. Cutler (2001), Larry A. Professor Cook was a Scholar of the (former) Wasserman (2002), Charmaine B. Dean (2003), Medical Research Council of Canada from 1996 Randy Sitter (2004), Jiahua Chen (2005) and Jef- to 2000. He also held an Investigator Award of frey Rosenthal (2006). the Canadian Institutes of Health Research from 2000 to 2005 and a Premier’s Research Excellence Award from the Ontario Ministry of Energy, Sci- ence and Technology and GlaxoSmithKline from 1999 to 2004. That the medical community has awarded him several major awards to develop new theory in his areas of expertise is evidence of the great respect in which this community holds him. Richard Cook is gifted with great in- sight and a passion for closely knit collaborative work, one that truly embodies the sorts of interdisciplinary connections forming the corner- stone of rapid advances in medical and biosta- tistical research.

47 The CRM Outreach Program THE CRMOUTREACH PRCOGRAM

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 feature outstanding lecturers able to convey the beauty and power of mathematical research to a wide audience. Les Grandes Conférences du CRM are now well established and there were three lectures geared towards a general audience in 2006 – 2007. The first lecture was given by Bart de Smit and entitled The mathematics of Escher’s Print Gallery; it was held in the Stewart Biology Building of McGill University on November 15, 2006. During the winter term of 2007, the two lectures were held at the Université du Québec à Mont- réal. The first of these, entitled Les limites logiques et mathématiques, was given by Jean-Paul Delahaye on March 19, 2007. The program of the Grandes Conférences for 2006 – 2007 concluded on May 3 with a lecture by Francis Clarke entitled Euler, la vie, l’univers, l’optimisation, to celebrate the 300th anniversary of the birth of the great mathematician. Each of the lectures attracted between 150 and 200 people of all ages, and was followed by a “vin d’honneur” that enabled the participants to ask questions to the lecturers, reconnect with friends and colleagues, and meet people interested in mathematics and science in general. In 2006 – 2007, the Grandes Conférences program was under the stewardship of Christiane Rousseau and Yvan Saint-Aubin, professors at the Département de mathématiques et de statistique of the Uni- versité de Montréal. The following description of the mathematical contents of the lectures is due to Christiane Rousseau. The Mathematics of Escher’s Print Gallery Bart de Smit, Universiteit Leiden

Many among us are fascinated by Escher’s work, how to complete the etching. The necessary and this fascination owes a lot to the mathemat- transformations are analytic functions of a com- ical aspects of his work, in spite of the fact that plex variable and are therefore angle-preserving. Escher did not have any mathematical training. If we apply the transformation z 7→ Z = ln z One of Escher’s engravings, Print Gallery, has in- to the initial picture, which is invariant under trigued mathematicians because the artist was z 7→ Cz, then the transformed picture is invari- unable to complete it. The children always have ant under the translation Z 7→ Z + ln C. Since fun looking at the cover of The Laughing Cow Z = ln z is already a multi-form transformation cheese: on the cow’s earring, one sees a cow with of period 2πi the transformed picture yields a an earring, on which is pictured another cow, doubly periodic tiling of the plane. and so on. Escher’s starting point is an etching of One can wrap the plane into a cylinder this type: a man looks at a painting in a gallery, whose circumference is the segment [0, 2πi]; which represents a man looking at a painting, the picture is then repeated infinitely often on etc. As in the case of The Laughing Cow, if one small slices of the cylinder. But one can also zooms correctly within this etching, one recog- wrap the plane with a slant so as to obtain pic- nizes the same picture. In mathematical terms, tures repeated infinitely often on spirals. This if a point (x, y) within the picture is represented “wrapping” amounts to considering the trans- by the complex number z = x + iy, the picture formation Z 7→ αZ, where the complex num- is said to be invariant under the transformation ber α is chosen so that the picture be periodic z 7→ Cz, where C is a constant. of period 2πi. One then uses the reciprocal of In the case of Escher’s original etching, the the complex logarithm function, and the prob- constant C is a positive real number smaller lem is settled: the hole in Escher’s engraving than 1. In the case of The Laughing Cow, the con- is no more! Although the ideas involved can stant C has a nonzero argument defining the ro- be explained through mathematical formulas, tation needed to recognize the basic picture af- they can be conveyed in a different manner to ter the zoom. So far there is no surprise. Escher, a general audience. In his lecture, Bart de Smit however, applies a transformation to his origi- explained those ideas without using formulas, nal etching, so that in order to recover the basic but the mathematicians present recognized the picture, we tumble down an infinite spiral! Es- mathematical concepts underlying this remark- cher drew the beginning of the spiral but did not able lecture, which also included graphical ani- complete it. Two specialists of the theory of num- mations of a very high calibre. bers, Hendrik Lenstra and Bart de Smit, showed

49 CENTRE DE RECHERCHES MATHÉMATIQUES

Les limites logiques et mathématiques Jean-Paul Delahaye, Université Lille 1

Jean-Paul Delahaye is a French mathematician plete, which means that some true statements who publishes a monthly column in Pour la about integers cannot be proved within the con- Science, the French equivalent of the Scientific fines of a formal system! One could say that American, and has published several books on Gödel himself was astounded. . . The 20th cen- mathematical topics, including the prime num- tury also witnessed the birth of theoretical com- bers, the number π and the mathematical foun- puter science, to which the mathematician Alan dations of computer science. Jean-Paul Delahaye Turing made a fundamental contribution. In- is a master of popularization and a large audi- deed, Turing gave a formal definition of the con- ence went to UQÀM to hear him talk on the cept of “computable function”: a function is said limits of logic and mathematics. Although Jean- to be computable if and only if it can be computed Paul Delahaye is a professor of computer science by a relatively simple automaton known as a at the Laboratoire d’Informatique Fondamentale Turing machine. For mathematicians and com- de Lille, he considers himself to be a mathemati- puter scientists, Turing’s definition still captures cian. In his lecture, he surveyed the important the notion of computability. questions in mathematical logic, which held the Jean-Paul Delahaye also surveyed some im- mathematicians and computer scientists of the portant problems of computer science whose so- 20th century in thrall. After the paradoxes of lutions are a source of awe. One of these is Tur- logic were discovered at the beginning of the ing’s halting problem: given a computer program, 20th century, the mathematicians felt that it was is it possible to predict whether it will halt even- necessary to build solid foundations for math- tually or be caught in an infinite loop? Naturally, ematics and mathematical logic became a full- to answer this question, it would be highly desir- fledged branch of mathematics. able to use a program able to determine whether Researchers don’t always find what they are any given program halts or not. Unfortunately, looking for, however. Mathematicians were as- Turing proved that such a program could not ex- tounded when Kurt Gödel proved the famous ist; in the parlance of theoretical computer sci- theorem stating that Peano arithmetic is incom- ence, the halting problem is undecidable. Euler, la vie, l’univers, l’optimisation Francis Clarke, Université Lyon 1

Francis Clarke, a Montrealer by birth, was di- scribe natural phenomena in terms of optimiza- rector of the CRM from 1984 until 1993. He tion. transformed the CRM into a national insti- Francis Clarke rose to the challenge and gave tute financed by NSERC and FCAR (as the a vivid portrait of Euler and his life. He also Québec granting agency was then called). He put Euler’s contributions in a historical per- also founded the Institut des Sciences Mathéma- spective by comparing them to the contribu- tiques, a consortium of Québec universities that tions of his contemporaries (Maupertuis, La- coordinates graduate studies in mathematics in grange, etc.). The lecturer explained the scien- the province. The organizers of the Grandes Con- tific and mathematical notions in simple lan- férences had asked Francis Clarke to give a lec- guage and his examples illustrated the genesis ture on Euler, to celebrate the 300th anniversary of the great ideas that have revolutionized sci- of the birth of the famous mathematician. Born ence. Francis Clarke discussed the famous ex- on April 15, 1707, Leonhard Euler is one of the ample of the Lagrange column: among all the most prolific mathematicians of all times and the columns of revolution of given height and vol- mathematical star of the 18th century. His contri- ume, which one will offer the greatest resistance butions cover a very broad spectrum of mathe- when crushed by a weight? For a long time, peo- matics, from number theory to differential equa- ple believed (falsely) that it must be the cylin- tions, geometry, optics and astronomy. Euler was drical column. Indeed, people believed that the the first scientist to formulate one of the most best column was smooth, but actually it con- profound scientific notions, the principle of least tains angles. Nowadays mathematicians know (or stationary) action, which enables us to de- that many optimization and control problems

50 THE CRMOUTREACH PRCOGRAM have nonsmooth or even discontinuous solutions. Francis Clarke illustrated this fact in a modern setting by describing a ﬁsheries model for which the best solution is a discontinous control.

51 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 col- laborates 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 École Normale Supérieure, the Isaac Newton Institute for the Mathematical Sciences Institute, the Institut des Hautes Études Scien- (PIMS) tiﬁques (IHÉS), and BIRS.

Since the early 1990s two other research insti- Associations and Professional Societies tutes have joined the CRM on the Canadian scene: Toronto’s Fields Institute (FI) and the The CRM maintains close ties with the different Pacific Institute for the Mathematical Sciences professional societies in the mathematical sci- (PIMS). As well as coordinating their scien- ences: CMS, CAIMS, SSC and CAP. The presi- tific activities, the three institutes have worked dent of the CMS is an ex-officio member of the closely on a variety of initiatives, the most im- CRM Scientific Advisory Committee. The CRM portant of which is the Mathematics of Infor- also supports financially certain initiatives of the mation Technology and Complex Systems net- CMS, such as the mathematical camps. Together work (MITACS). The three institutes were also with the other institutes, the CRM organizes or involved in other initiatives, such as the CRM – sponsors special sessions at the CMS, CAIMS Fields Prize awarded in recognition of outstand- and SSC meetings. The CRM awards a prize each ing accomplishments in the mathematical sci- year jointly with the SSC; similarly, it awards a ences in Canada. It was created in 1994 and in prize each year with the CAP in mathematical 2006 became the CRM – Fields – PIMS Prize. The and theoretical physics. administrative responsibility for this prize ro- tates between the three institutes. The Mathematics of Information Technology and Complex Systems International and National Collaborations Network (MITACS) In 2006 – 2007, the CRM collaborated with or re- MITACS was conceived by the three Cana- ceived financial assistance from the following indian mathematical sciences institutes. They en- stitutions: INSERM, Paris; INRIA; the ALGANT visioned a pan-Canadian network of projects program; the Banff International Research Sta- each using sophisticated mathematical tools for tion (BIRS); the Universidad de La Habana, modelling industrial problems in key sectors of Cuba; and the Groupe d’études et de recherche the Canadian economy. MITACS was officially en analyse des décisions (GERAD). launched on February 19, 1999. By March 1999, In its publishing activities, the CRM is con- all 21 initial research projects were under way. tinuing its partnership with the American Math- MITACS leads Canada’s effort in the genera- ematical Society (AMS), in particular through its tion, application and commercialization of new two series of joint publications, the CRM Mono- mathematical tools and methodologies within a graph Series and the CRM Proceedings and Lec- world-class research program. The network ini- ture Notes Series. Two CRM series, in statistics tiates and fosters linkages with industrial, gov- and in mathematical physics, are published by ernmental, and not-for-profit organizations that Springer. The CRM has exchange agreements require mathematical technologies to deal with with the Fields Institute, PIMS, MSRI, the Insti- problems of strategic importance to Canada. MI- tute for Mathematics and its Applications (IMA), TACS is driving the recruiting, training, and

53 CENTRE DE RECHERCHES MATHÉMATIQUES placement of a new generation of personnel ical, epidemiological and medical studies. More with highly mathematical skills that is vital to specific objectives of the program include the de- Canada’s future social and economic well-being. velopment of collaborations between university MITACS creates links between academia, in- and extra-university researchers, and the provi- dustry and the public sector to develop cutting sion of training for graduate students in impor- edge mathematical tools vital to a knowledge- tant scientific areas through these collaborations. based economy. The only Network of Centres NPCDS Projects of Excellence (NCE) for the mathematical sciences, MITACS currently has 305 scientists, 611 STATISTICAL METHODSFOR COMPLEX SURVEY students and 169 partner organizations working DATA on 32 ongoing projects, involving 48 Canadian Project Leader: Changbao Wu (Waterloo) universities. To improve Canada’s international CANADIAN CONSORTIUMON STATISTICAL GE- competitiveness, MITACS research focuses on NOMICS five key sectors of the economy: Project Leader: Rafal Kustra (Toronto) • biomedical and health; DATA MININGWITH COMPLEX DATA STRUC- • environment and natural resources; TURES • information processing; Project Leaders: Hugh Chipman (Acadia), • risk and finance; Antonio Ciampi (McGill), Theodora Kourti • communication, networks and security. (McMaster), Helmut Kröger (Laval) MITACS Inc. is a federally incorporated not-for- profit society formed to administer the MITACS DESIGNAND ANALYSIS OF COMPUTER EXPERI- Network of Centres of Excellence. MENTSFOR COMPLEX SYSTEMS MITACS also gives financial support to some Project Leader: Derek Bingham (Simon Fraser) events organized by the CRM and other institu- FORESTS,FIRESAND STOCHASTIC MODELING tions. For instance, in 2006 – 2007, it gave sup- Project Leaders: John Braun (Western Ontario), port to three workshops or conferences partially Charmaine Dean (Simon Fraser), Dave Martell sponsored by the CRM: the 6th Annual MOPTA (Toronto) Conference and CanaDAM 2007 (whose reports SPATIAL/TEMPORAL MODELINGOF MARINE are included in the section on the CRM general ECOLOGICAL SYSTEMS program), and the Workshop on Data Mining Project Leaders: Michael Dowd (Dalhousie), and Mathematical Programming (whose report Joanna Flemming (Dalhousie), Chris Field (Dal- is included in the section on the CRM thematic housie), Rick Routledge (Simon Fraser) program). NPCDS Workshops National Program on Complex Data SUMMER WORKSHOPON MODERN APPLIED Structures (NPCDS) METHODSIN BIOSTATISTICS This initiative was developed in partnership August 14 – 17, 2006, University of Toronto with the three mathematical sciences insti- Director: Paul Corey (Toronto) tutes and the reallocations committee during Atlantic Association for Research in the the recently completed reallocations exercise at Mathematical Sciences (AARMS) NSERC. The program was funded by NSERC for four years for a total of $687,000. An additional AARMS was founded in March 1997 at a time $200,000 has been committed to the program by when the National Network for Research in the the institutes. The NPCDS is a national network Mathematical Sciences was being discussed and in the statistical sciences, conceived in partner- planned. AARMS exists to encourage and ad- ship with the mathematics institutes. The broad vance research in all mathematical sciences, in- goal of the proposal is to foster nationally co- cluding statistics and computer science, in the ordinated projects with substantial interactions Atlantic region. In addition, AARMS acts as a with the large community of scientists involved regional voice in discussions of the mathemat- in the analysis of complex data sets, and to es- ical sciences on a national level. Since its incep- tablish a framework for the national network- tion, AARMS has played an important role in the ing of research activities in the statistical com- research activities in the Atlantic region, spon- munity. The original proposal targeted the de- soring or co-sponsoring numerous meetings and velopment and application of statistical methods workshops. In the summer of 2002, AARMS for the analysis of data obtained from complex initiated an annual Summer School for grad- survey sample designs and longitudinal biolog- uate students and promising undergraduates.

54 CRMPARTNERSHIPS

AARMS is grateful to Canada’s three mathemat- April 18 – 19, 2007, Mount Allison University ical institutes, the Centre de recherches mathé- Organizer: Catharine Baker (Mount Allison) matiques, the Fields Institute, and the Paciﬁc In- WORKSHOPON MATHEMATICAL KNOWLEDGE stitute for the Mathematical Sciences, as well as MANAGEMENT to the member universities, for providing fund- April 26, – 28, 2007, Dalhousie University ing for its activities. Its member universities are Organizer: Jonathan Borwein (Dalhousie) Acadia University, Cape Breton University, Dal- housie University, Memorial University, Mount BLACK HOLES VI Allison University, St. Francis Xavier University, May 12 – 16, 2007, White Point Beach Resort Saint Mary’s University, the Université de Monc- Organizer: Jack Gegenberg (New Brunswick) ton, the University of New Brunswick and the 12TH CANADIAN CONFERENCEON GENERAL University of Prince Edward Island. RELATIVITY AND RELATIVISTIC ASTROPHYSICS May 17 – 20, 2007, University of New Brunswick AARMS Scientiﬁc Activities Organizer: Jack Gegenberg (New Brunswick)

INTERNATIONAL CATEGORY THEORY CONFER- Academic Partners ENCE June 25 – July 1, 2006, White Point Beach Resort, The activities of the CRM rest on a solid basis Nova Scotia of cooperation with regional universities, in par- Organizers: Dorette Pronk (Dalhousie), Robert ticular the Montréal universities, and most par- Dawson (Saint Mary’s), Peter Selinger (Dal- ticularly the Université de Montréal, whose sup- housie) port for the CRM has been unfailing. The Uni- BLUENOSE NUMERICAL ANALYSIS DAY 2006 versité de Montréal releases five of its faculty June 23, 2006, St. Francis Xavier University members to work at the CRM each year, and Organizers: Jeffrey McNally (St. Francis Xavier), the support of these faculty members is an es- Patrick Keast (Dalhousie), Richard Karsten (Aca- sential asset for the CRM’s scientific activities. dia), Ronald Haynes (Acadia), Paul Muir (Saint There is in addition a regular program of teach- Mary’s) ing releases with the other Montréal universi- GAMES-AT-DAL 4 ties, bringing the equivalent of another two po- August 21 – 25, 2006, Dalhousie University sitions to the CRM each year. On an ad-hoc ba- Organizer: Richard Nowakowski (Dalhousie) sis linked to the thematic program, the CRM has also been arranging the release of research per- ATLANTIC OPTIMIZATION DAYS sonnel from nearby universities such as Laval, October 5 – 6, 2006, University of New Sherbrooke, Queen’s and Ottawa. The partner- Brunswick ships of the CRM with the other research insti- Organizers: David Bremner (New Brunswick), tutes in the Montréal area have been very prof- Hugh Thomas (New Brunswick) itable. APICS 2006: SPECIAL SESSIONON MATHEMAT- With the financial support of the Université ICAL MODELLINGAND SIMULATION de Montréal, McGill University, the Université October 14, 2006, Cape Breton University du Québec à Montréal, Concordia University, Organizers: George Chen (Cape Breton), Ronald and Université Laval, as well as grants from Haynes (Acadia) NSERC and the Fonds québécois de recherche APICS 2006: SPECIAL SESSIONON MULTIVARI- sur la nature et les technologies (FQRNT), the ATE STATISTICAL ANALYSIS CRM finances the activities of its nine laborato- October 15, 2006, Cape Breton University ries, which collectively represent the most active Organizer: Edmund Rudiuk (Cape Breton) branches of the mathematical sciences. These ATLANTIC COMMUNITY MATH NETWORK laboratories are the perfect illustration of scien- CONFERENCE tific vitality and serve to feed the national and November 25, 2006, Acadia University international scientific programs of the CRM. Organizer: Jeff Hooper (Acadia) Please refer to the section “Research Laborato- ries” for reports describing the activities of each 2ND AARMS/DALHOUSIE ATLANTIC ANALY- of these laboratories. SIS DAYS March 30 – 31, 2007, Dalhousie University Organizer: Karl Dilcher (Dalhousie) Association with the University of Ottawa EAST COAST COMBINATORIAL CONFERENCE In 2003, the Department of Mathematics and 2007 Statistics of the University of Ottawa became a

55 CENTRE DE RECHERCHES MATHÉMATIQUES member of the Centre de recherches mathéma- Centre for Interuniversity Research and Analy- tiques (CRM). In partnership with the Univer- sis of Organizations (CIRANO), the Centre for sity of Ottawa, the CRM co-finances the CRM – Research on Transportation (CRT), the Group University of Ottawa Distinguished Lecture Se- for Research in Decision Analysis (GERAD), ries, postdoctoral fellowships, and teaching re- the Centre de Recherche Informatique de Mont- leases so that University of Ottawa faculty mem- réal (CRIM), and the Institut National de la bers can undertake research with colleagues in Recherche Scientifique-Énergie, Matériaux et the CRM’s laboratories or participate in CRM Télécommunications (INRS-EMT). scientific activities. Laboratoires universitaires Bell (LUB) CRM – University of Ottawa Distinguished Lecture Series The CRM is an active participant in Labora- toires universitaires Bell, a joint project between The series features talks by prominent mathe- the ncm2 and Bell. The goal of the LUB is to maticians from Canada and abroad on topics at make innovations in the field of multimedia re- the forefront of today’s mathematical research. search and applications (mainly interactive ap- Algebraic relativism: encoding the higher structure of plications aimed at the general public, electronic morphisms commerce applications and new generations of Kathryn Hess (EPFL), February 23, 2007 networks), as well as to promote the training of a Eigenvalue problem and a new product in cohomol- highly qualified, international calibre workforce ogy of flag varieties in these areas. Shrawan Kumar (UNC Chapel Hill), April 13, Québec Neuroimaging Initiative (RNQ) 2007 Network for Computing and Mathematical In recent years, CRM’s PhysNum laboratory Modelling (ncm ) has developed a strong collaborative network 2 with various partners in neuroimaging in the The CRM is one of the founding members of Montréal area. This network became an offi- the Network for Computing and Mathematical cially recognized network with the founding Modelling (ncm2), a network created by several of the “Regroupement Neuroimagerie Québec” research centres in order to respond to the needs (RNQ), under the umbrella of the Institut Uni- of industry in fields related to computing and versitaire de Gériatrie in Montréal. RNQ, with mathematical modelling. The research of the net- its 70 researchers, has recently purchased some work focuses on five major themes: risk man- key equipment in neuroimaging thanks to a very agement, information processing, imaging and large grant ($11M). One of the strongest alliances parallel computing, transport and telecommu- of the CRM within that network is its association nications, and health and electronic commerce. with the INSERM laboratory for brain imaging The ncm2 was founded by the CRM, the Cen- at Jussieu–La Salpêtrière (Paris), whose director tre de recherche en calcul appliqué (CERCA), the is Dr. Habib Benali. Joint Initiatives The annual meetings of the CMS, SSC and CAIMS, as well as some of their training and promotion activities, are jointly sponsored by the CRM, the Fields Institute, PIMS and MITACS. The reader will find below summaries of the meetings that took place in 2006 – 2007.

