Centre de recherches mathématiques, Annual Report 1996-1997

Coming Events

Theme Year 1997-1998: Statistics

Org.: Jerry F.Lawless (Waterloo), Marc Moore (École polytechnique), Nancy Reid (Chair, Toronto), Yannis Yatracos (Montréal)


The Canadian school of statistics is extremely active and a theme year in statistics is most timely. Theoretical work is done in essentially all Canadian universities. Moreover there are many professionals using and developing statistics in governmental service (Statistics Canada and its provincial counterparts, etc.), in other disciplines (like the human, environmental and health sciences), and in private companies (e.g.independent poll services).

The theme year in statistics will emphasize several current directions in the theory and application of statistics, with particular emphasis on problems involving dependent data. Five areas of concentration have been selected: the interface between computation and theoretical statistics, spatial statistics, nonparametric functional estimation, statistical methods in epidemiology and genetic epidemiology, and longitudinal data analysis. The organizers for these programs have emphasized, as much as is feasible, interaction with researchers having special expertise in applications.

Since the participants will form a blend of university professors, postdoctoral fellows, students, and users and practitioners of statistics, the theme-year organizers have favoured short, focused workshops to allow a larger participation of professionals. The year offers 12 workshops, 2 symposia, 3 lectures series of which two will be given under the auspices of the CRM's prestigious Chaire Aisenstadt, and the CRM Summer School at Banff. Professor Peter Hall (The Australian National University) will give the first part of the André-Aisenstadt Lectures at the CRM in conjunction with the workshop on Nonparametric Functional Estimation in October 1997. Sir David Cox will hold the second part of the Chaire, and will deliver a series of lectures in May 1998. The events are presented below in the order they are to take place. They will be held at the CRM unless otherwise indicated.

CRM Summer School at Banff:
Likelihood and Asymptotics

1-10 August 1997, Banff
Org.: Thomas J. DiCiccio (Cornell)

The 7th CRM Summer School will be on Likelihood and Asymptotics. Likelihood and related concepts, which are of central importance in statistical theory and methodology, have recently undergone intensive development. Some of the topics receiving special attention include: ancillarity and conditionality; prediction; the construction of likelihood-like objects, such as modified profile likelihoods and nonparametric likelihoods; and the connections between frequentist and Bayesian inference. Old and new asymptotic methods have been essential to these investigations. The purpose of the summer school is to bring junior and senior researchers and graduate students together to explore the recent developments and new directions in the area of likelihood, interpreted in a very broad sense.

The list of the invited lecturers includes: O.E.Barndorff-Nielsen, J.G.Booth, R.W.Butler, A.C.Davison, B.Efron, C. A.Field, D.V.Hinkley, D.A. S.Fraser, J. L.Jensen, J. E.Kolassa, B.G.Lindsay, P.McCullagh, A. C.Monti, P.Mykland, D. A.Pierce, N.Reid, E.M.Ronchetti, T.A.Severini, I.M. Skovgaard, S.E.Stern, T.J.Sweeting, M.E.Thompson, S.Wang, G.A.Young.

Workshop on Resampling Methods

14-20 September 1997
Org.: Christian Léger (Montréal), Joseph Romano (Stanford), Rob Tibshirani (Toronto)

Since the advent of fast computing, resampling methods have played a major role in developing new tools for statisticians. In recent years, resampling methods have been developed for more complicated problems, including time and spatially dependent data, nonparametric regression methods, and model selection. This workshop will present the latest theoretical and practical advances in the field.

The list of the invited speakers includes: P.J.Bickel, A.C.Davison, T.J.DiCiccio*, T.C.Hesterberg*, S.N.Lahiri, R.Y.Liu, S.Paparoditis*, D.N.Politis, J.Shao, M.Sherman*, R.R.Sitter, L.A.Thombs. (* indicates a speaker to be confirmed.)