Annual Meeting of the Statistical Society Chair of the Local Arrangements Committee: of Canada David Bellhouse (Western Ontario) May 28 – 31, 2006, University of Western Ontario The thirty-fourth Annual Meeting of the Statistical Society of Canada has brought to- Program Committee: Richard Lockhart (Simon gether researchers in statistics and probability Fraser), Chair; Michael Escobar (Toronto), Bio- and users from academia, government and in- statistics Section; François Pageau (SNC Tech- dustry. The meeting featured three workshops nologies), Business and Industrial Statistics Sec- and seventy-two paper sessions (including a tion; Patricia Whitridge (Elections Canada), Sur- contributed poster session). SSC 2006 was spon- vey Methods Section; André Dabrowski (Ot- sored by the CRM, the Fields Institute, PIMS, tawa), Probability Section MITACS, the National Program on Complex

56 CRMPARTNERSHIPS

Data Structures (NPCDS), the Robarts Research GAME THEORY/NUMBER THEORY Institute, the SAS Institute, and the Department Organizers: Richard Nowakowski (Dalhousie), of Statistical and Actuarial Sciences, the Faculty Bill Sands (Calgary), Hugh Williams (Calgary), of Science and Research Western (University of Robert Woodrow (Calgary) Western Ontario). JOINT CMS/CMESGEDUCATION SESSION The Presidential Invited Address was given Organizer: Peter Taylor (Queen’s) by Ivars Pederson (Science News), the Gold L-FUNCTIONS,AUTOMORPHIC FORMSAND Medal Address by David Andrews (Toronto) REPRESENTATION THEORY and the CRM – SSC Award Address by Jef- Organizers: Amir Akbary (Lethbridge), Clifton frey Rosenthal (Toronto). The Pierre-Robillard Cunningham (Calgary) Award Address was given by Jean-François Quessy (UQTR) and the Canadian Journal of MATHEMATICAL FINANCE Statistics Award Address by Jennifer Asimit and Organizers: Len Bos (Calgary), Anatoliy W. John Braun (Western Ontario). The Special Swishchuk (Calgary) Invited Address of the Biostatistics Section was MODEL THEORY given by Donald Berry (M.D. Anderson Can- Organizer: Patrick Speissegger (McMaster) cer Center), the Isobel Loutit Invited Address on POSITIVITYIN FUNCTIONAL ANALYSIS AND Business and Industrial Statistics by Geoff Vin- APPLICATIONS ing (Virginia Tech), and the Special Invited Ad- Organizers: Charalambos Aliprantis (Purdue), dress of the Survey Methods Section by Michael Vladimir Troitsky (Alberta) Larsen (Iowa State). RECENT WORKIN HISTORYOF MATHEMATICS CMS Summer 2006 Meeting Organizer: Tom Archibald (Simon Fraser) June 3 – 5, 2006, University of Calgary SET THEORYAND INFINITARY COMBINATORICS Organizer: Stevo Todorcevic (Toronto) Meeting director: Claude Laﬂamme (Calgary) SYMMETRYIN GEOMETRY The Summer 2006 Meeting of the Cana- Organizers: Ted Bisztriczky (Calgary), Ferenc dian Mathematical Society welcomed 271 par- Fodor (Szeged & Calgary), Richard K. Guy (Cal- ticipants. The public lecture was given by gary), Asia Weiss (York, Toronto) William R. Pulleyblank from IBM and was titled “From paper tape to the internet to BlueGene — CONTRIBUTED PAPERS SESSION forty years of computing history.” The plenary Organizer: Alexander Brudnyi (Calgary) speakers were Steve Awodey (Carnegie Mel- The meeting was sponsored by the Univer- lon), John Conway (Princeton), Nicole El Karoui sity of Calgary, the CRM, the Fields Institute, MI- (École Polytechnique, Palaiseau), Nigel Kalton TACS, and PIMS. (Missouri), Alexander S. Kechris (Caltech), Lás- zló Lovász (Microsoft) and Dave Marker (Illinois CAIMS – MITACS 2006 Joint Annual at Chicago). Conference The CMS was pleased to present lectures June 16 – 20, 2006, York University from its prize winners, namely, the Coxeter – Event coordinator: Jo-Anne Rockwood (MI- James Lecture, given by Jim Geelen (Water- TACS) loo), the Krieger – Nelson Prize Lecture, given In 2006 MITACS and CAIMS (the Cana- by Penny Haxell (Waterloo), and the CMS Ex- dian Applied and Industrial Mathematics So- cellence in Teaching Award Lecture, given by ciety) held their ﬁrst joint conference at York Frédéric Gourdeau (Laval). The meeting hosted University. The conference attracted over 500 13 sessions, listed below. delegates who took part in 18 sessions, includ- CATEGORY THEORY ing the Canadian Symposium on Fluid Dynam- Organizer: Robin Cockett (Calgary) ics and the Summer School on Mathematical Modeling of Infectious Diseases. MITACS and DIFFERENTIAL EQUATIONS AND DYNAMICAL CAIMS were pleased to host Plenary Speakers SYSTEMS Dr. John Ockendon (Oxford), Dr. John Glasser Organizers: Elena Braverman (Calgary), (Emory) and Dr. Charles Williamson (Cornell), Michael Y. Li (Alberta) as well as the CAIMS Research Prize Win- DISCRETEAND CONVEX GEOMETRY ner, Dr. Michael Mackey (McGill). The confer- Organizers: Karoly Bezdek (Calgary), Jozsef Soly- ence was sponsored by York University (Vice- mosi (UBC) Principal Research, Vice-Principal Academic,

57 CENTRE DE RECHERCHES MATHÉMATIQUES

Faculty of Arts), Simon Fraser University (Fac- MATHEMATICAL OUTBREAKS:EPIDEMICSAND ulty of Science, Faculty of Applied Science), INVASIONS Bombardier, Bell Canada, CRM, the Fields Insti- Organizers: James Watmough (New Brunswick), tute and PIMS. Here is a list of the sessions. Huaiping Zhu (York) 7TH CANADIAN SYMPOSIUMON FLUID DY- RECENT ADVANCES IN ALGORITHMSAND NAMICS SOFTWARE FOR THE NUMERICAL SOLUTIONOF Organizers: Nicholas Kevlahan (McMaster), DIFFERENTIAL EQUATIONS Marek Stastna (Waterloo), Francis Poulin (Wa- Organizers: Paul Muir (Saint Mary’s), Ray Spiteri terloo) (Saskatchewan) BIOINFORMATICS USEOF UNSTRUCTURED GRID METHODSFOR Organizers: Anne Condon (UBC), Peter Swain OCEAN MODELING (McGill), Shelley Bull (Mount Sinai Hospital), Organizer: Paul Myers (Alberta) David Tritchler (Ontario Cancer Institute) First Joint CMS/SMM Meeting COMMUNICATION AND SECURITYIN AD HOC NETWORKS September 21 – 23, 2006, Guanajuato, Mexico Organizer: Evangelos Kranakis (Carleton) Scientific Committee — CMS: Alejandro DATA MINING (joint with the Statistical Society Adem (UBC), Chair, Andrew Granville (Mont- of Canada) réal), Walter Craig (McMaster) Organizer: Steven Wang (York, Toronto) Scientific Committee — SMM: José C. Gómez FINANCIAL MATHEMATICS Larrañaga (CIMAT), Chair, Lourdes Palacios Organizers: Matt Davison (Western Ontario), (UAM Iztapalapa), Fernando Brambila (UNAM) John Walsh (UBC) The Canadian Mathematical Society (CMS) and the Sociedad Matemática Mexicana (SMM) IMAGE PROCESSING/INVERSE PROBLEMS held their first joint meeting in 2006. This meet- Organizers: Hongmei Zhu (York, Toronto), Huax- ing was hosted by the Centro de Investigación iong Huang (York, Toronto) en Matemáticas (CIMAT) and took place in STOCHASTIC MODELSIN INDUSTRIAL MATHE- Guanajuato from September 21 to 23. The Ple- MATICS nary Speakers were Francisco González Acuña Organizers: Rachel Kuske (UBC), Israel Ncube (UNAM & CIMAT), David Brydges (UBC), Gon- (Wilfrid Laurier) zalo Contreras (CIMAT), Pengfei Guan (McGill), NONLINEAR DYNAMICSINTHE HEALTH SCI- Jorge Urrutia (UNAM) and Maciej Zworski (UC ENCES Berkeley). In addition, there were 11 sessions, Organizers: Sue Ann Campbell (Waterloo), listed below. Michael Mackey (McGill) ALGEBRA OPERATIONS RESEARCHAND OPTIMIZATION Organizers: Ragnar-Olaf Buchweitz (Toronto), Organizers: Tamas Terlaky (McMaster), Warren José Antonio de la Peña (UNAM), Arturo Pi- Hare (Simon Fraser) anzola (Alberta) SCIENTIFIC COMPUTING I DIFFERENTIAL GEOMETRY Organizer: Anne Bourlioux (Montréal) Organizers: Pengfei Guan (McGill), L. Hernan- SCIENTIFIC COMPUTING II dez (CIMAT), McKenzie Wang (McMaster) Organizer: Chen Greif (UBC) FUNCTIONAL ANALYSIS APPLICATIONS AND RECENT DEVELOPMENTS Organizers: Hugo Arizmendi (UNAM), Anthony IN SYMBOLIC COMPUTATION Lau (Alberta), Lourdes Palacios (UAM Izta- Organizers: Rob Corless (Western Ontario), Dha- palapa) vide Aruliah (Western Ontario) GRAPH THEORYAND COMBINATORICS VISUAL MATHEMATICS Organizers: Isidoro Gitler (CINVESTAV), Luis Organizer: Karan Singh (Toronto) Goddyn (Simon Fraser), Bruce Reed (McGill) MATHEMATICS AND SPACE EXPLORATION (con- LOCALIZATION AND PARTIAL DIFFERENTIAL ference by Canadian astronaut Chris Hadfield) EQUATIONS Organized by the MITACS Student Advisory Organizers: Tim Minzoni (UNAM), Michael Committee Ward (UBC) CAREER PANEL LOW-DIMENSIONAL TOPOLOGY Organized by the MITACS Student Advisory Organizers: Victor Nuñez (CIMAT), Dale Rolfsen Committee (UBC)

58 CRMPARTNERSHIPS

MATHEMATICAL PHYSICS COMPLEXITYAND COMPUTABILITY IN ANALY- Organizers: David Brydges (UBC), Stephen Bruce SIS,GEOMETRY, AND DYNAMICS Sontz (CIMAT), Carlos Villegas (UNAM Cuer- Organizers: Alex Nabutovsky and Michael Yam- navaca) polsky (Toronto) MATHEMATICS EDUCATION DIFFERENTIABLE DYNAMICSAND SMOOTH ER- Organizers: Carolyn Kieran (UQÀM) and M. San- GODIC THEORY tillana (UPN) Organizers: Giovanni Forni (Toronto), Kon- PROBABILITY stantin Khanin (Toronto) Organizers: M.-E. Caballero (UNAM), Victor FUNCTIONAL ANALYSIS Pérez-Abreu (UAM Cuajimalpa), Tom Salisbury Organizers: Robb Fry (Thompson Rivers), S. (York, Toronto) Swaminathan (Dalhousie) TOPOLOGY HARMONIC ANALYSIS Organizers: Alejandro Adem (UBC), J. González Organizers: Izabella Laba (UBC), Malabika Pra- (CINVESTAV), Ian Hambleton (McMaster), D. manik (Caltech & UBC) Juan (UNAM Morelia) HISTORYOF MATHEMATICS VARIATIONAL METHODSIN PARTIAL DIFFER- Organizer: Tom Archibald (Simon Fraser) ENTIAL EQUATIONS Organizers: Lia Bronsard (McMaster), P. Padilla KNOT HOMOLOGIES (UNAM) Organizer: Dror Bar-Natan (Toronto) CMS Winter 2006 Meeting MATHEMATICAL ASPECTSOF CONTINUUM December 9 – 11, 2006, University of Toronto PHYSICS:ANALYSIS,COMPUTATION, AND MODELING Meeting director: Ian Graham (Toronto) Organizers: Rustum Choksi (Simon Fraser), Mary The Winter 2006 Meeting of the Canadian Pugh (Toronto) Mathematical Society welcomed approximately MATHEMATICAL BIOLOGY 430 participants. The plenary speakers were Organizer: Gail Wolkowicz (McMaster) Brent Davis (UBC), Dmitry Dolgopyat (Mary- land), Dimitri Shlyakhtenko (UC Los Angeles), MATHEMATICS EDUCATION Karen Smith (Michigan), Susan Tolman (Illinois Organizer: Walter Whiteley (York, Toronto) at Urbana-Champaign), and Shmuel Weinberger NONLINEAR SCHRÖDINGER EQUATIONS (Chicago). The Prize Lectures were given by Organizers: James Colliander (Toronto), Robert Andrew Granville (Montréal), Jeffery-Williams Jerrard (Toronto) Prize, Michael Newman (Waterloo), Doctoral POISSON GEOMETRYAND MATHEMATICAL Prize, and Peter Taylor (Queen’s), CMS Adrien PHYSICS Pouliot Award. The public lecture was given by Organizer: Eckhard Meinrenken (Toronto) V. Kumar Murty from the University of Toronto and was titled What is a Proof ? A list of the ses- PROBABILISTIC METHODSIN ANALYSIS AND sions and their organizers may be found below. ALGEBRA ALGEBRAIC COMBINATORICS Organizers: Matthias Neufang (Carleton), Balint Organizers: Nantel Bergeron (York, Toronto), Virag (Toronto) Christophe Hohlweg (Fields), Michael Zabrocki REPRESENTATIONS OF ALGEBRAS (York, Toronto) Organizers: Ibrahim Assem (Sherbrooke), CALABI –YAU VARIETIESAND MIRROR SYMME- Thomas Brüstle (Sherbrooke), Shiping Liu (Sher- TRY (with a feature lecture by Shing-Tung Yau) brooke) Organizers: James Lewis (Alberta), Noriko Yui CONTRIBUTED PAPERS SESSION (Queen’s) Organizer: Bill Weiss (Toronto) CLUSTER ALGEBRAS The following institutions sponsored the Organized jointly by the sessions on Algebraic CMS Winter 2006 Meeting: CRM, Fields Insti- Combinatorics and on Representations of Alge- tute, MITACS, PIMS, the University of Toronto bras (Department of Mathematics, Department of COMMUTATIVE ALGEBRAAND ALGEBRAIC GE- Mathematical and Computational Sciences at OMETRY UTM, Department of Computer and Mathemat- Organizers: Ragnar-Olaf Buchweitz (Toronto), ical Sciences at UTSC, Faculty of Arts and Sci- Graham Leuschke (Syracuse), Greg Smith ence, Ofﬁce of the Vice-President, Research, Of- (Queen’s) ﬁce of the Vice-Principal, Research, UTM)

59 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).

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 univer- The ISM produces the Accromαth journal and sities, the ISM is a consortium of seven Québec distributes it freely in all the cégeps and sec- universities (Concordia University, Université ondary schools in Québec. In this way, it con- Laval, McGill University, Université de Mont- tributes to spreading mathematical knowledge réal, UQÀM, UQTR, and Université de Sher- among teachers, young students and the gen- brooke), six of which offer a Ph.D. program in eral public. Each year, ISM professors give talks mathematics. As an institute to which belong attended by thousands of cégep students; these almost all the Québec researchers in the math- talks present the latest breakthroughs in mathe- ematical sciences, the ISM has at its disposal matics and the careers available to mathematics vast material and intellectual resources, and as graduates. a result, Montréal and Québec itself have be- As the above list demonstrates, the CRM has come one of the main centers of training and several joint activities with the ISM, in particu- research in the mathematical sciences in North lar two colloquia, a joint program of postdoc- America. The ISM is funded by the Ministère toral fellowships, and the planning of gradu- de l’Éducation, du Loisir et du Sport du Québec ate courses related to the thematic programs of and by the seven universities in the consortium. the CRM. Since the summer of 2003, the CRM The reader will find below an overview of has also supported the Undergraduate Summer the 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 The CRM – ISM postdoctoral fellowships en- to turn them into a great school of mathematics. able promising young researchers to devote Thus the ISM coordinates the graduate studies themselves to their research work. The ISM orga- of the mathematics departments, supports the nizes a single competition on behalf of the seven sharing of expertise among its researchers and universities of the consortium, and it receives facilitates student mobility between the Mont- a large number of applications, which are then réal universities. evaluated by the 150 ISM professors. The selec- • Scholarships and financial support tion of the fellows is rigorous and only one in The ISM helps students and beginning re- forty applicants is awarded a fellowship. The ap- searchers carry out their research activities in plications are handled electronically in order to several ways, for instance through the ISM streamline the selection process and economize Scholarships for Graduate Studies, the Carl Herz the resources consumed during the selection. Scholarship (financed by the Carl Herz Founda- The postdoctoral fellows play a crucial role in tion), the Travel Bursaries, the Undergraduate the Montréal universities: they collaborate with Summer Scholarships and the CRM – ISM post- the established researchers, stimulate their work doctoral fellowships. and bring new ideas from other great centres of mathematical research. Also they are a vital link • Scientific activities between the professors and the students, espe- Since its creation, the ISM has initiated several cially when they organize on their own study activities that are by now an integral part of the groups on emerging topics. Québec scientific scene: the CRM – ISM Math- 2006 – 2007 Postdoctoral Fellows ematics Colloquium, the CRM – ISM – GERAD Statistics Colloquium, the ISM Graduate Student Félix Carbonell (Ph.D. 2006, La Habana) is Conference and the ISM Graduate Student Sem- working with Keith Worsley (McGill) in medical inar. imaging.

61 CENTRE DE RECHERCHES MATHÉMATIQUES

Stefan Friedl (Ph.D. 2003, Brandeis) is work- The CICMA laboratory financed half of this ing with Olivier Collin and Steven Boyer scholarship. (UQÀM) on the topology of 3-dimensional and Julia Evans 4-dimensional manifolds. His research article Topic: Rational points on elliptic curves 1 3 “Symplectic S × N , surface subgroup separa- Duration: 4 months bility, and totally degenerate Thurston norm” (in Supervisor: Christian Wuthrich collaboration with Stefano Vidussi) will be pub- Professor Henri Darmon financed half of this lished in the prestigious Journal of the American scholarship. Mathematical Society. Friedl has accepted a posi- Gabriel Gauthier-Shalom tion at the University of Warwick starting in June Topic: Number theory and elliptic curves 2008. Duration: 3 months (May – July) Ba¸sakGürel (Ph.D. 2003, UC Santa Cruz) is Supervisor: Christian Wuthrich working in symplectic topology and Hamilto- Professor Henri Darmon financed half of this nian dynamical systems with Octav Cornea and scholarship. François Lalonde. She is one of the organizers of Rachel Kidd the weekly seminar in symplectic topology. Topic: Study of nodal sets and nodal domains of Emmanuel Lorin de la Grandmaison (Ph.D. eigenfunctions of elliptic operators 2001, ENS Cachan) works in quantum chemistry Duration: 2 months and numerical analysis for hyperbolic systems. Supervisor: Igor Wigman Lorin has published four research articles in col- Professor Dmitry Jakobson financed half of this laboration with André Bandrauk (Sherbrooke). scholarship. Dan Mangoubi (Ph.D. 2006, Technion) works in Alexandre Lang geometry and differential analysis with Dmitry Topic: Complex networks Jakobson (McGill) and Iosif Polterovich (Uni- Duration: 3 months (May – July) versité de Montréal). Mangoubi has written the Supervisor: Navin Goyal article “Tubular neighborhoods of nodal sets Professor Pascal Tesson financed half of this and Diophantine approximation” in collabora- scholarship. tion with Jakobson. He was awarded the presti- Vincent Quenneville-Bélair gious scholarship of the European Postdoctoral Topic: Arithmetic on elliptic curves Institute for Mathematical Sciences and is now Duration: 4 months a postdoctoral fellow at the Institut des Hautes Supervisor: Christian Wuthrich Études Scientifiques à Paris. Professor Henri Darmon financed half of this Andrew McIntyre (Ph.D. 2002, Stony Brook) scholarship. studies the spectral geometry of 2-dimensional Philippe Sosoe and 3-dimensional hyperbolic manifolds in col- Topic: Number of zeroes of random trigonome- laboration with Dmitry Korotkin (Concordia). tric polynomials He is currently visiting the Max Planck Institut Duration: 2 months für Mathematik in Bonn (Germany). Supervisor: Igor Wigman Professor Dmitry Jakobson financed half of this Undergraduate Summer Scholarships scholarship. In collaboration with the CRM and the ISM professors, the ISM awards summer scholarships to ISM Graduate Student Conference promising undergraduates who want to do re- The ninth ISM Graduate Student Conference search during the summer and plan to study (Colloque panquébécois annuel des étudiants), mathematics at the graduate level. These un- which took place at Concordia University on dergraduates are supervised by postdoctoral fel- May 11 – 13, 2007, was attended by 76 students lows, who in general are supervising students from seven Québec universities and Queen’s for the first time. The reader will find below the University (Kingston, Ontario). For students, list of the undergraduate scholars. the Conference afforded a great opportunity to Marc Desgroseilliers meet one another, present their research work Topic: Calculer explicitement des sommes expo- and exchange ideas with their peers. Valérie nentielles en petite caractéristique Hudon, Ahmad Lavasani, Alexandra Lemus, Duration: 2 months (July – August) Rami Tabri, Maiko Ishii and Jeremy Porter were Supervisor: Emmanuel Letellier the members of the organizing committee. The