Workshop on Symbolic Computation

21-27 September 1997
Org.: James Stafford (Western Ontario)

In recent years we have witnessed an increase in the use of computer algebra environments in statistical research, teaching, and consulting. The goals of the workshop are to emphasize:

  1. the structure of symbolic environments,
  2. computer algebra research in statistics,
  3. statistical research that involves computer algebra.

There will be a major emphasis on the third of these, as a thorough understanding of this is needed to address the second and to design symbolic environments for statistics.

The list of the invited speakers includes: D.Andrews, D.Bellhouse, J.Borwein, D.Broadhurst, R.Corless, A.C.Davison, F.-X.de Rossi, T.DiCiccio, C.Field, R.Gatto, D.Hinkley, Z.A.Karian, W.S.Kendall, J.Kolassa, M.Lesperance, N.Lazar, P.Mykland, P.McCullagh, W.Olford, D.Pierce, J.Rao, G.Roberts, E.Ronchetti, A.Salvan, B.Smith, R.Thomas, K.Viraswami, R.Waterman, H.Wynn.

Symposium on Nonparametric Functional Estimation

13-24 October 1997
Org.: Luc Devroye (McGill), George Roussas (UCDavis), Yannis Yatracos (Montréal)

Nonparametric functional estimation is widely used in theory and applications, with emphasis on the estimation of density functions, distribution functions, quantile functions, regression functions, and nonlinear functionals of the density. Most results to date have been obtained in the framework of independent sampling, but current research directions motivated by applications consider nonparametric functional estimation under various types of dependence.

The list of the invited speakers includes: A.Barron, R.Beran, A.Berlinet, P.Burman, R.Eubank, R.Fraiman, A.Feuerverger, I.Gijbels, W.Gonzalez-Manteiga, L.Gyorfi, N.Heckman, E.Isogai, A.Krzyzak, R.C.Liu, G.Lugosi, B.MacGibbon, J.S.Marron, E.Masry, H.Mueller, D.-T.Pham, J.Ramsay, J.Rice, P.Robinson, J.Rojo, U.Stadtmueller, L.T.Tran, Y.Truong, F.Udina, J.-L.Wang, S.Yakowitz, B.Yu.

Workshop on Empirical Bayes and Likelihood Inference

9-15 November 1997
Org.: S.Ejaz Ahmed (Regina) and Nancy Reid (Toronto)

Empirical Bayes and likelihood-based methods continue to play vital roles in statistical inference. Empirical Bayes/shrinkage estimation and meta-analysis provide extremely useful techniques for combining data from various sources. Asymptotic theory has advanced understanding of the fundamental role of the likelihood function. This workshop will explore connections between empirical Bayes methods and likelihood inference, with emphasis on recent developments and their application in various fields.

The list of the invited speakers includes: J.O.Berger, J.Bernardo, D.R.Cox*, B.Efron*, D.Fraser, E.George*, M.Ghosh, V.Godambe, I.Guttman, D.Krewski*, T.A.Louis, B.MacGibbon, J.N.K.Rao, C.Roberts*, E.Saleh, P.K.Sen, B.K.Sinha, D.Sprott, L.Wasserman*, J.Zidek.

Workshop on Time Series Analysis

23-27 March 1998
Org.: Roch Roy (Montréal)

Time series analysis continues to be a subject of major interest in statistics since almost every scientific discipline is concerned with data collected over time. This workshop will focus on recent developments in nonlinear and nonparametric methods.

The list of the invited speakers includes: D.R.Brillinger, D.Guegan, M.Hallin, K.Knight, A.Latour, D.-T.Pham, B.W.Silverman*.

Lecture Series on Recent Advances and Trends in Spatial Statistics

23-24 March 1998
Speaker: Noel A.C.Cressie

Workshop on Image Analysis

30 March - 3 April 1998
Org.: Marc Moore (École polytechnique)

In many applications data come in the form of images. Often these observations reveal a stochastic behaviour in the image. Appropriate stochastic models are needed to represent these stochastically generated images. Also, the statistical tools used to analyse these data must be able to take into account the morphological character of the image. This workshop plans to present results to deal with these problems, and also illustrations of their use.