62 MATHEMATICAL EDUCATION conference was supported by the CRM, Concor- each issue have been printed and distributed. dia University, the Graduate Student Associa- Accromαth is designed by an exceptional team tion of Concordia University, the Concordia Uni- of researchers and instructors with a broad expe- versity Alumni Association and Meloche Mon- rience in the promotion of mathematics; it pro- nex. vides high school and cegep teachers with stim- The plenary speakers, all of which were ulating and topical articles on the most recent ISM professors, presented five of the most ac- discoveries and applications, as well as articles tive fields of research in mathematics. François on the history of mathematics and its links with Bergeron (UQÀM) gave a lecture entitled “À the arts. questions symétriques, réponses symétriques.” In 2007, the quality of Accromαth was high- Steven Boyer (UQÀM) spoke on the topol- lighted in two ways. First, Jean-Paul Delahaye, ogy of 3-dimensional manifolds, and Gilles who has published several articles in the French Brassard (Université de Montréal) spoke on magazine Pour la science, has agreed to collabo- pseudo-telepathy. Andrew Granville (Université rate with Accromαth on a regular basis by con- de Montréal) gave a lecture on patterns in the tributing a column on paradoxes (Rubrique des primes and Wei Sun (Concordia) a lecture on paradoxes), starting in the Summer-Fall issue of stochastic filtering and its applications. 2007. Second, the design of Accromαth won a The following students gave talks at the Con- bronze medal in the “image brochure” category ference: Antonio Reiser, Jérôme Grand’Maison, at the “Summit Creative Awards” international Ian Marquette, Liam Watson, Andreea Prun- contest, which features thousands of submis- cut, Tamara Diaz Chang, Ferenc Balogh, John sions from 23 countries. Chapman, François Charrette, Clément Hyvrier, André Ross, instructor of mathematics at Tuan Xing, Frédérick Tremblay, Hong Yue, Émi- the Cégep de Lévis-Lauzon, is the editor-in- lie Dufresne, Maiko Ishii, Baptiste Chantraine, chief of Accromαth. The members of its edi- Klara Kelecsenyi, Daniel Simeone, Alexandre torial board are France Caron (Université de Girouard, Shiva Gol Tabaghi, Zanin Kava- Montréal), Louis Charbonneau (UQÀM), Jo- zovic, Valérie Hudon, Christopher Brav, Quentin celyn Dagenais (Commission scolaire Marie- Rajon, Patrice Rivard, Ahmad Lavasani, Eu- Victorin), Jean-Marie De Koninck (Université gene Kritchevski, Steven Rayan, Érik Pronovost, Laval), André Deschênes (Petit Séminaire de Yafang Wang. Québec), Christian Genest (Université Laval), Frédéric Gourdeau (Université Laval), Bernard Promotion of the mathematical sciences R. Hodgson (Université Laval), and Christiane Rousseau (Université de Montréal). Alexandra Produced by the ISM and financed by the ISM, Haedrich (ISM) is responsible for the maga- the CRM, the MITACS network and the Cana- zine production and its iconography, and Pierre dian Mathematical Society, the Accromαth mag- Lavallée (Neograf design) is responsible for its azine aims to draw more young people to the graphical design. The linguistic revision is under mathematical sciences. Accromαth is available the responsibility of Jean-Claude Girard (Cégep free of charge in all the high schools and cegeps Saint-Jean-sur-Richelieu) and Jacques Sormany of Québec. Three issues of Accromαth have (Cégep de Chicoutimi). been published so far; five thousand copies of Other joint initiatives

CMS Math Camps 2006 thirteen regional math camps in ten provinces, as well as a national camp. The CMS Math Camp Program (initially called Organized by Daniel Gatien and Matthieu the ESSO/CMS Math Camp Program) started Dufour, the national camp was held at the John in 1999 with three camps, and the program has Abbott cegep from July 2 to 8, 2006. The Na- now grown to include at least one camp in every tional Camp is designed primarily for younger province. The support received from the spon- Canadian students with at least two years re- sors enables the Canadian Mathematical Society maining in high school and with the potential to make these camps accessible to students from to compete at the Mathematical Olympiad level. across Canada who demonstrate an interest and The selection of invited students is based upon excellence in mathematics. In 2006, there were

63 CENTRE DE RECHERCHES MATHÉMATIQUES their results in various mathematics competi- ciety, the CRM, the Fields Institute, the Paciﬁc In- tions. Presentations on speciﬁc topics and the stitute for the Mathematical Sciences, the Associ- various problem solving sessions are run by lo- ation mathématique du Québec, the host univer- cal area teachers and faculty members as well as sities, and the governments of New Brunswick, former IMO team members. Alberta, the Northwest Territories, Newfound- The Regional Camps are intended to pro- land and Labrador, Nova Scotia, Québec, On- vide some mathematics enrichment in a fun and tario, and Saskatchewan. rewarding environment. Each camp invites between 20 and 30 students (from grade 9 to 11) 2006 AMQ Mathematics Camp on the basis of national or regional mathemat- June 2 – 13, 2006, Bishop’s University ics competitions as well as recommendations from teachers. The 2006 regional camps took Organizers: François Huard (Bishop’s), Pierre- place at Sir Wilfred Grenfell College, the Uni- Yves Leduc (Sherbrooke) versity of Prince Edward Island, the University The AMQ Mathematics Camp allows ap- of New Brunswick, the Université du Québec proximately thirty cegep students, mostly laure- à Rimouski, Simon Fraser University (Burnaby ates of the Concours mathématique du Québec, and Surrey campuses), the University of Ottawa, to participate in a series of workshops coordi- Dalhousie University, Brock University, the Uni- nated by Québec mathematicians. versity of Western Ontario, the University of Al- berta, the University of Manitoba, and the Uni- Sciences et mathématiques en action versity of Regina. Finally, the Summer 2006 IMO Training Sem- The CRM also contributed to the “Sciences et inar, designed to prepare a team of Cana- mathématiques en action” program, created by dian students for the International Mathematical Professor Jean-Marie De Koninck from Univer- Olympiad (IMO), took place from June 24 to July sité Laval in order to popularize mathematics 2, 2006, and was organized by Dalhousie Univer- and science in high schools and the general pub- sity. The Winter 2007 IMO Training Seminar took lic. Within the framework of this program, math- place on January 2-7, 2007, and was organized ematics shows were presented to the students of by York University. many high schools and other institutions during The sponsors of the Math Camp Program in the year 2007. 2006-2007 were the Canadian Mathematical So-

64 Research Laboratories CENTRE DE RECHERCHES MATHÉMATIQUES

n 2006 – 2007 the CRM was encompassing nine research laboratories at the heart of the Québec Imathematical community, including the new INTRIQ laboratory (Institut transdisciplinaire d’informatique quantique), devoted to quantum computing. These research groups act as focal points for local scientiﬁc activity and participate actively in the scientiﬁc programs of the CRM.

Applied Mathematics

Description The Laboratory organizes the Montreal Sci- entific Computing Days each February, as well The applied mathematics laboratory is a flour- as other workshops. It has two regular seminars ishing research-based network of 17 members or running during the academic year, a weekly ap- associate members drawn from 6 different uni- plied mathematics seminar and a biweekly com- versities and spanning departments of computer putational science and engineering seminar. It science, chemistry, atmospheric and ocean sci- also supports postdoctoral fellows and summer ences and, of course, mathematics and statistics. students as well as Canadian and international Members are very actively engaged in cutting visitors. edge research in areas as diverse as numerical simulation, applied dynamical systems, quan- News and highlights tum chemistry, turbulence, combustion, biome- André Bandrauk has been nominated Fellow chanics, numerical methods in fluid mechanics by the Humboldt Foundation, Berlin. He will and electromagnetism, finite element methods, make three visits, each of four months, to the molecular dynamics, control, optimization, pre- Free University of Berlin and to the Max Born conditioners and large-scale eigenvalue prob- Institute in 2007, 2008 and 2009, respectively. lems. As testimony to the excellence of the re- Jacques Bélair will be President of the Cana- search pursued in the laboratory and the inter- dian Applied and Industrial Mathematics Soci- national reputation enjoyed by its members, we ety (CAIMS) from 2008 – 2009. Nilima Nigam ob- detail below some distinctions awarded to and tained a grant from the Discovery Accelerator invited talks and courses given by its members. Supplements Program, which amounts to 40,000 The objectives of the laboratory are princi- dollars per year for three years. pally to foster and encourage collaboration and Laboratory members received a very large scientific interchange between its own members, number of invitations to speak at conferences with other researchers in Montréal and with and seminars during this past year. Regrettably, the numerous visitors and conference and sem- these are too numerous to enumerate here, but inar speakers invited to Montréal by members we mention a short course of invited lectures of the laboratory. Lab members have always delivered by Eusebius Doedel on the theme of been active in interdisciplinary research. André “Numerical methods for bifurcation problems” Bandrauk and Nilima Nigam, for example, are at the National Center of Theoretical Sciences, members of RQMP (Regroupement québécois National Tsing-Hua University (Taiwan), in May sur les matériaux de pointe). Nilima Nigam is 2007, and at the Research Institute of Mathemat- an associate member of the CRM mathematical ical Sciences of Kyoto University in July 2006. analysis laboratory. Sebius Doedel and Jacques Paul Tupper was one of the two applied mathe- Bélair are members of the Centre for Nonlin- maticians (the other being Michael Brenner, from ear Dynamics in Physiology and Medicine at Harvard) to give a talk in the CRM mathematics McGill. Michel Delfour is a member of GIREF colloquium series in 2006 – 2007. He was also an (Groupe Interdisciplinaire de Recherche en Éléments invited panelist for a panel discussion on the am- Finis) at Université Laval and Anne Bourlioux bitious theme “The next 50 years” at the confer- and Jacques Bélair are members of MITACS ence “Stanford 50: The state of the art and future sponsored industrial project teams. Indeed, the directions of computational mathematics and diversity of the members’ research expertise is numerical computing,” held at Stanford Univer- regarded by the laboratory as positive and en- sity on March 31, 2007. Tucker Carrington, an as- riching and leads to stimulating common semi- sociate member of the applied maths lab, was nars and workshops, where ideas are exchanged a visiting professor at the ETH Zürich during and links forged between different people and July 2006 and gave a number of invited talks in subject areas. Details of some of the numerous Germany and Switzerland at that time. Robert conferences, workshops and seminars organized Owens was invited to be a plenary speaker at the by lab members are supplied below.

66 RESEARCH LABORATORIES

International Conference on Spectral and High shops will be preceded by mini-courses for grad- Order Methods in Beijing in June 2007, but de- uates (Eusebius Doedel being one of the lectur- clined the invitation. ers); two semester-long advanced courses will Michel Delfour was a member of the board also be offered. In addition to being on the sci- of the International Congress on Industrial and entific committee of the thematic semester, Eu- Applied Mathematics (ICIAM) held in Zürich in sebius Doedel was a member of the advisory July 2007; he represented the Canadian Mathe- board for the International Workshop on Topics matical Society. M. Delfour was also a member of in Nonlinear Dynamics and Complexity, held in the ICIAM 2007 International Scientific Commit- Puebla, Mexico, in February 2007, and a member tee and the organizer of two mini-symposia that of the scientific committee for the Workshop on took place during this meeting. Thomas Wihler Applied Dynamical Systems held at the Univer- was one of the organizers of a mini-symposium sity of Ghent (Belgium) in June 2006. on “Advances in Discontinuous Galerkin Meth- Looking further into the future, Michel ods” at ICIAM 2007. Michel Delfour was a mem- Delfour is one of the organizers of the first ber of the planning committee for the meet- CRM – INRIA congress to be held in early May ing in memory of Maurice L’Abbé (September 2008. In June 2008, the second Canada – France 10, 2007). Michel Delfour and Jean-Paul Zolésio Congress will take place in Montréal, and Paul were organizers of a session entitled “Static and Arminjon is preparing, together with Emmanuel Moving Geometries as Modeling and/or Con- Lorin (CRM) and Marc Laforest (Polytechnique trol Variables” at the 23rd IFIP TC 7 Conference Montréal), a session on hyperbolic problems en- on System Modelling. This conference took place titled “Numerical Analysis for Hyperbolic Sys- on July 23 – 27, 2007, in Krakow (Poland). tems of Conservation Laws.” Anne Bourlioux is Members of the laboratory have been in- involved in the same congress as a session orga- volved in the organization of events promot- nizer on the theme of scientific computing. Pe- ing industrial applied mathematics recently. Nil- ter Bartello will be one of the organizers of the ima Nigam was on the organizing commit- program entitled “The Nature of High-Reynolds tee of the Fields – MITACS Industrial Problem- Number Turbulence,” to be held in the autumn Solving Workshop held in Toronto on August of 2008 at the Isaac Newton Institute (University 14 – 18, 2006, and Anne Bourlioux was one of of Cambridge). He has also agreed to organize a the organizers of the first Montréal Industrial workshop on Cloud Turbulence to be hosted by Problem Solving Workshop (held in August the Institute for Mathematical Sciences of Impe- 2007). The annual meeting of CAIMS in Banff rial College (London) in March 2009. on May 20 – 24, 2007, brought together applied Finally, in 2006 – 2007, the Lab contributed mathematicians from across Canada for four to the signing of a letter of intention between days of sessions, mini-symposia, and invited the CRM and the Tata Institute of Fundamen- and contributed talks. In 2007, Anne Bourlioux tal Research of Bangalore (India), thus laying (as a CAIMS board member) organized a ses- the foundations for exchange visits for students sion on numerical PDEs, and Paul Tupper and and faculty members of the two institutions. Robert Owens were responsible, together with This was achieved through the involvement of Peter Swain (McGill) and Ian Frigaard (British Michel Delfour in the provincial government’s Columbia), for mini-symposia on stochastic spa- “Québec Trade and Innovation” mission, which tial models of biochemical systems and the spent eight days in India earlier this year. mathematical modelling and numerical simula- Students, postdoctoral fellows, and tion of complex fluids, respectively. visitors Part of the summer and all of the autumn term 2007 at the CRM were devoted to Applied In 2006 – 2007 the laboratory allocated a larger Dynamical Systems, and the applied maths lab- part of its budget than before to the employ- oratory earmarked 5000 dollars to support the ment and support of postgraduate students and event. This thematic program was a major un- postdoctoral researchers. The laboratory has ap- dertaking for the organizing committee, which proximately 40 graduate students and 10 post- included four members of the applied maths lab- doctoral researchers, supervised and directed by oratory: Tony Humphries, Paul Tupper, Euse- the lab’s 17 members or associate members. The bius Doedel and Jacques Bélair. Altogether there applied maths lab now partially finances (to a will be six main workshops with five taking level of at least 9000 dollars per year) three of place at the CRM and one to be held in Hali- the postdocs (Miguel Moyers-Gonzalez, Jason fax (Nova Scotia). Two of the Montréal work- Cooper and Abderrazak Ramadane), and some

67 CENTRE DE RECHERCHES MATHÉMATIQUES money is available for their travel expenses, so • MINI-WORKSHOPON COMPUTATIONAL AS- that they make research visits and attend con- PECTSOF DYNAMICAL SYSTEMS ferences. The quality of the research environ- July 7, 2006, Concordia ment provided by the laboratory is in part mea- Organizer: Eusebius J. Doedel (Concordia) sured by the success of postdocs in getting good • THE 4TH MONTREAL SCIENTIFIC COMPUT- academic positions; we are pleased to mention ING DAYS that Emmanuel Lorin de la Grandmaison has April 16 – 17, 2007, CRM been offered a tenure track assistant professor- Organizers: Emmanuel Lorin de la Grandmai- ship at the University of Ontario Institute of son (Montréal), Robert G. Owens (Montréal), Technology, and Miguel Moyers-Gonzalez has Thomas P. Wihler (McGill) been offered a lectureship at Durham Univer- One of the main goals of the Montreal Sci- sity (United Kingdom). A travel bursary scheme, entific Computing Days is to nurture the young whereby an amount of 400 dollars was made researchers of the Applied Mathematics Labora- available to each lab member or associate mem- tory. Michel Delfour will be the organizer of the ber to refund travel expenses by one or more of 5th Montréal Scientific Computing Days, to be their research students, was initiated in 2006 – held in April 2008. 2007. Altogether, in 2006 – 2007, one undergradu- Members of the laboratory ate student, 21 master’s students, 30 Ph.D. stu- Regular members dents and 13 postdoctoral fellows were supervised or cosupervised by regular or associate ROBERT G.OWENS (Montréal), Director members of the laboratory. Visitors hosted by lab Mechanics, numerical simulation of complex members in 2006 – 2007 included Bob Skeel (Pur- fluids due), Bob Batterman (Western Ontario), Marek PAUL ARMINJON (Montréal) Stastna (Waterloo), Marc Thiriet (INRIA and Numerical methods in fluid mechanics Paris 6), Christoph Schwab (ETH Zürich), Do- ANDRÉ D.BANDRAUK (Sherbrooke) minik Schoetzau (UBC) and Adimurthi (TIFR Quantum chemistry Bangalore). PETER BARTELLO (McGill) Seminars Turbulence, CFD JACQUES BÉLAIR (Montréal) The main regular event in the applied math- Dynamical systems in physiology ematics laboratory is the weekly seminar. The organizers for 2006 – 2007 were Nilima Nigam ANNE BOURLIOUX (Montréal) and Eusebius Doedel, and twenty-five seminars Modeling, numerical simulation in turbulent on a wide range of topics of interest to mem- combustion bers of the lab were delivered over the two MICHEL C.DELFOUR (Montréal) semesters. One of these (a seminar by Profes- Control, optimization, design, shells, calculus, sor Harold W. Kuhn of Princeton on September biomechanics 1, 2006) was sponsored jointly with the ncm2; EUSEBIUS J.DOEDEL (Concordia) this “Grande conférence rcm2” was organized by Numerical analysis, dynamical systems, differ- Michel Delfour. The idea of the seminars is not ential equations, bifurcation theory, scientific only to stimulate and inform those who attend software the talks, but to forge or strengthen research col- ANTONY R.HUMPHRIES (McGill) laborations with the speakers. A number of ap- Numerical analysis, differential equations plied maths talks were given in a two-semester SHERWIN A.MASLOWE (McGill) series organized by Nilima Nigam at McGill. In Asymptotic methods, fluid mechanics 2006 – 2007, Thomas Wihler and Peter Bartello were the organizers of the Computational Sci- PAUL F. TUPPER (McGill) ences and Engineering Seminar, held on alter- Numerical analysis, stochastic processes, statis- nate Fridays during the two semesters. tical mechanics THOMAS P. WIHLER (McGill) Workshops, special sessions, and others Numerical analysis, computational methods for In 2006 – 2007 the following workshops were PDEs sponsored by the Applied Mathematics Labora- JIAN-JUN XU (McGill) tory. Reports on these workshops may be found Asymptotics and numerical analysis, nonlinear in the section on the CRM General Program. PDEs, materials science

68 RESEARCH LABORATORIES

Associate members NILIMA NIGAM (McGill) Applied analysis, numerical methods in electro- TUCKER CARRINGTON (Montréal) magnetism Chemical dynamics JEAN-PAUL ZOLÉSIO (INRIA Sophia-Antipolis) MARTIN J.GANDER (Genève) Control, optimization Domain decomposition, preconditioning

CICMA

Description ican Mathematical Society; he gave this lecture in Davidson (North Carolina) in 2007. This centre comprises researchers working in Henri Darmon gave a 45-minute lecture in number theory, group theory and algebraic ge- the Number Theory Section of the International ometry. Contemporary number theory follows Congress of Mathematicians, held in Madrid in two major courses. On the one hand, there is August 2006. In July 2006, he organized in Göt- the theory of special values of L-functions at- tingen a Summer School on Arithmetic Geome- tached to arithmetic objects, originating in the try sponsored by the Clay Mathematics Institute work of Gauss and Dirichlet and leading to the (CMI); several other members of CICMA (Pierre modern conjectures of Deligne, Beilinson and Charollois, Hugo Chapdelaine, Matthew Green- Bloch – Kato. On the other hand, the Langlands berg, and John Voight) were involved in this program postulates a close link between arith- school. In March 2007, at Les Diablerets, he also metic L-functions and automorphic representa- gave a mini-course to Swiss doctoral students tions. An area where these two currents inter- with a CICMA postdoctoral fellow, Christian sect is the study of elliptic curves. This area is Wuthrich. In April 2007, he gave the “Koweit particularly well represented in the Centre, with Foundation Lecture” at the University of Cam- Darmon, Iovita, and Kisilevsky. CICMA also ac- bridge. quired an expertise in many aspects of analytic number theory when Andrew Granville, one of Students, postdoctoral fellows, and the leaders in the field, became a member of visitors CICMA. On the group theory side, Kharlampov- ich and Miasnikov are world-renowned special- Many CICMA postdoctoral fellows were offered ists on group varieties and McKay is one of the tenure-track positions recently. Guillaume Ri- originators of the moonshine program. cotta was offered a position at the Université The problems to be studied by the group in Bordeaux 1, Nathan Ng at the University of Ot- the coming years include the construction of ra- tawa, Pierre Charollois at the Université Paris tional points on elliptic curves both from the al- 6, Mak Trifkovic at the University of Victo- gorithmic and theoretical viewpoints; zeta func- ria, Adriano Marmora at the Université Stras- tions of varieties over finite fields and the al- bourg 1, Payman Kassei and Ambrus Pàl at gorithmic approach; canonical lifting of ellip- King’s College (University of London), Mat- tic curves and Abelian varieties; cryptography, teo Longo at the Università degli Studi di Mi- Abelian varieties, and many aspects of analytic lano, Gonzalo Tornaria at the Universidad de la number theory, for instance averages of spe- República (Uruguay), Alex Ghitza at Colby Col- cial values of L-functions, distribution of prime lege (Maine), Peter Clark at the University of numbers and prime divisors, and problems in Georgia (Athens), and Ye Tian at the Academy additive number theory. of Sciences (Beijing). CICMA hired four new postdoctoral fellows News and highlights in 2007: Bryden Cais (Michigan), Riad Masri (UT Austin), Jeehoon Park (Boston), and Arnaud Andrew Granville was awarded the prestigious Chadozeau (Bordeaux 1). Altogether, in 2006 – Chauvenet Prize (2008) of the Mathematical As- 2007, 27 master’s students, 33 Ph.D. students sociation of America (MAA), and the Lester R. and 23 postdoctoral fellows were supervised or Ford Award (2007) of the MAA. He was elected cosupervised by laboratory members. member of the Royal Society of Canada in 2006, and in the same year, was awarded the Jeffery- Seminars Williams Prize of the Canadian Mathematical Society. He was the first Canadian to give the The Québec – Vermont Number Theory Semi- prestigious Erd˝osmemorial lecture of the Amer- nar is the main scientific activity of CICMA,

69 CENTRE DE RECHERCHES MATHÉMATIQUES is held every second Thursday for a full day CHANTAL DAVID (Concordia) and is attended by about 30 regular participants Analytic number theory, L-functions from Montréal, Vermont, Québec and Ottawa. JEAN-MARIE DE KONINCK (Laval) In 2006 – 2007, Eyal Goren and Henri Darmon Analytic number theory: distribution of prime were the organizers of the seminar and the latter numbers, factorization of numbers, asymptotic consisted of 40 lectures. In the fall of 2006, the behaviour of arithmetic functions, Riemann zeta seminar was devoted (albeit not exclusively) to function the recent proof of the Sato – Tate conjecture. We DAVID S.DUMMIT (Vermont) also mention an activity related to the seminar, a Algebraic number theory, arithmetic algebraic mini-course on cohomological invariants given geometry, computational mathematics by Jean-Pierre Serre from September 6 to Octo- DAVID FORD (Concordia) ber 6. The complete program of the Québec – Computational number theory, algorithmic Vermont Number Theory Seminar may be found number theory at the address www.math.mcgill.ca/darmon/ qvnts/qvnts.html. EYAL Z.GOREN (McGill) Arithmetic geometry, algebraic number theory, Workshops, special sessions, and others moduli spaces of abelian varieties, Hilbert modular forms, p-adic modular forms In 2006 – 2007 CICMA sponsored two confer- ANDREW GRANVILLE (Montréal) ences. Jean-Pierre Serre, from the Collège de Analytic number theory, arithmetic geometry, France, was the distinguished plenary speaker combinatorics of the Québec – Maine Conference on Number ADRIAN IOVITA (Concordia) Theory and Related Topics. The second confer- Number theory, p-adic cohomology ence honoured the contributions of John McKay, a member of CICMA who is one of the most in- OLGA KHARLAMPOVICH (McGill) fluential Canadian mathematicians. Reports on Combinatorial theory of groups and Lie algebras these two conferences may be found in the sec- HERSHY KISILEVSKY (Concordia) tion on the CRM general program. L-functions, Iwasawa theory, elliptic curves, class field theory • QUÉBEC –MAINE CONFERENCEON NUMBER THEORYAND RELATED TOPICS JOHN LABUTE (McGill) September 30 – October 1, 2006, Université Laval Pro-p-groups, Lie Algebras, Galois Theory Financed by the Number Theory Foundation, CLAUDE LEVESQUE (Laval) CICMA and the Department of mathematics and Algebraic number theory, units, class number, statistics of Université Laval cyclotomic fields Organizers: Claude Levesque (Laval), Jean-Marie MICHAEL MAKKAI (McGill) De Koninck (Laval) Mathematical logic • “GROUPSAND SYMMETRIES:FROMTHE NE- JOHN MCKAY (Concordia) OLITHIC SCOTSTO JOHN MCKAY” Computational group theory, sporadic groups, CONFERENCE HONOURINGTHE CONTRIBU- computation of Galois groups TIONSOF JOHN MCKAY ALEXEI G.MIASNIKOV (McGill) April 27 – 29, 2007, CRM Group theory Sponsored by CRM, Concordia University and M.RAM MURTY (Queen’s) the CICMA Number theory: Artin’s conjecture, elliptic Organizers: John Harnad (Concordia), Pavel curves, modular forms, automorphic forms, Winternitz (Montréal) Langlands program, Selberg’s conjectures, sieve methods, cryptography Regular members of the laboratory DAMIEN ROY (Ottawa) HENRI DARMON (McGill), Director Transcendental number theory Algebraic number theory, geometry, arithmetic, PETER RUSSELL (McGill) L-functions, diophantine equations, elliptic Algebraic geometry curves FRANCISCO THAINE (Concordia) CHRIS CUMMINS (Concordia) Cyclotomic fields, cyclotomy, rational points on Group theory, modular functions, moonshine curves

70 RESEARCH LABORATORIES

CIRGET

Description Chuai, Jianjun (Ph.D. 2003, Queen’s) Invariant theory Geometry and topology are fundamental disciplines of mathematics whose richness and vi- Duchemin, David (Ph.D. 2004, Strasbourg 1) tality have been evident throughout human his- Low-dimensional quaternionic geometry tory and reflect their deep link to our experience David Duchemin left in February 2007 for a post- of the universe. They are a focal point of mod- doctoral position at the École Polytechnique in ern mathematics and in effect several domains of Palaiseau, France. mathematics have recently shown a strong trend Friedl, Stefan (Ph.D. 2003, Brandeis) towards a geometrization of ideas and meth- Low-dimensional topology and knot theory ods: two cases in point are mathematical physics Stefan Friedl has been offered an Assistant Pro- and number theory. During the last twenty-five fessor position at the University of Warwick, years, several researchers of international calibre starting in 2008. in geometry and topology have been hired by Gambino, Nicola (Ph.D. 2002, Manchester) Québec universities. The research centre, based Combinatorics, homotopy algebra at UQÀM, now comprises eighteen professors Gambino will be continuing as a postdoctoral together with a large number of postdoctoral fel- fellow at the Centre de Recerca Matemàtica in lows and graduate students. The main themes to Barcelona, Spain. be pursued in the coming years include the topological classification of 3-dimensional manifolds; Ghiggini, Paolo (Ph.D. 2004, Pisa) quantization of Hitchin systems and the geomet- Low-dimensional contact topology ric Langlands program; classification of special Paolo Ghiggini has accepted a postdoctoral po- Kähler metrics; the study of symplectic invari- sition at Caltech. ants, especially in dimension 4; and Hamiltonian Gürel, Ba¸sak (Ph.D. 2003, UC Santa Cruz) dynamical systems. Hamiltonian dynamical systems, symplectic News and highlights topology and geometry Hu, Shengda (Ph.D. 2003, Wisconsin – Madison) Many of our postdoctoral fellows have left for Algebraic geometry of toric varieties, Gromov – new positions, and we are particularly pleased Witten invariants and orbifolds to note that they have been offered positions at prestigious institutions around the world, such Lisi, Samuel (Ph.D. 2005, Courant Institute, as Caltech, Duke, École Polytechnique, Stanford NYU) and Warwick. Likewise, several of our Ph.D. Symplectic and contact geometry students have finished last summer, and then Samuel Lisi has started a postdoctoral position left for various postdoctoral positions around at Stanford University in September 2007. the world. We would like in particular to high- Mohammadalikhani, Ramin (Ph.D. 2003, light the contributions of Baptiste Chantraine, Toronto) founder and organizer of the CIRGET Junior Equivariant cohomology, moduli spaces of fiber Seminar and a very promising young mathe- bundles, quantum homology matician. Throughout his stay, he worked to cre- Walsh, Genevieve (Ph.D. 2003, UC Davis) ate the dynamic student life that has become one Virtual properties of three-dimensional mani- of the great assets of CIRGET. folds Students, postdoctoral fellows, and Genevieve Walsh is now an Assistant Professor visitors at Tufts University. Altogether, in 2006 – 2007, 12 undergraduate Here is a list of the CIRGET postdoctoral fellows students, 34 master’s students, 20 Ph.D. students for 2006 – 2007, including their research interests. and 27 postdoctoral fellows were supervised or Ceyhan, Özgür (Ph.D. 2006, Strasbourg 1) cosupervised by regular or associate members of Real algebraic geometry and enumerative prob- the laboratory. lems Charbonneau, Benoit (Ph.D. 2004, MIT) Seminars Gauge theory Charbonneau has accepted a visiting professor CIRGET’s everyday scientific life revolves position at Duke University. around its weekly seminars and working groups

71 CENTRE DE RECHERCHES MATHÉMATIQUES where professors, postdoctoral fellows and stu- (Alberta), Steven Shin-Yi Lu (UQÀM), Peter dents meet on a regular basis. The CIRGET Ge- Russell (McGill) ometry and Topology Seminar, organized by Olivier Collin, is a general seminar series at- Members of the laboratory tended by all CIRGET members. Of the 24 talks given this year, 18 were given by invited speak- Regular members ers who stayed at the centre for short research STEVEN BOYER (UQÀM), Director visits. To complement this general seminar, CIR- Topology of manifolds, low-dimensional geom- GET organized two more specialized seminars etry and topology and one working group, so that three poles of research were developed: the Geometric Group VESTISLAV APOSTOLOV (UQÀM) Theory Seminar with 20 talks given (organizer: Complex geometry, Kähler geometry Dani Wise), the Symplectic Topology Seminar ABRAHAM BROER (Montréal) with 25 talks given (organizers: Ba¸sakGürel and Algebraic transformation groups, invariant the- Samuel Lisi), and the Working Group on Hee- ory gaard Floer Homology (organizer: Paolo Ghig- VIRGINIE CHARETTE (Sherbrooke) gini). Discrete group actions on affine varieties, CIRGET graduate students from UQÀM, Lorentz manifolds, Riemann surfaces discretiza- Université de Montréal and McGill continued to tion, discrete differential geometry participate in the CIRGET Junior Seminar, organized by Baptiste Chantraine, a doctoral student. OLIVIER COLLIN (UQÀM) This seminar gives graduate students a forum Invariants of knots and 3-manifolds arising from to present their research to their peers and to global analysis practice giving talks in a relaxed setting. It has OCTAVIAN CORNEA (Montréal) also created a natural meeting place for the stu- Algebraic topology, dynamical systems dents, who now form a cohesive interuniversity PENGFEI GUAN (McGill) student body. This year a total of 20 talks were Partial differential equations, geometric analy- given. sis, several complex variables JACQUES HURTUBISE (McGill) Workshops, special sessions, and others Algebraic geometry, integrable systems, gauge In 2006 – 2007, the members of CIRGET orga- theory, moduli spaces nized three conferences at the CRM. The first ANDRÉ JOYAL (UQÀM) two of these were actually sponsored by CIR- Algebraic topology, category theory GET. Reports on these conferences may be found NIKY KAMRAN (McGill) in the section on the CRM general program. Geometric approach to partial differential equa- • CONFERENCEON 3-MANIFOLD TOPOLOGYIN tions HONOUROF PETER SHALEN’S 60TH BIRTHDAY FRANÇOIS LALONDE (Montréal) June 12 – 15, 2006, CRM Symplectic topology and geometry, global Organizers: Steven Boyer (UQÀM), Richard analysis on manifolds, infinite dimensional Canary (Michigan), Marc Culler (Illinois at transformation groups Chicago), Nathan Dunfield (Caltech), Benson Farb (Chicago) STEVEN LU (UQÀM) Chern number inequalities, semi-stability of ten- • MINI-COURSESAND CONFERENCEON GEO- sorial sheaves, log jets, log and hyperbolic geom- METRIC GROUP THEORY etry, algebraic degeneracy July 3 – 14, 2006, CRM IOSIF POLTEROVICH (Montréal) Organizers: Mladen Bestvina (Utah), Steven Geometric analysis, spectral theory, functional Boyer (UQÀM), Tadeusz Januszkiewicz (Ohio), analysis, differential geometry, partial differen- Michah Sageev (Technion), Daniel T. Wise tial equations (McGill) PETER RUSSELL (McGill) • WORKSHOPONTHEGEOMETRYOFHOLO- Algebraic geometry MORPHICANDALGEBRAICCURVESINCOMPLEX ALGEBRAIC VARIETIES DANIEL T. WISE (McGill) April 30 – May 4, 2007, CRM Geometric group theory, low-dimensional topol- Organizers: Xi Chen (Alberta), James D. Lewis ogy

72 RESEARCH LABORATORIES

Associate members tems, group theoretical methods, random matrices, isomonodromic deformations, isospectral SYED TWAREQUE ALI (Concordia) ﬂows Coherent states, wavelets, quantization techniques, harmonic analysis, Wigner functions JOHN A.TOTH (McGill) JOHN HARNAD (Concordia) Spectral theory, semi-classical analysis, microlo- Mathematical physics, classical and quantum cal analysis, Hamiltonian mechanics physics, geometrical methods, integrable sys- LaCIM

Description sively with its regular members. A new UQÀM professor, Christophe Hohlweg, is a collaborat- LaCIM (French acronym meaning “Combina- ing member of LaCIM and will become a regu- torics and Mathematical Informatics Labora- lar member as soon as he is awarded an NSERC tory”) is home to mathematics and theoreti- grant. cal computer science researchers whose interests comprise discrete mathematics and the mathe- Students, postdoctoral fellows, and matical aspects of computer science. LaCIM was visitors founded in 1989 and is associated with the De- partment of Mathematics, the Department of In 2006 – 2007 five postdoctoral fellows were Computer Science, and the Canada Research working at LaCIM (the names of the supervi- Chair in Algebra, Combinatorics and Mathemat- sors are within parentheses): Nicola Gambino ical Informatics of the Université du Québec (André Joyal), Amy Glen (Srecko Brlek and à Montréal. LaCIM includes 13 regular mem- Christophe Reutenauer), Aaron Lauve (François bers (of whom 8 are UQÀM professors), 5 asso- Bergeron and Christophe Reutenauer), Sarah ciate members, and 14 collaborating members. Mason (François Bergeron) and Franco Saliola It welcomes postdoctoral fellows and its reg- (François Bergeron). Sarah Mason is now As- ular members supervise or cosupervise many sistant Professor at Davidson College (North M.Sc. or Ph.D. students, undergraduate students Carolina) and Aaron Lauve Visiting Assistant who do research work during the summer, and Professor in the Department of Mathematics of some cégep students. Many renowned mathe- Texas A&M University. Nicola Gambino is cur- maticians visit LaCIM and collaborate with its rently a postdoctoral fellow at the Centre de Re- members in the following areas: enumerative cerca Matemàtica in Barcelona (Spain). and bijective combinatorics, theory of species, Christophe Paul, of LIRMM (Montpellier), algebraic combinatorics, combinatorics of finite spent a sabbatical year at LaCIM working with and infinite words, discrete geometry, theory of Srecko Brlek and Cédric Chauve. Laurent Vuil- languages and automata, Gray codes, bioinfor- lon, of LAMA (Chambéry), visited LaCIM from matics, and combinatorial optimization. February to April 2007 and collaborated with Srecko Brlek and Christophe Reutenauer. Kia News and highlights Dalili visited LaCIM to work with Aaron Lauve. In 2006 – 2007, the following mathematicians vis- Gilbert Labelle retired in September 2006 but is ited François Bergeron: Christian Kassel (Stras- still a very active member of LaCIM. He was bourg 1), Jim Haglund (Pennsylvania), Mark made an Emeritus Professor by UQÀM. On Oc- Haiman (UC Berkeley), Richard Stanley (MIT), tober 18, 2006, during a convocation ceremony, Ernst Dieterich (Uppsala), Stéphanie van Willi- UQÀM awarded an honorary doctorate to Mau- genburg (UBC), and Adriano Garsia (UC San rice Nivat, Emeritus Professor at the Univer- Diego). As part of a CNRS project (“Projet In- sité Paris 6 and collaborator of Srecko Brlek ternational de Coopération Scientifique”) be- and Christophe Reutenauer. LaCIM is becom- tween LaBRI (Bordeaux 1) and LaCIM, Srecko ing ever more international, and in 2007 the fol- Brlek supervised the students Abdelaziz Hi- lowing distinguished researchers joined LaCIM: baoui from July 5 to August 5, 2006, and Omer- Jean Berstel (Marne-la-Vallée), Michel Mendès Landry Nguena-Timo from June 26 to August France (Bordeaux 1), Mark Haiman (UC Berke- 16, 2006. As part of Cédric Chauve’s coopera- ley) and Laurent Vuillon (Chambéry). These four tion project, Sylvie Hamel supervised the fol- mathematicians have been visiting LaCIM regu- lowing students: Sébastien Angibaud (Ph.D. stu- larly over the years and have collaborated exten- dent, LINA, Nantes), from November 27 to De-

73 CENTRE DE RECHERCHES MATHÉMATIQUES cember 16, 2006, Emric Gioan (CNRS, LIRMM, CRM Thematic Program. The semester was or- Montpellier), from November 22 to December ganized by several members of LaCIM, in- 2, 2006, and Annelyse Thevenin (Ph.D. student, cluding François Bergeron, Srecko Brlek, Pierre LRI, Paris-Sud), from November 6 to December Leroux and Christophe Reutenauer, and con- 16, 2006. sisted of schools and workshops on varied top- Altogether, in 2006 – 2007, 5 undergraduate ics. Students from all parts of the world took part students, 31 master’s students, 30 Ph.D. students in those events, which were of a very high cali- and 7 postdoctoral fellows were supervised by bre. Laboratory members. Seminars Members of the laboratory The LaCIM Combinatorics and Theoretical In- Regular members formatics Seminar, held weekly on Friday morn- SRECKO BRLEK (UQÀM), Director ings, is attended regularly by LaCIM mem- Combinatorics of words, algorithmics bers, graduate students and postdoctoral fellows. The lectures are sometimes given by mem- ROBERT BÉDARD (UQÀM) bers of other CRM laboratories (for instance Representations of ﬁnite groups, Lie theory Andrew Granville and Alexei Miasnikov), but FRANÇOIS BERGERON (UQÀM) most of them are given by visitors. Let us men- Combinatorics, algebra, representations of ﬁnite tion Jeff Remmel (San Diego), Luigi Santocanale groups (LIF/CMI, Marseille), Angèle Hamel (Wilfrid Laurier), Damien Roy (Ottawa), Christian Kas- CEDRIC CHAUVE (Simon Fraser and UQÀM) sel (Strasbourg), Christophe Hohlweg (Fields, Enumerative combinatorics, trees, bioinformat- Toronto), Kia Dalili (Dalhousie), Pierre Cartier ics (IHÉS), Denis Serbin (McGill), Mark Haiman ALAIN GOUPIL (UQTR) (Berkeley) and George Lusztig (MIT). There Combinatorics, algebra, linear representations of were no lectures during the Winter 2007 term, groups, symmetric group because at that time the focus of LaCIM mem- SYLVIE HAMEL (Montréal) bers was the Thematic Semester on Recent Ad- Bioinformatics and algorithms, theory of lan- vances in Combinatorics (see below). guages and automata, algebraic combinatorics

Workshops, special sessions, and others GILBERT LABELLE (UQÀM) In September 2006, François Bergeron, Srecko Enumerative combinatorics, analysis Brlek and Christophe Reutenauer organized a PIERRE LEROUX (UQÀM) Conference in honour of Pierre Leroux. The goal Enumerative and algebraic combinatorics of the conference was to highlight his contri- VLADIMIR MAKARENKOV (UQÀM) butions to the development of combinatorics Computational biology, mathematical classiﬁca- at UQÀM and elsewhere, and especially to the tion founding of LaCIM. Although Pierre Leroux is now retired, he is actively involved in research JOHN MULLINS (Polytechnique Montréal) and remains one of the driving forces of LaCIM. Analysis of cryptographic protocols and e- A detailed report on this conference may be commerce protocols, formal semantics, secure found in the section on the CRM General Pro- mobile code speciﬁcation, operational concur- gram. rency models • CONFERENCEINHONOUROF PIERRE CHRISTOPHE REUTENAUER (UQÀM) LEROUX Algebraic combinatorics, noncommutative alge- September 8 – 9, 2006, Université du Québec à bra, automata theory, coding theory, free alge- Montréal bras Organizers: Srecko Brlek (UQÀM), Christophe DENIS THÉRIEN (McGill) Reutenauer (UQÀM), François Bergeron Complexity theory, logic, combinatorics, proba- (UQÀM) bility theory On the other hand, the Thematic Semester on Recent Advances in Combinatorics was a TIMOTHY R.S.WALSH (UQÀM) resounding success; a detailed report on this Algorithmics, enumerative combinatorics, semester may be found in the section on the graph theory

74 RESEARCH LABORATORIES

Associate members maps and cacti, theory of species, Lagrange in- version formulas PIERRE LALONDE (Cégep Maisonneuve) Enumerative and bijective combinatorics, alter- YVES CHIRICOTA (UQÀC) nating sign matrices, enumeration of involutions Computer graphics, mathematical methods in with respect to various parameters, use of pfafﬁ- computer graphics, combinatorics, computa- ans and determinants in enumeration tional geometry, symbolic computation CÉDRIC LAMATHE (UQÀM) SYLVIE CORTEEL (LRI, Paris-Sud) Combinatorics of tree-like structures, theory Enumerative and bijective combinatorics, parti- of species, indicator series of partially labeled tions of integers and q-series structures and asymmetric structures ADRIANO GARSIA (UC San Diego) LUC LAPOINTE (Talca) Algebraic combinatorics, symmetric functions, Algebraic combinatorics, symmetric functions, harmonic and co-invariant spaces, quasihar- integrable systems, supersymmetries monic and quasi-invariant functions ODILE MARCOTTE (UQÀM and CRM) ANDRÉ JOYAL (UQÀM) Combinatorial optimization, integer program- Algebraic topology, category theory ming, graph theory JACQUES LABELLE (UQÀM) DOMINIC ROCHON (UQTR) Combinatorics, topology Complex analysis, hypercomplex numbers LOUISE LAFOREST (UQÀM) Collaborating members Data structures, combinatorics, asymptotic analysis, quaternary trees MARCELLO AGUIAR (Texas A&M) DANIEL LEMIRE (TELUQ) Algebraic combinatorics, non-commutative al- Database theory, data warehousing, multidi- gebra, Hopf algebras and quantum groups, cat- mensional databases (OLAP), data mining, time egory theory series, collaborative ﬁltering, information re- LUC BÉLAIR (UQÀM) trieval Mathematical logic, model theory SIMON PLOUFFE NANTEL BERGERON (York) Integer sequences, generalized expansions of Applied algebra real numbers PIERRE BOUCHARD (UQÀM) XAVIER G.VIENNOT (Bordeaux 1) Commutative algebra, algebraic geometry and Enumerative, algebraic, and bijective combina- combinatorics torics, interactions between combinatorics, theo- MICHEL BOUSQUET (Cégep du Vieux-Montréal) retical informatics, and theoretical physics Enumeration of combinatorial structures, planar Mathematical Analysis

Description ematics, probability, nonlinear analysis, nonlinear differential equations, topological methods At the same time classical and central to modern in differential equations, ﬂuid dynamics, and mathematics, analysis involves the study of con- turbulence. tinuous systems, from dynamical systems to solutions of partial differential equations and spec- News and highlights tra of operators. Currently the Laboratory has 32 regular and 6 associate members working at Eugene Kritchevski, a Ph.D. student in Analysis eight different universities in Québec, the United at McGill, won the Carl Herz Prize. Congratu- States and France. The members of the Labo- lations! The Carl Herz Prize, awarded annually, ratory work in the following areas: harmonic recognizes a research contribution to mathemat- analysis, complex analysis and several complex ics or statistics made by a doctoral student regis- variables, potential theory, functional analysis, tered at one of the ISM member universities (see Banach algebras, microlocal analysis, analysis on the section on Mathematical Education). manifolds, nonsmooth analysis, spectral theory, Alina Stancu (Concordia) has become a reg- partial differential equations, geometric analy- ular member of the laboratory in 2006 – 2007 and sis, ergodic theory and dynamical systems, con- Alexey Kokotov (Concordia) an associate mem- trol theory, mathematical physics, applied math- ber in 2007 – 2008. Welcome!