The list of the invited speakers includes: S.Geman, P.J.Green, H.Kunsch, M.Schmitt, L.Younes.

Workshop on Statistical Inference for Spatial Processes

6-9 April 1998
Org.: Xavier Guyon (Paris I)

It is known that many of the tools for statistical inference developed in the context of independent data, or in the context of standard one-dimensional stochastic processes, are not applicable to spatial processes. In this workshop we plan to present recent results pertaining to statistical inference for some important classes of spatial processes, e.g. Markov random fields, random set processes. The inference tools considered will include those based on simulations.

The list of the invited speakers includes: F.Comets, B.C.Gidas, J.L.Jensen, J.Moller, M.L.Stein.

Workshop on Applications of Spatial Statistics in Earth, Environmental and Health Sciences

27 April - 1 May 1998
Org.: Richard Lockhart (Simon Fraser)

This workshop will look at techniques in spatial statistics applied to a variety of applied problems in the earth, environmental, and health sciences. Spatial covariance modelling, applied to meteorological problems such as acid precipitation, to environmental problems such as spatial distribution of cancer and related problems will be a focus but other applications in the earth, environmental, and health sciences will be looked at.

The list of the invited speakers includes: D.Billheimer, P.Diggle*, P.Guttorp, P.Sampson, R.L.Smith, J.V.Zidek.

Workshop on Statistics and Epidemiology

3-9 May 1998
Org.: Gerarda Darlington (Toronto) and Shelley Bull (Toronto)

This workshop will look at recent developments in descriptive epidemiology, etiologic studies, and clinical epidemiology.

The list of the invited speakers includes: N.E.Breslow*, A.Donner, N.Kreiger, J.Neuhaus.

Workshop on Genetic Epidemiology

9-16 May 1998
Org.: Gerarda Darlington (Toronto) and Ken Morgan (McGill)

A discussion of statistical and genetic principles (segregation analysis, linkage analysis, association analysis, population genetics, isolated populations, linkage disequilibrium mapping) and complex pedigrees and complex traits (gene identity by descent families, gene identity by descent individuals).

The list of the invited speakers includes: R.Elston, J.Ott, N.Risch*, E.Thompson, B.Weir, A.Whittemore, E.Wijsman*.

Workshop and Symposium on Longitudinal Data Analysis for Complex Surveys

18-22 May 1998, Statistics Canada, Ottawa
Org.: Michael Hidiroglou (Statistics Canada), Sylvie Michaud (Statistics Canada), David Binder (Statistics Canada)

Longitudinal data analyses are increasingly used in the social sciences in the past decade. The tools for this type of analysis include event history methods, gross flows, conditional and marginal models, and hierarchical linear modelling. These techniques have been developed without taking into account complex surveys. This workshop will focus on recently developed methods in longitudinal data analysis and in particular on the required adjustments for use for data arising from complex surveys.

Workshop on Event History Analysis

25-29 May 1998
Org.: Richard J. Cook (Waterloo) and Jerry F. Lawless (Waterloo)

Event history analysis is now commonly applied in most branches of science, including demography, epidemiology, medicine, engineering, and economics. The purpose of this workshop is to stimulate a critical appraisal of existing models and techniques and to consider future developments.

The list of the invited speakers includes: O.O.Aalen, P.K.Andersen, V.T.Farewell, J.D.Kalbfleisch, N.Keiding, J.P.Klein, S.W.Lagakos, D.Lin, R.J.A.Little, S.A.Murphy, D.Oakes, R.L.Prentice, B.W.Turnbull, L.J.Wei.