75 CENTRE DE RECHERCHES MATHÉMATIQUES

Students, postdoctoral fellows, and etry and Topology that featured 10 talks in 2006 – visitors 2007. At the Université de Montréal, Paul Gau- thier organized a Séminaire d’analyse featuring In 2006 – 2007, the following postdoctoral fel- 7 talks and Iosif Polterovich a Working Semi- lows were working with members of the Math- nar in Spectral Geometry that featured 12 talks. ematical Analysis Laboratory (the names of the Finally, Eugene Kritchevski and Ivo Panayotov supervisors are within parentheses): Constantin organized a Student Seminar in Analysis and Costara (Thomas Ransford), Sara Derivière Probability (Concordia/McGill/Montréal) that (Tomasz Kaczynski), Dan Mangoubi (Dmitry featured 11 talks. Jakobson and Iosif Polterovich), Andrew McIn- tyre (D. Korotkin), Julie Rowlett (Dmitry Jakob- Workshops, special sessions, and others son, John Toth and Iosif Polterovich), Igor Wigman (Dmitry Jakobson, John Toth, An- In 2006 – 2007 the following conferences were or- drew Granville, Iosif Polterovich and Alexander ganized by members of the Mathematical Analy- Shnirelman), and Chang Zhong Zhu (Paul Gau- sis Laboratory. Detailed reports on these confer- thier). Altogether, in 2006 – 2007, 9 undergradu- ences may be found in the section on the CRM ate students, 40 master’s students, 39 Ph.D. stu- General Program. dents and 15 postdoctoral fellows were super- • GILLES FOURNIER MEMORIAL CONFERENCE vised or cosupervised by regular or associate ON CLASSICALAND COMPUTATIONAL TOPO- members of the laboratory. LOGICAL METHODS The Mathematical Analysis Laboratory also September 22 – 24, 2006, Université de Sher- welcomed the following researchers: M. Aizen- brooke man (Princeton), P. Bachurin (Toronto), A. Sponsored by the CRM, the Mathematical Blanco (Queen’s University Belfast), A. Bourhim Analysis Laboratory (CRM), Bishop’s University (Moncton), D. Chang (Georgetown), D. G. de and the Faculty of Sciences of the Université de Figueiredo (Campinas, Brazil), D. Dryanov, E. Sherbrooke Fricain (Lyon), F. Germinet (Cergy-Pontoise), Organizers: Madjid Allili (Bishop’s), Tomasz A. Koldobsky (Missouri), J.-P. Lessard (Georgia Kaczynski (Sherbrooke) Tech), M. Levitin (Heriot-Watt), V. Matsaev (Tel Aviv), M. Monastyrski (Moscow), A. Moudaﬁ • ANALYSIS DAY 2007 (Université des Antilles et de la Guyane), Y. Pau- May 2, 2007, CRM trat (Orsay), R. Pereira (Saskatchewan), M. Pra- Organizer: Dmitry Jakobson (McGill) manik (UBC), R. Roussarie (Dijon), D. Ruelle (IHÉS), Y. Safarov (King’s College London), D. Members of the laboratory Schenker (Princeton), R. Schubert (Bristol), R. Regular members Shvydkoi (Chicago), L. Stolovitch (Toulouse), E. Stredulinsky (Wisconsin), A. Strohmaier (Bonn), DMITRY JAKOBSON (McGill), Director S. Warzel (Princeton), M. White (Newcastle), and Pure mathematics, global analysis, spectral ge- S. Zelditch (Johns Hopkins). ometry, quantum chaos, harmonic analysis, eigenvalues and eigenfunctions Seminars LINE BARIBEAU (Laval) Complex and functional analysis, Banach alge- The members of the Mathematical Analysis bras, holomorphic iterations, discrete groups Laboratory organize several seminars at four main locations. Laval University hosts an Analy- ABRAHAM BOYARSKY (Concordia) sis Seminar, which featured 20 talks in 2006 – Dynamical systems 2007, and an Analysis Workshop, which fea- FRANCIS H.CLARKE (Lyon 1) tured 21 talks. Alex Shnirelman (Concordia) and Nonlinear and dynamic analysis, control theory, Dmitry Jakobson (McGill) organize jointly the calculus of variations McGill/Concordia Analysis Seminar, which fea- GALIA DAFNI (Concordia) tured 31 talks in 2006 – 2007. At the Université de Harmonic analysis, partial differential equa- Montréal, Christiane Rousseau organizes a Sem- tions, several complex variables inar in Nonlinear Analysis and Dynamical Sys- tems that featured 9 talks in 2006 – 2007. At the DONALD A.DAWSON (Carleton) Université de Sherbrooke, Madjid Allili, Virginie Probability, stochastic processes Charette, François Dubeau and Tomasz Kaczyn- S. W. DRURY (McGill) ski organize a Seminar in Computational Geom- Harmonic analysis, matrix theory

76 RESEARCH LABORATORIES

RICHARD DUNCAN (Montréal) CHRISTIANE ROUSSEAU (Montréal) Ergodic theory, martingale theory, probability Dynamical systems, bifurcations, qualitative theory in Banach spaces theory, polynomial systems, analytic invariants, RICHARD FOURNIER (Dawson College) integrable systems Complex analysis, function theory DANA SCHLOMIUK (Montréal) MARLÈNE FRIGON (Montréal) Global analysis, dynamical systems, singulari- Nonlinear analysis, differential equations, fixed ties, bifurcations, algebraic curves, primary inte- point theory, critical point theory, multivalent gral analysis ALEXANDER SHNIRELMAN (Concordia) Applications of geometric analysis to fluids and PAUL M.GAUTHIER (Montréal) “weak” solutions of the Euler and Navier – Complex analysis, holomorphy, harmonicity, an- Stokes equations alytic approximation ALINA STANCU (Concordia) PAWEL GORA (Concordia) Geometric analysis Ergodic theory, dynamical systems, fractal geometry RON J.STERN (Concordia) Functional analysis and theory of operators, lin- FRÉDÉRIC GOURDEAU (Laval) ear and nonlinear systems, non-smooth analysis, Banach algebras, cohomology, amenability, func- stability, optimal order tional analysis JOHN A.TOTH (McGill) KOHUR GOWRISANKARAN (McGill) Spectral theory, semi-classical analysis, microlo- Potential theory cal analysis, Hamiltonian mechanics ´ VOJKAN JAKŠIC (McGill) SAMUEL ZAIDMAN (Montréal) Mathematical physics, quantum statistical me- Functional analysis and differential equations in chanics, random Schrödinger operators abstract spaces, pseudo-differential operators TOMASZ KACZYNSKI (Sherbrooke) Associate members Topological methods, Conley index, applications to dynamical systems OCTAVIAN CORNEA (Montréal) IVO KLEMES (McGill) Algebraic topology, dynamical systems Harmonic analysis, trigonometric series PENGFEI GUAN (McGill) ALEXEY KOKOTOV (Concordia) Partial differential equations, geometric analy- Spectral geometry of Riemann surfaces, hyper- sis, several complex variables bolic partial differential equations JOHN HARNAD (Concordia) Mathematical physics, classical and quantum PAUL KOOSIS (McGill) Harmonic analysis physics, geometrical methods, integrable systems, group theoretical methods, random ma- JAVAD MASHREGHI (Laval) trices, isomonodromic deformations, isospectral Complex analysis, harmonic analysis, Hardy flows spaces NIKY KAMRAN (McGill) YIANNIS N.PETRIDIS (Lehman College, CUNY) Geometric approach to partial differential equa- Automorphic forms and their spectral theory, tions analytic number theory, spectral and scattering DMITRY KOROTKIN (Concordia) theory of manifolds Integrable systems, isomonodromic deforma- IOSIF POLTEROVICH (Montréal) tions, classical and quantum gravity, Frobenius Geometric analysis, spectral theory, functional varieties analysis, differential geometry, partial differen- NILIMA NIGAM (McGill) tial equations Applied analysis, numerical methods in electro- THOMAS J.RANSFORD (Laval) magnetism Complex and harmonic analysis, functional analysis and theory of operators, spectral analysis, potential theory DOMINIC ROCHON (UQTR) Complex analysis, hypercomplex numbers JÉRÉMIE ROSTAND (Laval) Complex analysis, experimental mathematics

77 CENTRE DE RECHERCHES MATHÉMATIQUES

Mathematical Physics

Description JiˇríPatera (2004). He was also the recipient, in October 2006, of the first Concordia University The mathematical physics group is one of the FAS Dean’s Award for Distinguished Scholar- oldest and most active at the CRM. It consists ship. of fourteen regular members, all full-time fac- John Harnad was an invited organizer, ulty at five Quebec Universities, and fourteen as- jointly with Jinho Baik (University of Michigan), sociate members. The Laboratory also includes of the session on Random Matrices at the Au- eight research associates and postdoctoral fel- gust 2006 International Congress of Mathemat- lows, and lab members supervise or cosupervise ical Physics (ICMP), which was held in Rio de the thesis work of approximately fifty students. Janeiro. The ICMP takes place every three years. The group hosts many visiting researchers and In October 2006, Pavel Winternitz was awarded carries out research in many of the most active a Doctorate Honoris Causa by the Czech Techni- areas of mathematical physics: coherent nonlin- cal University (Prague). The PhysMath Lab be- ear systems in fluids, optics and plasmas; classi- stowed its “best student” awards for 2006 – 2007 cal and quantum integrable systems; the spectral to two doctoral students completing their thesis theory of random matrices; percolation phenom- research under the supervision of Lab members. ena; conformal field theory; quantum statistical The recipients were: 1) Ferenc Balogh (Concor- mechanics; spectral and scattering theory of ran- dia), whose doctoral research, under the super- dom Schrödinger operators; quasi-crystals; rela- vision of John Harnad, is on equilibrium mea- tivity; spectral transform methods; asymptotics sures of log Coulomb gases, spectral distribu- of eigenstates; foundational questions in quanti- tions of random normal matrices, orthogonal zation; coherent states; wavelets; supersymme- polynomials in the plane and Laplacian growth; try; the symmetry analysis of PDE’s and dif- and: 2) Benoit Huard (Université de Montréal), ference equations; representation theory of Lie whose doctoral research, under the supervision groups and quantum groups; and the mathemat- of Michel Grundland, is on conditional symme- ical structure of classical and quantum field the- tries and Riemann invariants for hyperbolic sys- ories. tems of PDEs. News and highlights The preparatory work for the 2008 – 2009 CRM Thematic Program on Probabilistic Meth- After a major reorganization in the previous ods in Mathematical Physics began in May year (2005 – 2006), the PhysMath Lab member- 2006. This involved choosing, first of all, two ship, consisting of fourteen regular members further coordinators, Pavel Bleher (IUPUI) and and fourteen associate members, remained in- Steve Zelditch (Johns Hopkins), who, together variant during the 2006 – 2007 academic year. with Lab Director John Harnad, were respon- Five of the Associate members are “external” sible for selecting the Scientific Committee and members, three from France, one from Italy and guiding the program into existence. The Sci- one from the U.S., all close collaborators of reg- entific Committee consists of four Canadians: ular members of the Lab and frequent visitors at David Brydges (UBC), John Harnad (Concor- the CRM. dia), Yvan Saint-Aubin (Montréal), and Pavel John Harnad was recipient of the 2006 CAP – Winternitz (Montréal); four Americans: Pavel CRM Prize in Theoretical and Mathematical Bleher (IUPUI), Charles Newman (Courant In- Physics, which was conferred at the annual stitute), Craig Tracy (UC Davis), and Steve Congress of the Canadian Association of Physi- Zelditch (Johns Hopkins); and three Europeans: cists (CAP) at Brock University, in June 2006. Alice Guionnet (ENS, Lyon), Herbert Spohn (TU This award is given annually jointly by the CAP München), and Jean-Bernard Zuber (LPTHE, and the CRM, “in recognition of exceptional Paris 6). achievements in theoretical and mathematical The program was decided upon by the co- physics.” He gave a plenary talk at the CAP ordinators, in consultation with the Scientific congress entitled “Shadows on the Wall: Plato’s Committee and partly in consultation with a Parable of the Cave as a metaphor for Integrable committee based at PIMS (which is planning Dynamics and Spectral Statistics.” Harnad was a joint PIMS – CRM 2009 Program on New the third recipient of the award amongst the Trends in Probability Theory). It will consist members of the CRM PhysMath Lab — the pre- mainly of: eleven research workshops, each last- vious winners being Pavel Winternitz (2002) and ing one week, nine of which will take place

78 RESEARCH LABORATORIES in Montréal, one in the Laurentian Mountains plied Mathematics (OCIAM). Former doctoral and one at the Banff International Research Sta- student Oksana Yermolayeva was continuing as tion; three Aisenstadt Chairs: Wendelin Werner Marie Curie Research Fellow at the International (2006 Fields Medallist), Craig Tracy (2002 SIAM School for Advanced Studies (SISSA) in Trieste, Pólya Prize and 2007 SIAM Wiener Prize win- and former student Vasilisa Schramchenko di- ner), and Andrei Okounkov (2006 Fields Medal- vided her time over the past two years (2005 – list); twenty-four long-term visitors who will be 2007) between the Max Planck Institut in Bonn at the CRM for periods of three to four weeks, (where she held an Alexander von Humboldt plus one, Pavel Bleher, who will be staying for Fellowship) and the Mathematical Institute at a five-month period; five postdoctoral fellows the University of Oxford (where she held an EP- working under the supervision of Lab members SRC postdoctoral research fellowship and was a on subjects lying within the scope of the The- Junior Fellow of Worcester College). matic Year; and several preparatory courses on Altogether, in 2006 – 2007, 6 undergraduate related topics, given by lab members and long- students, 37 master’s students, 21 Ph.D. students term visitors. This CRM Thematic Program will and 17 postdoctoral fellows were supervised or take place between June 2, 2008 and June 14, cosupervised by regular or associate members of 2009. More details may be found on the CRM the laboratory. The following is a list of the re- web site. searchers who visited the Lab in the period July Two further events organized by Lab mem- 2006 – June 2007, as guests of one or more of the bers will take place in June 2008: the NATO Ad- Lab members. Many of these are collaborators vanced Study Institute (June 9 – 21, 2008), and and/or external Associate Members. Their affili- the international workshop SIDE 8 (June 22 – 28, ations and the names of their hosts are indicated 2008). Both events are on the same general theme within parentheses. (Symmetries and Integrability of Discrete Equa- • J. M. Antuna (La Habana), May 1 – August 28, tions). The main organizer for these events is 2006 (T. Ali and R. Hall) Pavel Winternitz, helped by Decio Levi (Roma 3) • L. Lapointe (Talca), June 10 – 15, 2006 (P. and Peter Olver (Minnesota). Other lab members Mathieu) on the organizing committee are John Harnad, • B. Doyon (Oxford), August 6 – 10, 2006 (P. Véronique Hussin and Luc Vinet. More details Mathieu) crm.math.ca/SIDE8/ may be found on the site • O. Sanchez (La Habana), September 1 – 30, contact_e.shtml . 2006 (T. Ali) Students, postdoctoral fellows, and • P. Desrosiers (Melbourne), September – visitors December, 2006 (P. Mathieu) • V. Enolskii (Kiev), September – December, The following postdoctoral fellows and research 2006 (J. Harnad) associates worked in 2006 – 2007 under the su- • L. Snobl (Czech Technical University), pervision of one or more of the regular mem- September 9 – 30, 2006 (P. Winternitz) bers of the PhysMath Lab (the names of the • M. Englis (Czech Academy of Sciences, supervisors are listed within parentheses): Iana Prague), September 5 – 17, 2006 (T. Ali) Anguelova (M. Bertola, J. Harnad, C. Cum- • W. Lucha (Austrian Academy of Sciences), mins), Armen Atoyan (research associate, J. October 2006 (R. Hall) Patera), Mhenni Benghorbal (R. Hall), Mickaël • A. Orlov (Oceanology Institute, Moscow), Germain (J. Patera), Andrew McIntyre (D. Ko- October 2 – 30, 2006, and January 8 – February 8, rotkin, M. Bertola), Man Yue Mo (J. Hurtubise, 2007 (J. Harnad) M. Bertola), Maryna Nesterenko (collaborator, J. • Z. Thomova (SUNY, IT Utica), October 26 – 31, Patera), Béla Gábor Pusztai (M. Bertola, J. Har- 2006, and January 8 – 14, 2007 (P. Winternitz) nad, D. Korotkin), David Ridout (P. Mathieu), Is- • D. Levi (Roma 3), October 28 – November 28, met Yurdusen (collaborator, Michel Grundland, 2006 (P. Winternitz) Véronique Hussin, Pavel Winternitz). • Maia Angelova (Newcastle, Northumbria), Amongst our recent postdoctoral fellows November 2006 (V. Hussin) and students, Man Yue Mo completed a year • Jean-Pierre Gazeau (Paris 6), November 4 – 11, on a postdoctoral research position at the Uni- 2006 (T. Ali, J. Patera and M. Grundland) versity of Bristol, where he is continuing in • Robert Conte (CEA, Saclay), November 4 – 11, 2007 – 2008, and Igor Loutsenko spent the two 2006 (M. Grundland) years 2005 – 2007 as Marie Curie Research Fel- • Jørgen Rasmussen (Melbourne), November low at the Oxford Centre for Industrial and Ap- 6 – 10, 2006 (Y. Saint-Aubin)

79 CENTRE DE RECHERCHES MATHÉMATIQUES

• Mark Bodner, November 29 – 30, 2006 (J. doctoral fellow) were the organizers of this sem- Patera) inar. • Erhard Neher (Ottawa), December 5 – 6, 2006 (J. Patera) • Patrick Jacob, Durham, December 19 – 21, 2006 (P. Mathieu) Workshops, special sessions, and others • John Van de Leur (Utrecht), January 20 – 30, 2007 (J. Harnad) S.T. Ali and members of the Department of • Pavel Bleher (IUPUI), January 25 – 27, 2007 (J. Physics of the University of Havana, with ac- Harnad) tive input from further members of the Phys- • Vyacheslav Furtony (São Paulo), January 30 – Math Lab (J. Harnad) and members of CICMA February 2, 2007 (J. Patera) (H. Kisilevsky), organized again an International • Iryna Kashuba (São Paulo), December 8, Workshop on Differential Equations, Number 2006 – February 28, 2007 (J. Patera) Theory, Data Analysis Methods and Geometry. • B. Eynard (CEA Saclay, France), March 18 – 30, This workshop was on a much larger scale than 2007 (J. Harnad) the previous ones, and took place at the beauti- • Slava Yukalov (Dubna, Russia), March 2007 fully located and historic Hotel Nacional in cen- (R. Hall) tral Havana. The PhysMath Lab provided some • Alexander Its (IUPUI), March 12 – 17, 2007 (J. resources (web site, poster), as well as some Harnad) modest ﬁnancial support. A detailed report on • Michael Gekhtman (Notre Dame), April 9 – 13, this event may be found in the section on the 2007 (M. Bertola) CRM general program. • Jacek Szmilgielski (Saskatchewan), April 9 – • XTH INTERNATIONAL WORKSHOPON DIF- 13, 2007 (M. Bertola) FERENTIAL EQUATIONS,NUMBER THEORY, • Philip Boalch (ENS, Paris), April 23 – 30, 2007 DATA ANALYSIS METHODSAND GEOMETRY (J. Harnad and J. Hurtubise) February 19 – 23, 2007, Universidad de La Ha- • Anatoliy Klimyk (Kiev, Ukraine), April 23 – bana May 31, 2007 (J. Patera) Sponsored by the Faculty of Mathematics and • Willy Hereman (Colorado School of Mines), Computation of the University of Havana, the May 12 – 31, 2007 (M. Grundland) Department of Mathematics and Statistics of • Robert Conte (CEA, Saclay), April 9 – 24, 2007 Concordia University, the Institute of Cybernet- (M. Grundland) ics, Mathematics and Physics of the Academy of • P.-G. Tempesta (SISSA, Trieste), Spring 2007 (P. Sciences of Cuba, and the CRM Winternitz) Organizers: Syed Twareque Ali (Concordia), • G. Pogosyan (Yerevan, Dubna), Spring 2007 (P. Reinaldo Rodriguez Ramos (La Habana), Winternitz) François Lalonde (Montréal) Seminars John Harnad was one of the organizers of a conference honouring John McKay. A detailed The usual weekly Seminar Series in Mathemat- report on this conference may be found in the ical Physics took place at the CRM every Tues- section on the CRM general program. day afternoon throughout both terms, with active participation by members, visitors, postdoc- • “GROUPSAND SYMMETRIES:FROMTHE NE- toral fellows and students. Michel Grundland OLITHIC SCOTSTO JOHN MCKAY” (UQTR) and S. Twareque Ali (Concordia) were CONFERENCE HONOURINGTHE CONTRIBU- the organizers for the 2006 – 2007 academic year. TIONSOF JOHN MCKAY Approximately half the talks were given by vis- April 27 – 29, 2007, CRM iting invited speakers, the rest by regular and Sponsored by CRM, Concordia University, and associate lab members, postdoctoral fellows and CICMA visitors. Organizers: John Harnad (Concordia), Pavel In addition, the Working Seminar on Inte- Winternitz (Montréal) grable Systems, Random Matrices, Random Pro- From May 12 to July 28, 2006, Yvan Saint- cesses continued, taking place every Thursday Aubin held a workshop on the renormalizaton afternoon at Concordia, with the active partici- group (Atelier d’étude sur le groupe de renormal- pation of many lab members, students, postdoc- isation). This was a weekly workshop geared toral fellows and visitors. In 2006 – 2007 Marco towards graduate students; 8 participants at- Bertola (Concordia) and Iana Anguelova (post- tended the workshop.