Workshop on Statistics of Brain Mapping

13-14 June 1998
Org.: Keith Worsley (McGill)

The theory of random fields, image analysis and multivariate statistics is finding new applications in the rapidly emerging area of brain mapping by Positron Emission Tomography (PET) and functional Magnetic Resonance Imaging (fMRI). This two-day workshop, to be held after the 4th International Conference on Functional Mapping of the Human Brain to be held in Montréal, June 7-12 1998, is designed to bring together statisticians interested in image analysis, and researchers interested in brain mapping.

The list of the invited speakers includes: R.Adler, F.Bookstein, E.Bullmore, B.Eddy, K.Friston, U.Grenander, N.Lange, R.McIntosh, M.Miller, J.-B.Poline, D.Siegmund, P.Thompson, S.Zeger, K.Zilles.

Extra-thematic activities 1997-1998

Here is a list of scientific events to be held in parallel to the theme year. The descriptions are taken from the proposals submitted to the CRM Advisory Committee.

International Linear Algebra Society Symposium on Fast Algorithms for Control, Signals and Image Processing

6-8 June 1997, Winnipeg
Org.: P.N.Shivakumar (Univ.of Manitoba)

The Symposium emphasizes modern methods in scientific computing and linear algebra relevant to digital control, signal and image processing. For such applications it is important to consider ingredients such as:

  1. sophisticated mathematical models of the problems, including a priori knowledge,
  2. rigorous mathematical theories to understand the difficulties of solving problems which are often ill-posed, and
  3. fast algorithms for either real-time or data-massive computations.

Aspects of each of these three ingredients will be discussed by the speakers.

Canadian Undergraduate Mathematics Conference

18-21 July 1997, Univ.de Montréal
Org.: J.Marcil (Chair), E.Pelletier, L.Corbeil, P.Larocque, Y.Delbecque

The CUMC gives Canadian students the opportunity to share ideas and to open up to new career possibilities. Participants are invited to present a lecture, either on personal work or any mathematical topic connected to a contemporary mathematical challenge. Furthermore, a few lectures will be given by professors, most of them coming from the Montréal region.

CRM-Fields-CAP Summer Workshop in Theoretical Physics
Solitons: Properties, Dynamics, Interactions and Applications

20-26 July 1997, Queen's Univ.
Org.: B.C.Castel (Queen's), R.B.Mackenzie (Univ.de Montréal), M.B.Paranjape (Univ.de Montréal), W.J.Zakrzewski (Durham)

Recent work on topological solitons and like objects has given rise to interesting results in both mathematics and physics. Mathematical applications include integrable models, the classification of 3- and 4 -manifolds, which has been related to soliton solutions of instanton and BPS monopole equations, etc. Physical applications include particle and nuclear physics (monopoles and skyrmions), solid state physics (vortices in superconductors, baby skyrmions in the quantum Hall effect, etc.), phase transitions, magnetostatics and ferromagnetodynamics, cosmology, etc. The workshop will bring together researchers from the following fields: BPS solitons and s-duality, soliton scattering, electroweak strings, baby skyrmions and applications to solid state, skyrmions and applications to nuclear physics, nontopological solitons.

Workshop on Differential Equations

21-25 July 1997 (tentative), Dalhousie
Org.: Alan Coley (Dalhousie)

This workshop will take place during the week preceding the international conference in differential equations held in Halifax during the week of July 25 -29 and will emphasize geometric techniques. Three series of lectures are planned.

International Conference on Differential Equations with Applications to Biology

25-29 July 1997, Dalhousie Univ.
Org.: S.Ruan (Dalhousie), G.Wolkowicz (McMaster), J.Wu (York)

The theory of differential equations and dynamical systems has advanced significantly, and various applications have been found in biology, chemistry, ecology, engineering, epidemiology, industry, medicine, neurobiology, oceanography, physics, physiology, psychology, zoology, and many other fields. The subject is of increasing importance, as witnessed by the current interest in population dynamics, neural computations, genetic algorithms, and similar subjects.

The plenary lectures feature current research in epidemiology (P.van den Driessche and G.Webb), physiology and neurobiology (L.Glass, M.Hirsch and M.Mackey), population dynamics (S.Levin, L.Segel, H.Smith and P.Waltman), and qualitative analysis (J.Mallet-Paret and K.Schmitt).

Conférence à la mémoire de Gilles Fournier

13-16 August 1997, Univ.de Sherbrooke
Org.: M.Frigon (Univ.de Montréal), A.Granas (Univ.de Montréal and U.Nicolas Copernicus) and T.Kaczynski (Univ.de Sherbrooke)

This is a memorial conference for the second anniversary of Gilles Fournier's death. Four commemorative conferences will be delivered. The lecturers will be A.Granas, Mario Martelli (California SU-Fullerton), Jean Mawhin (Louvain), Michel Willem (Louvain). There will be also eight plenary lectures.

12th Summer Conference on Topology and its Applications, and Workshop on Continuum Theory, Set-Theoretic Topology and Applied Topology

12-16 August 1997, Univ.of Nipissing (North Bay)
Org.: Stephen Watson (York)

The scientific scope of these summer meetings is traditionally quite broad. It has been decided to maintain this practice but to emphasize three important areas within topology. The event will do this by offering workshops consisting of a series of lectures in each of these topics. The three mathematicians invited to give these lectures are doing some of the best current work. All three are quite young. They are Kazuhiro Kawamura of Tsukuba University who has worked extensively in continuum theory and geometric topology, Stevo Todorãeviç of Beograd University and University of Toronto, who is the leading figure in applications of partition relations to set-theoretic topology, and Dmitri Shakhmatov of Moscow State University and Ehime University, who is a key figure in applied topology.

First Vancouver Meeting in Probability

19-28 August 1997, UBC
Org.: Martin Barlow and Ed Perkins (UBC)

This two-week workshop will consist of 6 minicourses on various applications of probability. Each minicourse will consist of four one-hour lectures. The speakers and their titles are: R.T.Durrett (Cornell), Stochastic spatial models; H.Foellmer (Berlin), Probabilistic Problems in Finance; T.Kurtz (Univ.of Wisconsin), Infinite systems of stochastic differential equations ; J.-F.Le Gall (Paris VI), Superprocesses, Markov snakes and partial differential equations; C.M.Newman (NYU), Random geometry of first passage percolation; D.W.Stroock (MIT), Applications of analysis on pathspace.

Theme Year 1998-1999: Number Theory

Org.: H.Darmon (McGill), M.Goresky (Institute for Advanced Study), F.Murnaghan (Toronto), K.Murty (Toronto), R.Murty (Queen's)


Number theory lies at the heart of mathematics and in fact goes under the appellation of 'Queen of Mathematics.' It has provided the source of research problems that have given rise to fundamental concepts in many parts of mathematics. The CRM thematic year 91-92 was related to number theory and was organized by Ram Murty. Earlier, during the spring of 1988, Robert Langlands and Dinakar Ramakrishnan held a workshop at the CRM on the zeta functions of Picard modular surfaces. Both the thematic year and the workshop were extremely successful, not only in terms of the number of participants and of their quality, but also of their legacy: four important publications came out of them (Elliptic Curves and Related Topics, CRM Proceedings and Lecture Notes, Vol. 4; Theta Functions, CRM Proceedings and Lecture Notes, Vol. 1; Introduction to Abelian Varieties, Kumar Murty, CRM Monograph series, Vol. 3; The Zeta Functions of Picard Modular Surfaces, eds. R.P.Langlands, D.Ramakrishnan, Les Publications CRM) and several recent results can be traced back to them.

Recently, Andrew Wiles using the work of Kenneth Ribet resolved the 350 year old problem of Fermat's Last Theorem. His work has opened the door of a new universe of methods that needs to be understood, simplified and explained so that further problems may be solved. It is the aim of the CRM thematic year 98-99 to address this need. It is expected that there will be active participation of the many number theorists from across Canada as well as their postdocs and students.