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Members of the laboratory Associate members

Regular members ROBERT CONTE (CEA Saclay) Integrable and partially integrable systems, JOHN HARNAD (Concordia), Director Painlevé analysis, exact solutions, finite differ- Mathematical physics, classical and quantum ence equations physics, geometrical methods, integrable sys- CHRIS CUMMINS (Concordia) tems, group theoretical methods, random ma- Group theory, modular functions, moonshine trices, isomonodromic deformations, isospectral flows STÉPHANE DURAND (Cégep Édouard- Montpetit) SYED TWAREQUE ALI (Concordia) Coherent states, wavelets, quantization tech- Classical and quantum physics, mathemati- niques, harmonic analysis, Wigner functions cal physics, symmetries, parasupersymmetries, fractional supersymmetries, KdV equations, MARCO BERTOLA (Concordia) quantum mechanics, relativity Axiomatic quantum field theory, invariant BERTRAND EYNARD (CEA Saclay) theory of discrete groups, random matrices, Matrix models, integrable systems, string theory, isomonodromic deformations relationship between matrix models, integrabil- ALFRED MICHEL GRUNDLAND (UQTR) ity and algebraic geometry Symmetry of differential equations in physics JEAN-PIERRE GAZEAU (Paris 7) RICHARD L.HALL (Concordia) Coherent states, wavelets, relativistic quantum Spectra of Schrödinger, Klein – Gordon, Dirac frames, symmetry groups for beta-lattices and Salpeter operators, many-body problems, ALEXANDER ITS (IUPUI) relativistic scattering theory, iterative solution to Soliton theory, integrable systems, special func- ODEs and boundary-value problems tions, mathematical physics ACQUES URTUBISE J H (McGill) DMITRY JAKOBSON (McGill) Algebraic geometry, integrable systems, gauge Pure mathematics, global analysis, spectral ge- theory, moduli spaces ometry, quantum chaos, harmonic analysis, VÉRONIQUE HUSSIN (Montréal) eigenvalues and eigenfunctions Group theory, Lie algebras and applications in VOJKAN JAKŠIC´ (McGill) physics, supersymmetries in classical and quan- Mathematical physics, quantum statistical me- tum mechanics chanics, random Schrödinger operators DMITRY KOROTKIN (Concordia) NIKY KAMRAN (McGill) Integrable systems, isomonodromic deforma- Geometric approach to partial differential equations, classical and quantum gravity, Frobenius tions varieties FRANÇOIS LALONDE (Montréal) JEAN LETOURNEUX (Montréal) Symplectic topology and geometry, global Symmetry properties of systems, special func- analysis on manifolds, infinite dimensional tions transformation groups PIERRE MATHIEU (Laval) DECIO LEVI (Roma 3) Conformal field theory, classical and quantum Symmetries of differential and difference equa- integrable systems, affine Lie algebras tions, integrable nonlinear equations on the lat- JIRÍˇ PATERA (Montréal) tice and reductive perturbation theory on the lat- Applications of group theory, quasi-crystals, Lie tice algebras ALEXANDER SHNIRELMAN (Concordia) YVAN SAINT-AUBIN (Montréal) Applications of geometrical analysis to fluids Conformal field theory, statistical mechanics, 2- and “weak” solutions of the Euler and Navier – dimensional phase transition model Stokes equations LUC VINET (Montréal) JOHN A.TOTH (McGill) Symmetry properties of systems, special func- Spectral theory, semi-classical analysis, microlo- tions cal analysis, Hamiltonian mechanics PAVEL WINTERNITZ (Montréal) CAROLYNE M.VAN VLIET (Miami) Methods of group theory in physics, nonlinear Non-equilibrium statistical mechanics, fluctua- phenomena, symmetries of difference equations, tions and stochastic processes, quantum trans- superintegrability port in condensed matter, electronic behavior in submicron quantum devices

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PhysNum

Description tracranial signals in the context of epilepsy), and to study the specters of singularities in the pre- PhysNum is a laboratory dedicated to the study ictal phase (i.e., the phase just before a fit of and solution of mathematical problems arising epilepsy). The work of the team relies on the in medicine and pharmacology. We first describe use of “wavelet leaders” within the framework the work of the PhysNum – MIC group, where of Daubechies complex wavelets. MIC stands for “Mathématiques de l’Imagerie The research interests of Fahima Nekka, a Cérébrale” (Mathematics of Brain Imaging). professor at the Faculty of Pharmacy of the The members of the PhysNum – MIC group Université de Montréal, are in pharmacokinetic specialize in brain imaging methodology and models and the application of fractal analysis functional neuroimaging, in particular the mod- to porous media. One of her projects consists elling of cerebral activity, the analysis method- of studying the pharmacokinetic variability in- ology for optical and bioelectrical signals, the duced by drug intake behaviour in animal col- solution of inverse problems that include mul- lective therapy. The non-uniform access to med- timodal data, time-frequency analyses, and the icated feed, influenced by swine individual feed- synchrony and specter of singularities of in- ing behaviour, is a determinant of antibiotic ex- tracranial electroencephalography signals. On posure. F. Nekka and her team used reported an- the other hand, Frédéric Lesage is developing imal behaviour to propose a feeding behaviour new imaging modalities for small animals, espe- pharmacokinetic model of in-feed chlortetracy- cially photo-acoustic imaging and intrinsic opti- cline; they were able to delineate the impact cal imaging; in his work, he uses recent results of different feeding behaviour components and from approximation theory (“compressed sens- characterize the induced model variability. This ing”) to develop ground-breaking innovations work enabled them to offer a practical tool, in- in methodology. corporated into medical practice, for choosing a Habib Benali works on the modelling of dosing regimen based on dose and age. physiological brain processes and has devel- In a second project, F. Nekka and her team oped models of interaction between the neuron are using a random time series approach to for- populations whose activity is detected through malize the drug intake behaviour of patients and functional magnetic resonance imaging (fMRI) make it an integral part of a general pharma- or electroencephalography (EEG). His goal is cokinetic model. They showed that the random to obtain a better interpretation of the signals features of drug intake behaviour, previously produced by these two modalities and, broadly treated as “noise,” are in fact an inherent compo- speaking, to understand better the functional nent of the mechanistic model. Thus the variabil- connectivity of the brain. Habib Benali’s research ity in compliance adds an additional variation to thus sheds light on the learning and adaptive the regular oscillation curves of the main drug processes of the brain, on the postoperative re- administration routes. F. Nekka and her team cuperation processes, and on the BOLD signal of have properly characterized this variation; their spinal chord imaging. work will allow an objective medical interven- All members of the PhysNum – MIC group tion and can be adapted to different compliance belong to a research team financed by FQRNT, patterns in various pathologies. the Québec government granting agency. The Fahima Nekka and her research group are goal of this team is to develop methods of analy- also working on the processing of complex data sis for signals produced by different method- and the application of complexity analysis to ologies (optical imaging, EEG, MEG, and fMRI). polymers and porous media (which are widely The team members use variational calculus tech- used as vehicles for drug delivery). The design niques and entropy-based methods to solve in- of synthetic polymers has been revolutionized verse problems arising in the detection of neu- by the recent achievements in high-resolution, ronal activity through several imaging modali- broad-mass-range spectrometry. Wave propaga- ties (including optical imaging). Jean-Marc Lina tion and scattering through porous media and uses techniques based on analytic wavelets to highly ramified materials give rise to (spatial) study bioelectrical signals in the brain. The two signals that can be considered as defined on frac- goals of the team are to study the synchronies tal systems. The autocorrelating process is a clas- and “skeletons” in the time/frequency plane sical mathematical method widely used in engi- of the signals (optical signals, EEG signals, in- neering and the applied sciences to reorganize

82 RESEARCH LABORATORIES intrinsic similarities hidden in a structure. On 5. J. Cohen-Adad, S. Chapuisat, J. Doyon, S. the other hand, fractal methods enable one to Rossignol, J.-M. Lina, H. Benali, F. Lesage, Ac- quantify efﬁciently complex information based tivation detection in diffuse optical imaging by on existing similarities. The inadequacy of tra- means of the general linear model, Medical Im- ditional methods and the known limitations of age Analysis, 2007 (in press). popular fractal methods led F. Nekka to combine 6. J. Daunizeau, C. Grova, G. Marrelec, J. Mat- both approaches in order to create more power- tout, S. Jbabdi, M. Pélégrini-Issac, J.-M. Lina, ful and less degenerate methods. H. Benali, Symmetrical event-related EEG/fMRI information fusion in a variational Bayesian Students framework, Neuroimage, 2007, 36(1):69 – 87. In 2006 – 2007, Frédéric Lesage supervised the 7. S. Jbabdi, P. Bellec, R. Toro, J. Daunizeau, M. Ph.D. students Sarah Chapuisat (in collaboration Pélégrini-Issac, H. Benali, Accurate anisotropic with H. Benali) and Mathieu Dehaes, and the fast marching for diffusion-based geodesic trac- master’s students Nicolas Brieu, Michèle Des- tography, International Journal of Biomedical jardins, Louis Gagnon, Carl-Matteau Pelletier Imaging, 2007 (in press). (in collaboration with J.-M. Lina), Jean Provost 8. E. Mandonnet, S. Jbabdi, L. Taillandier, D. and Ronan Quelever. Jean-Marc Lina supervised Galanaud, H. Benali, L. Capelle, H. Duf- the Ph.D. student Aude Donfack (in collabora- fau, Preoperative estimation of residual volume tion with R. Noumeir) and the master’s stu- for WHO II glioma operated with intraopera- dents Aude Guidini, François Laurent (in col- tive functional mapping, Neurooncology, 2007, laboration with J. Gotman), Hicham Mahkoum 9(1):63 – 69. and Yann Potiez. Fahima Nekka supervised the 9. G. Marrelec, H. Benali, Independence between following students: Frédérique Fenneteau, Liah two Gaussian variables given any condition- Fereydoonzad, Guillaume Gallois, Denis Gohore ing subset implies block diagonal covariance ma- Bi, Fabien Montiel, Caroline Emmanuelle Petit- trix, Statistics & Probability Letters, 2007 (in Jetté, and Alexandre Trudel. press). Altogether, in 2006 – 2007, 4 undergraduate 10. G. Marrelec, B. Horwitz, J. Kim, M. students, 14 master’s students, 10 Ph.D. students Pélégrini-Issac, H. Benali, J. Doyon, Using and 1 postdoctoral fellow were supervised or co- partial correlation to enhance structural equation supervised by regular or associate members of modelling of functional MRI data, Magnetic Res- PhysNum. onance Imaging, 2007 (in press). 11. V. Perlbarg, P. Bellec, J. L. Anton, M. Publications of the PhysNum – MIC group Pélégrini-Issac, J. Doyon, H. Benali, COR- (journals) SICA: Correction of structured noise in fMRI 1. J. Provost, F. Lesage, The application of com- by automatic identiﬁcation of ICA components, pressed sensing for limited angle photo-acoustic Magnetic Resonance Imaging, 2007, 25(1):35 – tomography, IEEE Medical Imaging, 2007 (sub- 46. mitted). 12. L. Thivard, P. F. Pradat, S. Lehéricy, L. La- 2. J.-M. Lina, M. Dehaes, C. Matteau-Pelletier, F. comblez, D. Dormont, J. Chiras, H. Benali, V. Lesage, Complex wavelets applied to diffuse opti- Meininger, Diffusion tensor imaging and voxel cal spectroscopy for brain activity detection, Op- based morphometry study in amyotrophic lat- tics Express, 2007 (submitted). eral sclerosis: relationships with motor disability, 3. A. Gallagher, M. Lassonde, D. Bastien, P. Van- Journal of Neurology, Neurosurgery, and Psy- nasing, F. Lesage, C. Grova, A. Bouthillier, chiatry, 2007, 78:889 – 892. L. Carmant, F. Lepore, R. Béland, D. Khoa 13. J. Cohen-Adad, H. Benali, S. Rossignol, Nguyen, A non-invasive pre-surgical investiga- Methodology for MR diffusion tensor imaging of tion in a 10-year-old epileptic boy using simul- the cat spinal cord, Proceedings of the 29th taneous NIRS-EEG: comparison with SPECT, Annual International Conference of the IEEE PET, fMRI-EEG, MEG-EEG and post surgical EMBS, 2007, pp. 323 – 326. neuroanatomical assessments, Brief Communi- 14. A. Lemay, R. Noumeir, J.-M. Lina, cation, Epilepsia, 2007 (submitted). Pseudonymisation of radiology data for research 4. K. Kahlaoui, F. Lesage, N. Senhadji, H. Benali, purposes, Journal of Digital Imaging, 2007 (in Y. Joanette, Hemispheric specialization for the se- press). mantic processing of words: a Near-Infrared Spec- 15. S. Chartier, G. Giguère, P. Renaud, J.-M. troscopy (NIRS) study, Brain and Language, Lina, R. Proulx, FEBAM: A feature-extracting 2007 (in press).

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Bidirectional Associative Memory, International els, Methods and Algorithms for Real World Joint Conference on Neural Networks, 2007. Problems (A.H. Siddiqi, L. S. Duff, O. Chris- 16. C. Grova, J.-M. Lina, J. Daunizeau, A.-S. tensen, eds.), 2007, pp. 125 – 139. Dubarry, J. Gotman, P. Jolicoeur, MEG sources 4. A. Khalil, G. Joncas, F. Nekka, P. Kestener, localization of single trial versus average data: an A. Arnéodo, Morphological analysis of H. I Fea- evaluation using realistic simulations, NeuroIm- tures. II. Wavelet-based multifractal formalism, age, 2007, 36 (Suppl. 1) (abstract). The Astrophysical Journal Supplement Se- 17. C. Grova, E. Kobayashi, L. Tyvaert, J.-M. ries, 2006, 165:512 – 596. Lina, F. Dubeau, P. Jolicoeur, J. Gotman, Mag- netoencephalogram of interictal spike activity: cor- Members of the laboratory relation with BOLD responses in EEG – fMRI Regular members studies, Proceedings of the American Epilepsy Society Conference, Philadelphia, 2007 (ab- JEAN-MARC LINA (ÉTS), Director stract). Wavelets, statistical modelling and brain imag- 18. C. Grova, J. Daunizeau, E. Kobayashi, A. P. ing, machine learning Bagshaw, J.-M. Lina, F. Dubeau, J. Gotman, ALAIN ARNÉODO (ENS Lyon) Assessing the concordance between EEG source Fractals and wavelets localization and simultaneous EEG – fMRI stud- HABIB BENALI (Paris 6) ies of epileptic spikes, NeuroImage, 2007 (in Quantitative analysis in brain imaging, medical press). imaging and multimodal systems Representative publications of Fahima LINE GARNERO (Paris 6) Nekka Magnetoencephalography BERNARD GOULARD (Montréal) A pharmacokinetic formalism ex- 1. J. Li, F. Nekka, Brain imaging plicitly integrating the patient drug compliance, Journal of Pharmacokinetics and Pharmaco- FRÉDÉRIC LESAGE (Polytechnique Montréal) dynamics, 2007, 34(1):115 – 139. Conformal theory, integrable systems, inverse 2. J. Li, F. Nekka, Is the classical autocorrelation problems, optical imaging function appropriate for spatial signals deﬁned FAHIMA NEKKA (Montréal) on fractal supports? The necessity of the general- Fractal analysis, porous systems, wavelets ized autocorrelation function, Physica A. 2007, Associate member 376:147 – 157. 3. F. Nekka, J. Li, Mathematical tools updated for a KEITH J.WORSLEY (McGill) variety of complexities and purposes: development Statistics of brain mapping, geometry of random and adaptation, Modern Mathematical Mod- images in medicine and astrophysics Statistics

Description One of the aims of the Laboratory is to structure the Québec statistical community so that it Statistics is central to many endeavours in so- take part in this revolution at a time when an ciety. Whether it be through surveys from sam- important renewal of the academic personnel is pling, clinical trials to study various biomedical taking place. This structure allows the Québec treatments or experimental designs in agricul- community to beneﬁt from a recently created ture or industry, statistical methodology can be Pan-Canadian program for complex data struc- found everywhere in science. Recently, statistics tures (NPCDS), organized by the three Canadian has undergone a revolution in its techniques and mathematics institutes. The Laboratory consists approaches. This revolution has been driven by of the leaders of the Québec school of statistics, the need to analyze very large data sets and data who work on topics such as statistical learning with more complex structure, and by the ad- and neural networks, survey sampling, analy- vent of powerful computers. For example, statis- sis of functional data, statistical analysis of im- tical methodology is now addressing problems ages, dependence structures, Bayesian analysis, whose structure is very complex, such as the analysis of time series and ﬁnancial data, and re- analysis of brain images or genome data, and sampling methods. new methodology is being developed for large data sets. Data mining is one of the tools used.

84 RESEARCH LABORATORIES

News and highlights man of the Board of the National Program on Complex Data Structures (NPCDS), at a time In 2006 – 2007, six new professors became mem- when the NPCDS was preparing the application bers of the Laboratory: Jonathan Taylor (Uni- for the first renewal of its grant. Christian Léger versité de Montréal, Canada Research Chair in was appointed to the Statistical Methods Advi- Statistical Imaging), Aurélie Labbe (Université sory Committee of Statistics Canada for a second Laval), Fabrice Larribe (UQÀM), Éric Marchand term. Belkacem Abdous is still a member of the (Université de Sherbrooke), Alejandro Murua Grant Selection Committee of NSERC for Statis- (Université de Montréal) and David Stephens tical Sciences. (McGill University). Their expertise in statistical genetics, Bayesian statistics, statistical learn- Students, postdoctoral fellows and visitors ing, Gaussian processes, and statistical imaging Laboratory members are very much involved complements the expertise of the other labora- in the training of HQP. Indeed, within their tory members. respective departments, statisticians are usu- Several prestigious lectures were delivered ally among those who train the largest num- by Laboratory members in 2006 – 2007. Jim Ram- ber of students. Altogether, in 2006 – 2007, 3 un- say had the great honour of being invited to read dergraduate students, 80 master’s students, 59 one of his papers, “Parameter estimation for Ph.D. students and 14 postdoctoral fellows were differential equations: A generalized smoothing supervised by regular or associate Laboratory approach” (co-authored with G. Hooker, J. Cao members. and D. Campbell), at the Royal Statistical Soci- ety in England. His article generated the submis- Seminars sion of 29 discussion papers and was published On a weekly basis, the scientific life of the labo- in 2007. Keith Worsley gave an invited lecture ratory revolves around the CRM – ISM – GERAD at the IPAM conference in Shanghai and another Statistics Colloquium in Montréal, the Statistics one at the IPAM conference in Rio de Janeiro; he Seminar at Université Laval in Québec City, and was also elected Chair of the Program Commit- the Statistics Seminar at the Université de Sher- tee of the Organization for Humain Brain Map- brooke in Sherbrooke. In 2006 – 2007, the Statis- ping at the OHBM Conference that took place in tics Seminar at Université Laval featured 17 lec- Chicago in June 2007. tures and the Statistics Seminar at the Univer- Christian Genest was an invited speaker at sité de Sherbrooke featured 16 lectures. The list conferences in Estonia and Brazil. While on sab- of lectures of the CRM – ISM – GERAD Statistics batical leave, he delivered series of lectures in Colloquium may be found at the end of the sec- Spanish, Swiss, German, Belgian, French, and tion on the CRM general program. A special note Italian universities. Jonathan Taylor was an in- must be made of the lectures given by David vited speaker in Rio de Janeiro, at the IPAM con- Siegmund (Stanford) and Kjell Doksum (Berke- ference, and at workshops organized by SAMSI ley). and MSRI. Bruno Rémillard was an invited speaker at the first joint meeting of the Canadian Workshops, special sessions, and others Mathematical Society (CMS) and the Sociedad Matemática Mexicana (SMM), held at Guanaju- The first “Journée de statistique Montréal- ato, Mexico. Québec” took place on June 1st, 2007, at Uni- Laboratory members are actively taking part versité Laval; statisticians from all regions of in the work of Canadian statistical associations. Québec participated in this Statistics Day, which In 2006 – 2007, Christian Genest was president was organized by Christian Léger, Alejandro of the Association des statisticiennes et statisti- Murua and Aurélie Labbe. The main talks were ciens du Québec, and President-Elect of the Sta- given by Martin Bilodeau (Montréal) and Bruno tistical Society of Canada (SSC). Bruno Rémil- Rémillard (HEC Montréal). Also four students lard is co-chair of the Scientific Program Com- and postdoctoral fellows presented their re- mittee of the joint meeting of the Statistical Soci- search work to an audience of around forty par- ety of Canada and the Société française de statis- ticipants. tique, which will take place in Ottawa in June Regular members of the laboratory 2008. As Program Secretary of the SSC, Christian Léger is playing an important role in the scien- LOUIS-PAUL RIVEST (Laval), Director tific planning and organization of this meeting. Linear models, robustness, directional data, In 2006 – 2007, he continued his work as Chair- sampling, applications in finance

85 CENTRE DE RECHERCHES MATHÉMATIQUES

BELKACEM ABDOUS (Laval) CHRISTIAN LÉGER (Montréal) Biostatistics, health research methodology, con- Resampling methods, adaptive estimation, struction and validation of measuring tools in model selection, robustness, applications in data the health sector mining JEAN-FRANÇOIS ANGERS (Montréal) BRENDA MACGIBBON (UQÀM) Decision theory, Bayesian statistics, robustness Mathematical statistics, decision theory, bio- with respect to prior information, function esti- statistics mation ÉRIC MARCHAND (Sherbrooke) MASOUD ASGHARIAN (McGill) Statistical inference, Bayesian statistics, multi- Survival analysis, changepoint problems, simu- variate analysis and probability lated annealing and its variants, optimization ALEJANDRO MURUA (Montréal) YOSHUA BENGIO (Montréal) Data mining, machine learning, object recogni- Statistical learning algorithms, neural networks, tion, signal processing, and various applications nucleus models, probabilistic models, data min- of statistics and probability to bioinformatics ing, applications in finance and statistical lan- and the social and health sciences guage modelling FRANÇOIS PERRON (Montréal) MARTIN BILODEAU (Montréal) Decision theory, multidimensional data analysis, Multivariate analysis, decision theory, asymp- Bayesian statistics totic methods JAMES RAMSAY (McGill) YOGENDRA P. CHAUBEY (Concordia) Functional data analysis, smoothing and non- Sampling, linear models, resampling, survival parametric regression, curve registration analysis BRUNO RÉMILLARD (HEC) PIERRE DUCHESNE (Montréal) Probability theory, empirical processes, time se- Time series, sampling, multivariate analysis ries, nonlinear filtering, applications in finance THIERRY DUCHESNE (Laval) Survival analysis, longitudinal data analysis, ROCH ROY (Montréal) missing data, modelling 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, sur- RUSSELL STEELE (McGill) vival analysis Bayesian approaches to mixing modelling, mul- DEBBIE J.DUPUIS (HEC) tiple imputation Extreme values, robustness DAVID STEPHENS (McGill) SORANA FRODA (UQÀM) Bayesian statistics, Markov Chain Monte Carlo Nonparametric methods in function estimation, and applications to bioinformatics, statistical ge- applications of stochastic modelling in biology netics, and time series analysis and medicine JONATHAN E.TAYLOR (Montréal) CHRISTIAN GENEST (Laval) Gaussian processes, multiple comparisons, neu- Multidimensional data analysis, dependence roimaging, HIV protein sequence analysis measures, nonparametric statistics, decision the- ALAIN C.VANDAL (McGill) ory, applications in actuarial science, finance and Biostatistics, nonparametric survival estimation psychology and graph theory, imaging, capture-recapture NADIA GHAZZALI (Laval) models Multidimensional data analysis, neural net- DAVID B.WOLFSON (McGill) works and genetic algorithms, applications in Changepoint problems, survival analysis, astrophysics and biostatistics Bayesian statistics, optimal design, applications AURÉLIE LABBE (Laval) in medicine Biostatistics and statistical genetics KEITH J.WORSLEY (McGill) FABRICE LARRIBE (UQÀM) Statistics of brain mapping, geometry of random Statistical genetics and biostatistics images in medicine and astrophysics

86 RESEARCH LABORATORIES

INTRIQ

Quantum information is an emerging ﬁeld The members of INTRIQ are David Avis of research, at the crossroads of mathemat- (Computer Science, McGill), Alexandre Blais ics, physics, computer science and chemistry. (Physics, Sherbrooke), Michel Boyer (Computer It could potentially bring about a fundamental Science, Montréal), Gilles Brassard (Computer revolution, not only in our way of processing in- Science, Montréal), Aashish Clerk (Physics, formation, but also in our way of understanding McGill), Claude Crépeau (Computer Sci- the world. INTRIQ is a French acronym mean- ence, McGill), José Manuel Fernandez (Com- ing “Transdisciplinary Institute for Quantum In- puter Engineering, Polytechnique), Patrick formation”; it refers to a CRM laboratory in Fournier (Physics, Sherbrooke), Guillaume Ger- which computer scientists and physicists study vais (Physics, McGill), Nicolas Godbout (En- this new paradigm of information processing. gineering Physics, Polytechnique), Peter Grüt- INTRIQ was launched recently and organized ter (Physics, McGill), Patrick Hayden (Com- two main activities in 2006-2007, a conference to puter Science, McGill), Michael Hilke (Physics, mark the laboratory lauch and a mini-course on McGill), Richard MacKenzie (Physics, Mont- quantum error correction given by David Poulin réal), Prakash Panangaden (Computer Science, (Caltech) from January 15 to 26, 2007. A detailed McGill), Alain Tapp (Computer Science, Mont- description of the lauch may be found in the sec- réal), and André-Marie Tremblay (Physics, Sher- tion on the CRM multidisciplinary and indus- brooke). trial program. LAUNCHOFTHE TRANSDISCIPLINARY INSTI- TUTEFOR QUANTUM INFORMATION (INTRIQ) November 9, 2006, CRM Organizer: Gilles Brassard (Montréal)