The format of the year puts the emphasis on both research and teaching. Number theory is an extremely wide area and most universities cannot offer as many courses as needed to provide young students with a sound basis. It was consequently judged that the usual format of several short workshops would not be ideal. Instead the organizers opted for the following format: five one-month courses given for the benefit of graduate students and postdoctoral fellows intertwined with four workshops. The courses will cover:

  1. Elliptic curves and automorphic forms,
  2. Representations of p-adic groups,
  3. Automorphic L-functions,
  4. p-adic L-functions,
  5. Algebraic Cycles and Shimura Varieties.

The four workshops will be devoted to:

  1. Arithmetic algebraic geometry,
  2. L-functions and related themes,
  3. p-adic L-functions and modular forms and
  4. Representations of p-adic groups.

The workshops will follow the various courses that they are connected with. Since the topics of elliptic curves, automorphic forms, and automorphic L-functions are closely connected, there will be only one workshop related to these courses. The optimal timetable has not yet been determined. Two major events will be added to these "course-workshop" cycles. They are the CRM Summer School at Banff (May 11-20, 1998, Orgs.: J.Lewis with B.Gordon, S.Mueller-Stach, S.Saito, N.Yui) and the Sixth Conference of the Canadian Number Theory Association (CNTA) that will be held during the summer of 1999 in Winnipeg (org.: H.Williams).

8th CRM Summer School at Banff:
The Arithmetic and Geometry of Algebraic Cycles

11-20 May 1998, Banff (Alberta)
Org.: J.Lewis (Univ.of Alberta) with B.Gordon (Univ.of Oklahoma), S.Mueller-Stach (Univ.Essen), S.Saito (Univ.of Tokyo), N.Yui (Queen's)

The purpose of the Summer School is to offer a full and in-depth account ranging from introductory courses on the subjects by leading experts to discussion of the latest developments in the fields.

As a subfield of algebraic geometry, the subject of algebraic cycles has thrived through its energetic interaction with algebraic K-theory, Hodge theory, arithmetic algebraic geometry, number theory, and topology (as in Lawson homology). These interactions have led to such developments as: a description of Chow groups (cycle groups) in terms of algebraic K-theory; the application of the Mercurjev-Suslin theorem to the arithmetic Abel-Jacobi mapping, with corresponding torsion results for Chow groups; progress on the celebrated conjectures of Hodge, and of Tate, which "compute" cycle class groups respectively in terms of Hodge theory or as the invariants of a Galois group action on étale cohomology; the conjectures of Bloch and Beilinson, which "explain" the zero or pole of a variety's L-function, as well as interpret the leading non-zero coefficient of its Taylor expansion at a critical point in terms of arithmetic and geometric invariants of the variety and its cycle class groups. The immense recent progress in algebraic cycles, based on interaction with many areas of mathematics (not unlike algebraic geometry itself), has contributed to a considerable degree of inaccessibility, especially for graduate students and non-specialists. Even specialists in one approach to algebraic cycles may not understand other approaches well.

To our knowledge, this would be the first conference to focus on the arithmetic and geometry of algebraic cycles, bringing together experts who approach this topic from different directions. Other conferences, such as the Motives conference (Seattle 1991) or conferences on Arithmetic Algebraic Geometry or Algebraic K-theory, overlap with the topic of this conference, but have a more narrow perspective.

The featured speakers will give 3 lectures each. All are confirmed except those marked by an asterisk who have agreed tentatively. They are: Spencer Bloch, J.-L.Colliot-Thelene*, Mark Green, Uwe Jannsen, Blaine Lawson, Dinakar Ramakrishnan, Shuji Saito, Don Zagier. Other major speakers (1 lecture) include: A.Beilinson, Ch.Deninger, E.Friedlander*, H.Gillet, B.Gordon, B.Gross*, J.Lewis, S.Mueller-Stach, K.Murty, J.Nekovar*, W.Raskind, Masahiko Saito, Takeshi Saito, C.Schoen, A.Scholl, C.Soule, A.Suslin*, V.Voevodsky, N.Yui, Y.Zarhin.