87 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 Chairholder. Recent Titles

The following list of recent titles contains books Andrew Granville, Melvyn B. Nathanson & that appeared in 2006 – 2007 or that will be pub- Jozsef Solymosi (eds.), Additive Combinatorics, lished soon. vol. 43, 2007. Donald A. Dawson, Vojkan Jakši´c& Boris Vain- American Mathematical Society berg (eds.), Probability and Mathematical Physics: CRM Monograph Series A Volume in Honor of Stanislav Molchanov, vol. 42, Olga Kharlampovich & Alexei Myasnikov, Alge- 2007. braic Geometry for a Free Group (to appear). André Bandrauk, Michel C. Delfour & Claude Le Bris (eds.), High-Dimensional Partial Differen- American Mathematical Society tial Equations in Sciences and Engineering, vol. 41, CRM Proceedings & Lecture Notes 2007. Jean-Marie De Koninck, Andrew Granville & Springer Florian Luca (eds.), Anatomy of Integers (to ap- CRM Series in Mathematical Physics pear). Panos M. Pardalos & Pierre Hansen (eds.), Data Marc Thiriet, Biology and Mechanics of Blood Flows Mining and Mathematical Programming (to ap- (to appear). pear). Les Publications CRM Stanley Alama, Lia Bronsard & Peter Sternberg (eds.), Singularities in PDE and the Calculus of Laurent Guieu & Claude Roger, L’Algèbre et le Variations (to appear). Groupe de Virasoro, 2007. Previous Titles

American Mathematical Society Andrei Tyurin, Quantization, Classical and Quan- CRM Monograph Series tum Field Theory and Theta Functions, vol. 21, 2003. Victor Guillemin & Reyer Sjamaar, Convexity Joel Feldman, Horst Knörrer & Eugene Properties of Hamiltonian Group Actions, vol. 26, Trubowitz, Riemann Surfaces of Inﬁnite Genus, 2005. vol. 20, 2003. *Andrew J. Majda, Rafail V. Abramov & Mar- *Laurent Lafforgue, Chirurgie des grassmanni- cus J. Grote, Information Theory and Stochastics for ennes, vol. 19, 2003. Multiscale Nonlinear Systems, vol. 25, 2005. *George Lusztig, Hecke Algebras with Unequal Pa- Dana Schlomiuk, Andrei A. Bolibrukh, Sergei rameters, vol. 18, 2003. Yakovenko, Vadim Kaloshin & Alexandru Buium, On Finiteness in Differential Equations and Michael Barr, Acyclic Models, vol. 17, 2002. Diophantine Geometry, vol. 24, 2005. *Joel Feldman, Horst Knörrer & Eugene Prakash Panangaden & Franck van Breugel Trubowitz, Fermionic Functional Integrals and the (eds.), Mathematical Techniques for Analyzing Con- Renormalization Group, vol. 16, 2002. current and Probabilistic Systems, vol. 23, 2004. Jose I. Burgos, The Regulators of Beilinson and Borel, vol. 15, 2002. Montserrat Alsina & Pilar Bayer, Quaternion Or- ders, Quadratic Forms, and Shimura Curves, vol. 22, Eyal Z. Goren, Lectures on Hilbert Modular Vari- 2004. eties and Modular Forms, vol. 14, 2002.

89 CENTRE DE RECHERCHES MATHÉMATIQUES

Michael Baake & Robert V. Moody (eds.), Direc- Pavel Winternitz, John Harnad, C.S. Lam & Jiˇrí tions in Mathematical Quasicrystals, vol. 13, 2000. Patera (eds.), Symmetry in Physics, vol. 34, 2004. Masayoshi Miyanishi, Open Algebraic Surfaces, André D. Bandrauk, Michel C. Delfour & Claude vol. 12, 2001. Le Bris (eds.), Quantum Control: Mathematical and Spencer J. Bloch, Higher Regulators, Algebraic Numerical Challenges, vol. 33, 2003. K-Theory, and Zeta Functions of Elliptic Curves, Vadim B. Kuznetsov (ed.), The Kowalevski Prop- vol. 11, 2000. erty, vol. 32, 2002. James D. Lewis, A Survey of the Hodge Conjecture, John Harnad & Alexander R. Its (eds.), Isomon- 2e édition, vol. 10, 1999 (with an appendix by odromic Deformations and Applications in Physics, B. Brent Gordon). vol. 31, 2002 *Yves Meyer, Wavelets, Vibrations and Scaling, John McKay & Abdellah Sebbar (eds.), Proceed- vol. 9, 1997. ings on Moonshine and Related Topics, vol. 30, 2001. *Ioannis Karatzas, Lectures on Mathematics of Fi- Alan Coley, Decio Levi, Robert Milson, Colin nance, vol. 8, 1996. Rogers & Pavel Winternitz (eds.), Bäcklund and John Milton, Dynamics of Small Neural Popula- Darboux Transformations, vol. 29, 2001. tions, vol. 7, 1996. John C. Taylor (ed.), Topics in Probability and Lie *Eugene B. Dynkin, An Introduction to Branching Groups: Boundary Theory, vol. 28, 2001. Measure-Valued Processes, vol. 6, 1994. Israel M. Sigal & Catherine Sulem (eds.), Nonlin- Andrew M. Bruckner, Differentiation of Real Func- ear Dynamics and Renormalization Group, vol. 27, tions, vol. 5, 1994. 2001. *David Ruelle, Dynamical Zeta Functions for Piece- John Harnad, Gert Sabidussi & Pavel Winternitz wise Monotone Maps of the Interval, vol. 4, 1994. (eds.), Integrable Systems: From Classical to Quan- tum, vol. 26, 2000. V. Kumar Murty, Introduction to Abelian Varieties, vol. 3, 1993. Decio Levi & Orlando Ragnisco (eds.), SIDE III — Symmetry and Integrability of Difference Maximilian Ya. Antimirov, Andrei A. Kolyshkin Equations, vol. 25, 2000. & Rémi Vaillancourt, Applied Integral Transforms, vol. 2, 1993. B. Brent Gordon, James D. Lewis, Stefan Müller- Stach, Shuji Saito & Noriko Yui (eds.), The Arith- *Dan V. Voiculescu, Kenneth J. Dykema & metic and Geometry of Algebraic Cycles, vol. 24, Alexandru Nica, Free Random Variables, vol. 1, 2000. 1992. Pierre Hansen & Odile Marcotte (eds.), Graph American Mathematical Society Colouring and Applications, vol. 23, 1999. CRM Proceedings & Lecture Notes Jan Felipe van Diejen & Luc Vinet (eds.), Al- gebraic Methods and q-Special Functions, vol. 22, Vestislav Apostolov, Andrew Dancer, Nigel 1999. Hitchin & McKenzie Wang (eds.), Perspectives Michel Fortin (ed.), Plates and Shells, vol. 21, 1999. in Comparison, Generalized and Special Geometry, vol. 40, 2006. Katie Coughlin (ed.), Semi-Analytic Methods for the Navier – Stokes Equations, vol. 20, 1999. Pavel Winternitz, David Gomez-Ullate, Arieh Iserles, Decio Levi, Peter J. Olver, Reinout Quis- Rajiv Gupta & Kenneth S. Williams (eds.), Num- pel & Piergiulio Tempesta (eds.), Group Theory ber Theory, vol. 19, 1999. and Numerical Analysis, vol. 39, 2005. Serge Dubuc & Gilles Deslauriers (eds.), Spline Jacques Hurtubise & Eyal Markman (eds.), Alge- Functions and the Theory of Wavelets, vol. 18, 1999. braic Structures and Moduli Spaces, vol. 38, 2004. Olga Kharlampovich (ed.), Summer School in Piergiulio Tempesta, Pavel Winternitz, John Har- Group Theory in Banff, 1996, vol. 17, 1998. nad, Willard Miller Jr., George Pogosyan & Alain Vincent (ed.), Numerical Methods in Fluid Miguel A. Rodriguez (eds.), Superintegrability in Mechanics, vol. 16, 1998. Classical and Quantum Systems, vol. 37, 2004. François Lalonde (ed.), Geometry, Topology and Hershy Kisilevsky & Eyal Z. Goren (eds.), Num- Dynamics, vol. 15, 1998. ber Theory, vol. 36, 2004. John Harnad & Alex Kasman (eds.), The Bispec- H. E. A. Eddy Campbell & David L. Wehlau tral Problem, vol. 14, 1998. (eds.), Invariant Theory in All Characteristics, Michel Delfour (ed.), Boundaries, Interfaces and vol. 35, 2004. Transitions, vol. 13, 1998.

90 PUBLICATIONS

Peter G. Greiner, Victor Ivrii, Luis A. Seco & S. Ejaz Ahmed & Nancy Reid (eds.), Empirical Catherine Sulem (eds.), Partial Differential Equa- Bayes and Likelihood Inference, 2001. tions and their Applications, vol. 12, 1997. Luc Vinet (ed.), Advances in Mathematical Sci- CRM Publications ences: CRM’s 25 Years, vol. 11, 1997. Luc Lapointe, Ge Mo-Lin, Yvan Saint-Aubin & Donald E. Knuth, Stable Marriage and Its Relation Luc Vinet, Proceedings of the Canada-China Meet- to Other Combinatorial Problems, vol. 10, 1996. ing on Theoretical Physics, 2003. Decio Levi, Luc Vinet & Pavel Winternitz (eds.), Armel Mercier, Fonctions de plusieurs variables : Symmetries and Integrability of Difference Equa- Différentiation, 2002. tions, vol. 9, 1995. Joel S. Feldman, Richard Froese & Lon M. Nadia El-Mabrouk, Thomas Lengauer & David Currents in Computational Molecu- Rosen (eds.), Mathematical Quantum Theory II: Sankoff (eds.), lar Biology Schrödinger Operator, vol. 8, 1995. , 2001. Joel S. Feldman, Richard Froese & Lon M. Rosen James G. Huard & Kenneth S. Williams (eds.), (eds.), Mathematical Quantum Theory I: Field The- The Collected Papers of Sarvadaman Chowla Vol- ory and Many-Body Theory, vol. 7, 1994. ume I 1925-1935; Volume II 1936-1961; Vol- ume III 1962-1986, 2000. Guido Mislin (ed.), The Hilton Symposium 1993, vol. 6, 1994. Michael Barr & Charles Wells, Category Theory for Computing Science, 1999. Donald A. Dawson (ed.), Measure-Valued Pro- cesses, Stochastic Partial Differential Equations and Maximilian Ya. Antimirov, Andrei A. Kolyshkin Interacting Systems, vol. 5, 1994. & Rémi Vaillancourt, Mathematical Models for Eddy Current Testing Hershy Kisilevsky & M. Ram Murty (eds.), Ellip- , 1998. tic Curves and Related Topics, vol. 4, 1994. Xavier Fernique, Fonctions aléatoires gaussiennes, Andrei L. Smirnov & Rémi Vaillancourt (eds.), vecteurs aléatoires gaussiens, Montréal, 1997. Asymptotic Methods in Mechanics, vol. 3, 1993. Faqir Khanna & Luc Vinet (eds.), Field Theory, In- Philip D. Loewen, Optimal Control via Nonsmooth tegrable Systems and Symmetries, Montréal, 1997. Analysis, vol. 2, 1993. Paul Koosis, Leçons sur le théorème de Beurling et M. Ram Murty (ed.), Theta Functions, vol. 1, 1993. Malliavin, 1996. David W. Rand, Concorder Version Three, 1996 Springer (software and user guide). CRM Series in Mathematical Physics Jacques Gauvin, Theory of Nonconvex Program- David Sénéchal, André-Marie Tremblay & ming, 1994. Claude Bourbonnais, Theoretical Methods for Decio Levi, Curtis R. Menyuk & Pavel Win- Strongly Correlated Electrons, 2003. ternitz (eds.), Self-Similarity in Stimulated Raman *Roman Jackiw, Lectures on Fluid Dynamics, 2002. Scattering, 1994. Yvan Saint-Aubin & Luc Vinet (eds.), Theoretical Rémi Vaillancourt, Compléments de mathématiques Physics at the End of the Twentieth Century, 2001. pour ingénieurs, 1993. Yvan Saint-Aubin & Luc Vinet (eds.), Algebraic Robert P. Langlands & Dinakar Ramakrishnan Methods in Physics, 2000. (eds.), The Zeta Functions of Picard Modular Sur- Jan Felipe van Diejen & Luc Vinet (eds.), faces, 1992. Calogero – Moser – Sutherland Models, 1999. Florin N. Diacu, Singularities of the N-Body Prob- Robert Conte (ed.), The Painlevé Property, 1999. lem, 1992. Richard MacKenzie, Manu B. Paranjape & Woj- Jacques Gauvin, Théorie de la programmation ciech J. M. Zakrzewski (eds.), Solitons, 1999. mathématique non convexe, 1992. Luc Vinet & Gordon Semenoff (eds.), Particles Pierre Ferland, Claude Tricot & Axel van de and Fields, 1998. Walle, Analyse fractale, 1992 (software and user guide). Springer Stéphane Baldo, Introduction à la topologie des en- CRM Subseries of the Lecture Notes in sembles fractals, 1991. Statistics Robert Bédard, Groupes linéaires algébriques, 1991. Marc Moore (ed.), Spatial Statistics: Methodologi- Rudolf Beran & Gilles R. Ducharme, Asymptotic cal Aspects and Applications, 2001. Theory for Bootstrap Methods in Statistics, 1991.

91 CENTRE DE RECHERCHES MATHÉMATIQUES

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

[CRM-3219] Kengne, E., Vaillancourt, R., “Stabi- 5 to 15,” The Canadian Applied Mathematics lized soliton in attractive Bose-Einstein conden- Quarterly, 14:1 (2006), 43–69. sate in hyperbolic potential,” in Boundary Field [CRM-3221] Hajji, M. A., Vaillancourt, R., “Ma- Problems and Computer Simulation, volume 48, trix derivation of Gaussian quadratures,” in Scientiﬁc Proceedings of the Riga Technical Uni- Boundary Field Problems and Computer Simu- versity — Computer Science, volume 29, Riga, lation, volume 48, Scientiﬁc Proceedings of the Riga Technical University, 2006. Riga Technical University — Computer Science, [CRM-3220] Nguyen-Ba, T., Yagoub, H., Li, Y., volume 29, Riga, Riga Technical University, 2006. Vaillancourt, R., “Variable-step variable-order 3- stage Hermite – Birkhoff ODE solver of order

92 PUBLICATIONS

[CRM-3222] Labbé, S., Lorin de la Grandmaison, order 3-stage Hermite – Birkhoff – Obrechkoff E., “On the reservoir technique convergence. ODE solver of order 4 to 14,” The Canadian Ap- Part I,” September 2006. plied Mathematics Quarterly, 14:4 (2006), 413– [CRM-3224] Lorin de la Grandmaison, E., Ben 437. Haj Ali, A., Soulaimani, A., “An accurate positiv- [CRM-3233] Lamontagne, Y., Coutu, C., ity preserving scheme for the Spalart-Allmaras Rousseau, C., “Bifurcation analysis of a turbulence model ,” September 2006. predator-prey system with generalised Holling [CRM-3227] Nguyen-Ba, T., Yagoub, H., Des- type III functional response,” Journal of Dynam- jardins, S. J., Vaillancourt, R., “Variable- ics and Differential Equations, submitted. step variable-order 4-stage Hermite-Birkhoff- [CRM-3236] Christopher, C., Schlomiuk, D., Obrechkoff ODE solver of order 5 to 14,” in “Center conditions for a class of polynomial dif- Boundary Field Problems and Computer Sim- ferential systems,” November 2006. ulation, volume 48, Scientific Proceedings of the [CRM-3237] Schlomiuk, D., Vulpe, N., “Integrals Riga Technical University — Computer Science, and phase portraits of planar quadratic differen- volume 29, Riga, Riga Technical University, 2006. tial systems with invariant lines of total multi- [CRM-3229] Dryanov, D., Fournier, R., “Equality plicity four,” November 2006. cases for two polynomial inequalities,” Annu- [CRM-3225] Murua, A., Stanberry, L., Stuetzle, aire de l’Université de Sofia “St Kliment Ohrid- W., “On Potts model clustering, kernel K-means ski,” Faculté de Mathématiques et Informatique, and density estimation,” Journal of Computa- 99, accepted. tional and Graphical Statistics, submitted. [CRM-3230] Fournier, R., Serban, M., “An ex- [CRM-3238] Fournier, R., “Asymptotics of the tension of Jack’s lemma to polynomials of fixed Bohr radius for polynomials of fixed degree,” degree ,” Computational Methods and Function Journal of Mathematical Analysis and Applica- Theory, 7:2 (September 2007), 371 – 378. tions, accepted. [CRM-3231] Vaillancourt, R., Zakharov, V. G., [CRM-3239] Bertola, M., Gekhtman, M., “Effec- “Biorthogonal wavelet bases for solving time- tive inverse spectral problem for rational Lax dependent PDEs,” in Boundary Field Problems matrices and applications,” International Math- and Computer Simulation, volume 48, Scientific ematical Research Notices, accepted. Proceedings of the Riga Technical University — [CRM-3254] Kengne, E., Vaillancourt, R., “Ex- Computer Science, volume 29, Riga, Riga Tech- act solutions of the Gross – Pitaevskii equation nical University, 2006. in periodic potential in the presence of exter- [CRM-3232] Nguyen-Ba, T., Yagoub, H., Zhang, nal source,” Journal of Mathematical Physics, 48 Y., Vaillancourt, R., “Variable-step variable- (July 2007), 073520, 13 pages.

93 Scientiﬁc Personnel SCIENTIFIC PERSONNEL

CRM Members in 2006 – 2007 n contrast with most other mathematics institutes around the world, the CRM can count on the Isolid foundation of regular, associate and invited members. Each regular member is also a professor at one of the partner institutions: Université de Montréal, Concordia University, McGill Univer- sity, Université du Québec à Montréal (UQÀM), Université Laval, Université de Sherbrooke and the University of Ottawa. Other members are researchers affiliated with the CRM in 2006 – 2007 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 facili- tated 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 grants 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 University Dafni, Galia, Concordia University Angers, Jean-François, Université de Montréal Darmon, Henri, McGill University Apostolov, Vestislav, Université du Québec à David, Chantal, Concordia University Montréal De Koninck, Jean-Marie, Université Laval Arminjon, Paul, Université de Montréal Delfour, Michel C., Université de Montréal Bandrauk, André D., Université de Sherbrooke Doedel, Eusebius J., Concordia University Baribeau, Line, Université Laval Dssouli, Rachida, Concordia University Bartello, Peter, McGill University Duchesne, Pierre, Université de Montréal Bédard, Robert, Université du Québec à Duchesne, Thierry, Université Laval Montréal El-Mabrouk, Nadia, Université de Montréal Bélair, Jacques, Université de Montréal Fortin, André, Université Laval Benali, Habib, CHU Pitié Salpêtrière Fournier, Richard, Dawson College Bengio, Yoshua, Université de Montréal Frigon, Marlène, Université de Montréal Bergeron, François, Université du Québec à Garon, André, École Polytechnique de Montréal Montréal Gauthier, Paul M., Université de Montréal Bertola, Marco, Concordia University Genest, Christian, Université Laval Bourgault, Yves, University of Ottawa Goren, Eyal Z., McGill University Bourlioux, Anne, Université de Montréal Goulard, Bernard, Université de Montréal Boyer, Steven, Université du Québec à Montréal Granville, Andrew, Université de Montréal Brassard, Gilles, Université de Montréal Grundland, Alfred Michel, Université du Brlek, Srecko, Université du Québec à Montréal Québec à Trois-Rivières Broer, Abraham, Université de Montréal Guan, Pengfei, McGill University Brunet, Robert C., Université de Montréal Hahn, Gena, Université de Montréal Bryant, David, McGill University Hall, Richard L., Concordia University Chauve, Cédric, Simon Fraser University Hamel, Sylvie, Université de Montréal Chvátal, Vašek, Concordia University Harnad, John, Concordia University Clarke, Francis H., Université de Lyon 1 Humphries, Tony R., McGill University Collin, Olivier, Université du Québec à Hurtubise, Jacques, McGill University Montréal Hussin, Véronique, Université de Montréal Cornea, Octavian, Université de Montréal Iovita, Adrian, Concordia University Cs˝urös,Miklós, Université de Montréal Jakobson, Dmitry, McGill University Cummins, Chris, Concordia University Jakši´c,Vojkan, McGill University

95 CENTRE DE RECHERCHES MATHÉMATIQUES

Joyal, André, Université du Québec à Montréal Murty, M. Ram, Queen’s University Kaczynski, Tomasz, Université de Sherbrooke Nekka, Fahima, Université de Montréal Kamran, Niky, McGill University Nigam, Nilima, McGill University Kharlampovich, Olga, McGill University Owens, Robert G., Université de Montréal Kisilevsky, Hershy, Concordia University Patera, Jiˇrí,Université de Montréal Koosis, Paul, McGill University Perron, François, Université de Montréal Korotkin, Dmitry, Concordia University Polterovich, Iosif, Université de Montréal Labelle, Gilbert, Université du Québec à Ramsay, James O., McGill University Montréal Ransford, Thomas J., Université Laval Labute, John, McGill University Rémillard, Bruno, HEC Montréal Lalonde, François, Université de Montréal Reutenauer, Christophe, Université du Québec Léger, Christian, Université de Montréal à Montréal Leroux, Pierre, Université du Québec à Rivest, Louis-Paul, Université Laval Montréal Rosenberg, Ivo G., Université de Montréal Lesage, Frédéric, École Polytechnique de Rousseau, Christiane, Université de Montréal Montréal Roy, Damien, University of Ottawa Lessard, Sabin, Université de Montréal Roy, Roch, Université de Montréal LeTourneux, Jean, Université de Montréal Russell, Peter, McGill University Levesque, Claude, Université Laval Saint-Aubin, Yvan, Université de Montréal Lina, Jean-Marc, École de Technologie Sankoff, David, Université de Montréal Supérieure Schlomiuk, Dana, Université de Montréal Lu, Steven, Université du Québec à Montréal Shnirelman, Alexander, Concordia University MacGibbon, Brenda, Université du Québec à Stern, Ron J., Concordia University Montréal Thaine, Francisco, Concordia University Mackey, Michael C., McGill University Toth, John A., McGill University Makarenkov, Vladimir, Université du Québec à Tupper, Paul F., McGill University Montréal Vinet, Luc, Université de Montréal Makkai, Michael, McGill University Walsh, Timothy R.S., Université du Québec à Mashreghi, Javad, Université Laval Montréal Maslowe, Sherwin A., McGill University Wihler, Thomas P., McGill University Mathieu, Pierre, Université Laval Winternitz, Pavel, Université de Montréal McKay, John, Concordia University Wise, Daniel T., McGill University Miasnikov, Alexei G., McGill University Worsley, Keith J., McGill University

Associate Members

Beaulieu, Liliane, Collège du Vieux-Montréal Li, Jun, Université de Montréal Bergeron, Nantel, York University Petridis, Yiannis N., Lehman College (CUNY) Conte, Robert, CEA Saclay Shahbazian, Elisa, Lockheed Martin Canada Durand, Stéphane, Collège Édouard-Montpetit Thiriet, Marc, INRIA Rocquencourt Gander, Martin J., Université de Genève Valin, Pierre, DRDC Valcartier Garnero, Line, CHU Pitié Salpêtrière Van Vliet, Carolyne M., University of Miami Levi, Decio, Università di Roma Tre Zolésio, Jean-Paul, INRIA Sophia-Antipolis

Invited Members

Bilodeau, Martin, Université de Montréal Gowrisankaran, Kohur, McGill University Doray, Louis G., Université de Montréal Haiman, Mark, University of California, Dugas, Charles, Université de Montréal Berkeley

96 SCIENTIFIC PERSONNEL

Larose, Benoît, Champlain College Morales, Manuel, Université de Montréal Saint-Lambert Murua, Alejandro, Université de Montréal 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.

Anguelova, Iana, University of Illinois at Maher, Joseph, University of California, Santa Urbana-Champaign Barbara Bourhim, Abdellatif, Université Mohammed V, Mangoubi, Dan, Technion Rabat Marmora, Adriano, Université Paris 13 Carbonell, Felix, Universidad de La Habana Mason, Sarah K., University of Pennsylvania Ceyhan, Özgür, Université Strasbourg 1 Masri, Riad, University of Texas at Austin Charollois, Pierre, Université Bordeaux 1 McIntyre, Andrew, Stony Brook University Chen, Chuan Zhong, Central South University, Mo, Man Yue, University of Oxford Changsha Mohammadalikhani, Ramin, University of Cooper, Jason, University of Calgary Toronto Derivière, Sara, Université de Rouen Moyers-Gonzalez, Miguel Angel, University of Desrosiers, Patrick, Université Laval British Columbia Dujmovic, Vida, McGill University Ndiaye, Ismaila, École Polytechnique Fédérale Friedl, Stefan, Brandeis University de Lausanne Germain, Mickaël, Université de Sherbrooke Nesterenko, Maryna, National Academy of Sciences, Ukraine Glen, Amy, University of Adelaide Pierre, Charles, Université de Nantes Gürel, Ba¸sak,University of California, Santa Cruz Pusztai, Bélà Gabor, University of Szeged Hu, Shengda, University of Wisconsin-Madison Ridout, David, University of Adelaide Jones, Nathan Conrad, University of California, Rowlett, Julie, Stanford University Los Angeles Tian, Ye, Columbia University Letellier, Emmanuel, Université Paris 6 Tore, Jensen Bernt, McMaster University Lisi, Samuel, Courant Institute, New York Urquiza, José Manuel, Université Paris 6 University Villani, Éric, Université Paris 6 Lorin de la Grandmaison, Emmanuel, École Wigman, Igor, Tel Aviv University Normale Supérieure de Cachan Yurdusen, Ismet, Middle East Technical Lucier, Jason Bryan, University of Waterloo University, Ankara 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 2006 – 2007, 1010 such participants registered in the thematic program workshops, 640 in activities of the general program and 320 in those of the industrial and multidisciplinary program. The CRM also contributed financially to around fifteen other scientific events. The following list only includes visitors who were in residence for at least four weeks.

Adimurthi, Adi, Tata Institute, Bangalore Benali, Habib, CHU Pitié-Salpêtrière Asatryan, Davit, National Academy of Sciences Boyko, Vyacheslav, National Academy of of Armenia Sciences of Ukraine

97 CENTRE DE RECHERCHES MATHÉMATIQUES

Clarke, Francis H., Université Lyon 1 Pouryayevali, Mohamad Reza, University of Croot, Ernest S., Georgia Institute of Technology Isfahan Donato, Paul, Université Aix-Marseille 1 Prasanna, Kartik, University of California, Los Angeles El Gradechi, Amine, Université d’Artois Safarov, Yuri, King’s College London Enolskii, Victor, National Academy of Sciences of Ukraine Soundararajan, K., University of Michigan Fleischer, Isidore, Montréal Stoll, Manfred, University of South Carolina Fricain, Emmanuel, Université Lyon 1 Sun, Chengjun, Shanghai Jiao Tong University Tanimoto, Ryuji, Osaka University Gao, Peng, University of Michigan Haglund, Jim, University of Pennsylvania Tardif, Camille, École Normale Supérieure de Cachan-Bretagne Kashuba, Iryna, Universidade de Sao Paulo Thiriet, Marc, INRIA Rocquencourt Khan, Rizwan, Institute for Advanced Study Thomas, Hugh, University of New Brunswick Klimyk, Anatoliy, Bogolyubov Institute for van Willigenburg, Stephanie, University of Theoretical Physics British Columbia Levi, Decio, Università di Roma Tre Vinuesa, Carlos, Universidad Autónoma de Luca, Florian, Universidad Autónoma de Madrid Mexico Vulpe, Nicolae, Academy of Sciences of Monastyrsky, Michael, Institute for Theoretical Moldova and Experimental Physics, Moscow Willems, Matthieu, Université de Mukhopadhyay, Anirban, Institute of Cergy-Pontoise Mathematical Science, Chennai Wooley, Trevor, University of Michigan Nang, Philibert, Gabon Zhang, Yuanli, Montréal Ng, Nathan, University of Ottawa Zhedanov, Alexei, Donetsk Institute for Physics Nobakhtian, Soghra, University of Isfahan and Technology Orlov, Aleksander Yu., Shirshov Institute for Zograf, Peter, Steklov Mathematical Institute Oceanology Short-term Visitors The following visitors were in residence for less than four weeks.

Adler, Robert, Technion Futorny, Vyacheslav, Universidade de São Paulo Alon, Noga, Tel Aviv University Gazeau, Jean-Pierre, Université Paris 7 Angelova, Maia, University of Northumbria Gekhtman, Michael, University of Notre Dame Anjos, Silvia, Instituto Superior Technico, Ginzburg, Victor, University of California, Santa Lisbon Cruz Banyaga, Augustin, Pennsylvania State Goemans, Michel, Massachusetts Institute of University Technology Bleher, Pavel, Indiana University-Purdue Grigoryan, Arthur, National Academy of University, Indianapolis Sciences of Armenia Boalch, Philip, École Normale Supérieure, Paris Hereman, Willy, Colorado School of Mines Bodner, Mark, MIND Institute Its, Alexander, Indiana University-Purdue Borodzik, Maciej, University of Warsaw University, Indianapolis Conte, Robert, CEA Saclay Moody, Robert V., University of Alberta de Smit, Bart, Universiteit Leiden Neher, Erhard, University of Ottawa Eynard, Bertrand, CEA Saclay Pacelli, Allison, Williams College Faridi, Sara, Dalhousie University Pinsonnault, Martin, Fields Institute Feigon, Brooke, Institute for Advanced Study Pogossian, Edward, National Academy of Sciences of Armenia Frid, Anna, Sobolev Institute of Mathematics

98 SCIENTIFIC PERSONNEL

Rosenthal, Jeffrey S., University of Toronto Tomczak-Jaegermann, Nicole, University of Roussarie, Robert, Université de Bourgogne Alberta Seymour, Paul, Princeton University Turbiner, Alexander, Universidad Autónoma de Snobl, Libor, Czech Technical University Mexico Stanley, Richard, Massachusetts Institute of Tyran-Kaminska, Marta, Silesian University, Technology Katowice Stolovitch, Laurent, Université Toulouse 3 Ujino, Hideaki, Gunma College of Technology Szmigielski, Jacek, University of Saskatchewan Vakil, Ravi, Stanford University Thomova, Zora, State University of New York van de Leur, Johan, University of Utrecht Institute of Technology, Utica Wilson, R. Eddie, University of Bristol Tolar, Jiˇrí,Czech Technical University Zakoïan, Jean-Michel, Université Lille 3

99 Governance and Scientiﬁc Guidance GOVERNANCEAND SCIENTIFIC GUIDANCE

Bureau de direction The Bureau adopts the policies of the Centre, recommends the nomination and the promotion of researchers and the appointment of regular and associate members, advises the Director on the prepa- ration of the budget and the Selection Committee on the choice of the Director.

Syed Twareque Ali Niky Kamran Concordia University McGill University Yoshua Bengio François Lalonde Université de Montréal Université de Montréal Michel Delfour Javad Mashreghi Université de Montréal Université Laval Joseph Hubert, Dean Faculty of Arts and Sciences, Université de Christiane Rousseau Montréal Université de Montréal Véronique Hussin Jacques Turgeon, Vice-Principal (Research) Université de Montréal Université de Montréal

Chantal David (Concordia University), Andrew Granville (Université de Montréal), Jean LeTour- neux (Université de Montréal), and Odile Marcotte (Université du Québec à Montréal), all Deputy Directors of the CRM, were invited members. Scientiﬁc Advisory Committee

The Scientific Advisory Committee consists of distinguished researchers from Canada and abroad. Its members are either mathematicians or scientists with close ties to the mathematical sciences. The Advisory Committee is kept informed regularly of the activities of the Centre through the Director. The Committee makes recommendations about the general scientific orientations of the CRM and gives advice about proposed scientific activities.

Jerry Bona is a Professor at ical theories: Dirac operators and spins, gen- the Department of Mathematics, eral relativity. His areas of specialty are the ge- Statistics and Computer Science ometrical estimation of eigenvalues of Laplace – at The University of Illinois at Beltrami operators, Kählerian geometry and, Chicago. He received a B.Sc. de- more recently, Finslerian geometry. Jean-Pierre gree from Washington University Bourguignon is a research leader at the highest in St. Louis (1966) and a Ph.D. echelon of the Centre national de la recherche from Harvard University (1971). His research ex- scientifique (CNRS). He is currently the Direc- perience is vast. His research interests include tor of the Institut des Hautes Études Scien- fluid mechanics, partial differential equations, tifiques (IHÉS) at Bures-sur-Yvette and Profes- computational mathematics and the associated sor of Mathematics at the École Polytechnique. numerical analysis, oceanography, coastal engi- From 1990 to 1992, he served as President of the neering, and mathematical economics. He is an Société Mathématique de France, and from 1995 Elected Fellow of the American Association for to 1998, as President of the European Mathemat- the Advancement of Science and a member of ical Society. He is a member of several scientific the editorial boards of twenty-five scientific jour- advisory committees in Europe. He has been a nals and of several academic committees and member of Academia Europaea since 1996 and a panels. Jerry Bona is a co-organizer of the Math- foreign associate of the Spanish Royal Academy ematicians and Educational Reform Network. since 2002. Jean-Pierre Bourguignon re- Jean-Louis Colliot-Thélène ceived an engineering degree is “directeur de recherche” from the École Polytechnique at the Centre national de la and a Ph.D. in mathematics. A recherche scientifique (CNRS) differential geometer by train- at the UMR 8628 (Université ing, he has also worked on the de Paris-Sud, Orsay). He spe- mathematical aspects of phys- cializes in algebraic geometry

101 CENTRE DE RECHERCHES MATHÉMATIQUES and its links to arithmetic. He obtained a Doc- ceived numerous prizes and awards including torat d’État (1978) from Paris-Orsay. He is a the Levi L. Conant Prize of the American Math- member of the editorial board of the Annales sci- ematical Society. He is one of the editors-in-chief entifiques de l’École Normale Supérieure (of which of Integers: The Electronic Journal of Combinatorial he was editor-in-chief until recently), as well Number Theory and a member of the editorial as the boards of the Journal of Number Theory board of the Journal of Supercomputing and the and the Journal of K-Theory. Jean-Louis Colliot- AMS Undergraduate Book Series. Thélène was one of the main organizers of the Thomas Salisbury is Presi- 2005 – 2006 Thematic Program at MSRI (Berke- dent of the Canadian Math- ley). ematical Society and a Pro- A mathematician and physicist fessor at the Department of by training, François Lalonde Mathematics and Statistics holds a Doctorat d’État (1985) of York University. He was from the Université de Paris- Deputy Director of the Fields Sud Orsay in the field of differ- Institute until May 2006. He ential topology. His fields of in- holds degrees from McGill University (B.Sc.) terests include symplectic topol- and the University of British Columbia (Ph.D.). ogy, Hamiltonian dynamics and His research is in probability theory and its the study of infinite-dimensional transformation connections to both finance and mathematical groups. He has been a member of the Royal So- analysis. He was Editor-in-Chief of the Cana- ciety of Canada since 1997 and held a Killam Re- dian Mathematical Bulletin, Associate Editor of search Fellowship in 2000 – 2002. He holds the the Canadian Journal of Statistics, and is presently Canada Research Chair in Symplectic Geometry on the editorial board of Potential Analysis. and Topology at the Department of Mathemat- Peter Shalen is a Professor ics and Statistics of the Université de Montréal. at the Department of Math- He was Plenary Speaker at the First Canada – ematics, Statistics and Com- China congress in 1997, and part of his collab- puter Science at The Univer- orative work with Dusa McDuff was presented sity of Illinois at Chicago. He in her plenary address at the ICM 1998 in Berlin. received his B.A. from Har- Professor Lalonde was an invited speaker at the vard College (1966) and his ICM 2006 in Madrid. Ph.D. from Harvard Univer- Richard Lockhart is a Professor at sity (1972). He also spent a year as an undergrad- the Department of Statistics and uate at the École Normale Supérieure in Paris. Actuarial Science of Simon Fraser His main research interests are 3-dimensional University. He received a B.Sc. in topology, hyperbolic geometry, and geometric Mathematics from the University and combinatorial group theory. He is associate of British Columbia (1975) and de- editor of the Journal of Knot Theory and its Ramifi- grees in Statistics from the Univer- cations and was the geometric topology editor of sity of California, Berkeley (M.A., the Transactions of the American Mathematical So- 1976, and Ph.D., 1979). A former Editor of the ciety from 1992 to 2000. Canadian Journal of Statistics, he has also served Catherine Sulem is a Profes- on the Advisory Committee on Statistical Meth- sor in the Department of Math- ods of Statistics Canada. He was President of ematics of the University of the Statistical Society of Canada in 1996 – 1997. Toronto. She received a Doc- Much of his work is in the area of model assess- torat d’État from the Univer- ment, generally in the form of goodness-of-fit. sité de Paris-Nord in 1983. Carl Pomerance is a Professor She was Keynote Speaker at at the Department of Mathe- IMACS2003 (International As- matics of Dartmouth College. sociation for Mathematics and Computers in From 1999 to 2003, he was a Simulation) and an invited speaker at a meet- member of the technical staff ing of the American Mathematical Society in of Bell Labs-Lucent Technolo- 1999. In 1998, she was awarded the Krieger – gies. He holds degrees from Nelson Prize by the Canadian Mathematical So- Brown University (B.A., 1966) ciety. Her research interests are in nonlinear par- and from Harvard University (M.A., 1970, Ph.D., tial differential equations arising in physics: non- 1972). A number theory specialist, he has re- linear partial differential equations, nonlinear

102 GOVERNANCEAND SCIENTIFIC GUIDANCE

Schrödinger equations and related systems, the Jean-Christophe Yoccoz is Pro- water wave problem, the Boltzmann equation, fessor at the Collège de France and computational fluid mechanics. Since 2000, where he holds a Chair in Math- she has been an Associate Editor of the SIAM ematics (Differential Equations Journal of Mathematical Analysis. From 1999 to and Dynamical Systems). He 2005, she was an Associate Editor of the Cana- obtained a Doctorat d’État in dian Journal of Mathematics. 1985. He was awarded the Mary F. Wheeler holds the Fields medal in 1994 and is a Ernest and Virginia Cockrell member of the Académie des sciences (France), Chair in Engineering at the a Chevalier de la Légion d’Honneur (1995) and University of Texas at Austin an Officer of the Ordre du Mérite (2000). His re- where she is also Professor at search work concerns the theory of dynamical the Department of Mathemat- systems and the Julia and Mandelbrot sets. ics. In addition, she is Direc- Steven Zelditch is a Professor tor of the Center for Subsur- of Mathematics at Johns Hop- face Modeling of the Texas Institute for Compu- kins University. He received tational and Applied Mathematics (TICAM) at his Ph.D. from the Univer- the same university. She obtained her Ph.D. from sity of California, Berkeley, in Rice University. She is currently an editor of six 1981. A past member of the journals and is Managing Editor of Computa- editorial board of the Annales tional Geosciences. In 1998, she was elected to the Scientifiques de l’École Normale National Academy of Engineering. Her research Supérieure, he is presently on the editorial board interests include parallel computation and nu- of the American Journal of Mathematics. His re- merical solution of partial differential systems search centers around applications of microlo- with applications to the modelling of subsurface cal analysis to problems in the following areas: and surface flows. asymptotics of eigenfunctions/eigenvalues on Riemannian manifolds, statistical algebraic geometry, mathematical physics (quantum chaos, 2D Yang – Mills, string/M-theory).

Jacques Turgeon, Vice-Principal (Research), Université de Montréal, is an ex-ofﬁcio member of the Advisory Committee. Chantal David (Concordia University), Andrew Granville (Université de Montréal), Jean LeTourneux (Université de Montréal), and Odile Marcotte (Université du Québec à Montréal), all Deputy Directors of the CRM, were invited members of the Committee.

103 CRM Administrative and Support Staﬀ CRMADMINISTRATIVE AND SUPPORT STAFF

The Director’s Oﬃce

François Lalonde Jean LeTourneux Director Deputy Director, Publications Chantal David Odile Marcotte Deputy Director, Bulletin du CRM Deputy Director, Annual Report and Coordina- Andrew Granville tion with Related Fields Deputy Director, CRM Prizes

Administration

Vincent Masciotra Guillermo Martinez-Zalce Head of Administration Research Laboratories Administrative Coordi- Muriel Pasqualetti nator Administrative Assistant Diane Brulé-De Filippis Secretary

Scientiﬁc Activities

Louis Pelletier Josée Simard Coordinator Project Manager (until August 2006) and Assis- Josée Laferrière tant (starting in September 2006) Assistant Louise Letendre Sakina Benhima Assistant Project Manager (starting in September 2006)

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 Communications Ofﬁcer and Webmaster

105 Mandate of the CRM MANDATE OF THE CRM

he Centre de recherches mathémati- cieties (CMS, SSC, CAIMS), the development Tques (CRM) was created in 1969 by the Uni- of the mathematical sciences in the Atlantic versité de Montréal through a special grant from provinces through AARMS, and other activities the National Research Council of Canada. It organized outside the three institutes. They also became an NSERC national research centre in participate in the National Program on Complex 1984. It is currently funded by NSERC (Natu- Data Structures jointly with the Canadian statis- ral Sciences and Engineering Research Coun- tical community. cil), by the Government of Québec through the This national mandate is complemented by, FQRNT (Fonds québécois de la recherche sur and indeed supported by, a long-standing voca- la nature et les technologies), by Université de tion of promoting research in the mathematical Montréal, as well as McGill University, Univer- sciences in Québec. For instance, sité du Québec à Montréal, Concordia Univer- • the CRM supports research through its nine sity, University of Ottawa, Université Laval and research laboratories spanning most of the im- by private donations. The mission of the CRM is portant areas of the mathematical sciences, to support research in mathematics and closely • it supports, through partnership agreements, related disciplines and to provide leadership in a group of local researchers chosen mainly from the development of the mathematical sciences in departments of mathematics and statistics, but Canada. 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- • it organizes each year a series of scientic ture courses on different areas of the mathemat- events on a specific theme (high-profile lectures, ical sciences, • workshops, summer schools, etc.), it sponsors joint activities with the ISM (Insti- • its general program and its multidisciplinary tut des sciences mathématiques) including the and industrial program provide funding for con- weekly CRM/ISM colloquia, graduate courses ferences and special events at the CRM and offered by distinguished visitors and a program across the country, of postdoctoral fellowships, • • each year it invites, through the Aisenstadt it works actively at developing contacts with Chair, one or more distinguished mathemati- industry. Its joint activities with liaison and re- cians to give advanced courses as part of its the- search centres (CIRANO, CRIM and MITACS) matic program, and research centres doing applied research • it awards four prizes yearly: the CRM – (CIRRELT, GERAD, INRS-EMT, and INSERM) Fields – PIMS Prize recognizing major contribu- led to the creation of industrial networks. The tions to mathematics, the Aisenstadt Prize given most recent ones involved, in 2004 – 2005, Bom- for outstanding work done by a young Canadian bardier Aerospace and the Brain Imaging Unit mathematician, the CAP – CRM Prize for excep- CRM – IUGM – INSERM. tional achievement in theoretical and mathemat- The CRM fulfils its national mission by in- ical physics, and the CRM – SSC Prize for excep- volving the largest possible number of Canadian tional contributions to statistics in early career, mathematicians in its scientific programs, both • it publishes technical reports and about ten as participants and as organizers. It also sup- books per year (and some of its collections ports many events taking place outside Mont- are published jointly with the AMS and with réal and the Province of Québec. It is recog- Springer), nized worldwide as one of the major institutes • it has an extensive postdoctoral fellowship in the mathematical sciences. The director of the program, with more than thirty postdoctoral fel- CRM is assisted by two managerial structures: lows in place last year, funded in partnership the Bureau de direction and the Scientific Advi- with other organizations and researchers, sory Committee. The Advisory Committee is a • it informs the community of its activities group of internationally renowned mathemati- through its newsletter, Bulletin du CRM, and its cians from Canada and abroad, who approve web site at crm.math.ca, scientific programs and thematic years, choose • it participates, with the other two Canadian recipients of the Aisenstadt Prize and suggest institutes, in groundbreaking national initia- new scientific ventures to explore. tives. One example is the MITACS (Mathemat- ics of Information Technology and Complex Sys- tems) network. The institutes sponsor the An- nual Meetings of the Mathematical Sciences So-

107