Courses: Elliptic Curves and automorphic forms; Automorphic L-functions;
Workshop: L-functions and related themes

The course on elliptic curves and automorphic forms will be given in three parts by Kumar Murty and Ram Murty, and Henri Darmon as a two-month course. This should be in the fall of 1998 and will cover the basic material in the theory of elliptic curves. Henri Darmon will give a quick survey, based on his 'Russian Math Surveys' article on the proof of the Shimura Taniyama conjecture à la Wiles, etc.

The second course will be on analytic aspects of automorphic L-functions and will be given by Ram Murty. The topics to be covered will be Hecke theory, Eisenstein series, L-functions of GL(n) and converse theory.

Course and Workshop: Representations of reductive p-adic groups

The course, given by Fiona Murnaghan, will be divided into two parts. The first part will include an overview of characters of admissible representations and orbital integrals. Results relating characters and orbital integrals will be discussed. One such result is Harish-Chandra's local character expansion, which expresses certain character values as linear combinations of Fourier transforms of nilpotent orbital integrals. It will summarize recent results concerning the coefficients and the domain of validity of the expansion. It will also give a general description of some conjectures and open problems.

The second part of the course will consist of a survey of recent work on K-types for p-adic groups. This is the study of admissible or, more generally, smooth representations of reductive p-adic groups via their restriction to compact open subgroups. It will indicate how certain K-types are defined in terms of filtrations of parahoric subgroups, and discuss results of Moy and G. Prasad on properties of these K-types and the admissible representations which contain them. The work of Bushnell and Kutzko on classifying smooth representations via K-types will also be described.

Course and Workshop: p-adic L-functions

Henri Darmon will explain recent progress in the theory of p-adic L-functions associated with the cohomology of algebraic varieties, with special emphasis on elliptic curves and modular forms. In particular, he will discuss the main conjectures of Iwasawa theory for modular elliptic curves. Two settings for the main conjecture (for non-CM curves) have been explored so far: the first corresponding to the cyclotomic Zp-extension of Q, and the second to the anticyclotomic extension of a quadratic field. He will discuss the work of Kato which gives a partial proof of the main conjecture in the cyclotomic case, and the work of Bertolini and himself which leads to similar results in the anticyclotomic case. The relation with the deformation theory of Galois representations will be discussed.

Course and Workshop: Algebraic Cycles and Shimura Varieties

There will be two courses in this area, one by Kumar Murty and another by Mark Goresky. Kumar Murty will give a two-week course on "The Hodge and Tate Conjectures" in the spring of 1999. These conjectures will be related to various conjectures about zeros and poles of zeta functions associated with varieties. Mark Goresky will give a course on "Compactifications and Cohomological Methods." It will concentrate on the real and complex geometry and topology of the various compactifications which are associated with Shimura varieties:

  1. locally, Hermitian and linear locally symmetric spaces and compactifications (Borel-Serre, reductive Borel-Serre, Baily-Borel Satake and toroidal),
  2. group, L2, intersection and weighted cohomologies,
  3. Hecke operators, the geometry of a Hecke correspondence, the induced correspondence on the boundary, counting fixed points, Lefschetz number of a Hecke correspondence.

A one week workshop in this area will follow.

6th Conference of the CNTA

The Canadian Number Theory Association (CNTA) was founded in 1987 at the International Number Theory Conference at Laval University. Later meetings were held in Banff (1988), at the University of British Columbia (1989), Queen's University (1991), Dalhousie University (1994), and Carleton University (1996). In keeping with the objectives of the CNTA of enhancing and promoting research in Number Theory across the country, the next international CNTA meeting will be held in Winnipeg during the Summer of 1999. It will be the conclusion of the CRM thematic year. The organizer is H. Williams (Manitoba) and the scientific committee for the conference consists of J.Borwein (SFU), D.Boyd (UBC), C.David (Concordia), R.Murty (McGill/Queen's), C.Stewart (Waterloo) and H.Williams (Manitoba).

The week long event will welcome 5 main speakers, about 20 invited speakers, and several contributed talks divided into a maximum of 3 parallel sessions. Five specific themes have been chosen by the organizers. These areas have seen rapid development in recent years, both in Canada and internationally. They also represent the interests of the members of the scientific committee. These themes are:

  1. Mahler's Measure and L-functions;
  2. Computational Combinatorial Number Theory;
  3. Diophantine Approximation;
  4. Arithmetic Algebraic Geometry;
  5. Computations and Curves.

Extra-thematic activities 1998-1999

The general scientific program for the year 98-99 will be decided by the CRM Advisory Committee during the Fall of 1997. At this point funds have been committed to the following three events.

Congrès de la Société Statistique du Canada

31 May - 3 June 1998, Univ.de Sherbrooke
Org.: Louis-Paul Rivest (Univ.Laval)

The theme of the 1998 annual congress of the SSC will be "From Sampling to Data Analysis." It will be held jointly with the yearly meeting of French-speaking statisticians, "Méthodes et applications de la statistique."

Formal Power Series and Algebraic Combinatorics '98

5 days in June 1998, Fields Institute
Org.: N.Bergeron (York, chair), M.Delest (Univ.de Bordeaux), F.Sottile (Toronto), W.Whiteley (York)

The relationship between algebraic and enumerative combinatorics, and computer science is very deep. On the one hand, complexity problems in computer science rely on counting techniques. Also, the development of efficient algorithms often depends on the understanding of some combinatorial structures: graphs, posets, matroids, polytopes, etc. On the other hand, combinatorialists are heavy users of computers for computations and visualisation of objects. Both aspects of this relationship are featured in FPSAC conferences.

The meeting will also consider the applications of algebraic combinatorics to other fields. To mention a few:

  1. finite geometry in connection with posets, polytopes, and oriented matroids,
  2. algebraic geometry using combinatorial models to describe (co)homology of certain varieties or to give computational algorithms,
  3. homology via posets (shellable, Cohen-MacCauley, etc.),
  4. physics (symmetric polynomials with parameters are eigenvalues of physical model operators),
  5. statistical physics via enumeration of polyominos, stacks of pieces, animals, etc.

International Federation for Information Processing Symposium
Modelling and Control of Distributed Parameter Systems: towards 2000
(tentative title)

10-14 August or 17-21 August 1998, Montréal
Org.: Michel Delfour (Univ.de Montréal)

Theme Year 1999-2000: Mathematical Physics


In view of the remarkable advances that are taking place in mathematical physics and of their striking impact on mathematics and physics, it was decided to devote the 1999-2000 theme activities at the CRM to this area.

The plan is to have a broad coverage with a wide range of activities: an extended program on integrable models and statistical systems, various workshops, mini-courses, etc.

The year will be coordinated by Yvan Saint-Aubin and Luc Vinet. A good number of people have already agreed to contribute to the organization of the year. The planned activities will include:

  1. Concentration period on integrable models and statistical systems.
    Org.: Ph. Di Francesco (Univ. of North Carolina and Saclay), J. Harnad (Concordia), A. LeClair (Cornell), P. Mathieu (Laval), P. Winternitz (CRM)
  2. Workshop on general relativity, astrophysics and cosmology. Org.: E. Poisson (Guelph)
  3. Workshop on Schrödinger operators and atomic physics. Org.: L. Seco (Univ. of Toronto)
  4. Workshop on Quantum Information Theory. Org.: G. Brassard (Univ. de Montréal)
  5. Workshop on the theoretical aspects of supraconductivity. Org.: A.-M. Tremblay (Univ. de Sherbrooke)
  6. Workshop on String Theory and Quantum Geometry. Org.: D.H. Phong (Univ. Columbia)
  7. CRM Summer School in Banff. Org.: Y. Saint-Aubin, L. Vinet

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