Throughout the 20th century there has been a remarkably fruitful interplay
between group theory and the geometry and topology of low-dimensional manifolds.
The study of 3-manifolds through their fundamental groups and symmetries has
turned out to be a particularly rich vein withapplications to such topics as
the tabulation of knots, geometrization problems, group actions, and surgery
theory. Conversely, results of 3-dimensional topology have been fundamental
in motivating many exciting developments in geometric group theory: actions
on R-trees, word-hyperbolic groups, decomposition theorems, quasiconvexity,
coherence, etc. Our goal is to bring together students and researchers from
these active research areas over a three week period in order to underline and
foster the connections between them.
WORKSHOP
ON GEOMETRIC GROUP THEORY
July 9-13, 2001
Organizer: Dani Wise (Brandeis & McGill Universities)
The theory of infinite groups was revolutionized by an infusion of geometric
ideas from geometry and topology. This has led to the resolution of many old
problems and the formulation of new problems and methods which have broadened
the scope of the field. This workshop will focus on these new developments
in geometric group theory. There will be four 50 minute talks per day, leaving
plenty of time for informal discussions amongst the participants.
Participants will include:
W. Ballmann (Universitat Bonn), M. Bestvina (University of Utah), B. Bowditch
(University of Southampton), M. Bridson (University of Oxford), R. Charney
(Ohio State University), B. Farb (University of Chicago), M. Feighn (Rutgers
University), I. Kapovich (University of Illinois at Urbana-Champaign), M.
Kapovich (University of Utah), O. Kharlampovich (McGill University), J. McCammond
(Texas A & M), A. Myasnikov (CCNY), P. Papazoglou (Universite Paris-Sud),
M. Sapir (Vanderbilt University), M. Sageev (Technion), Z. Sela (Hebrew University).
Registration
TOPOLOGY OF MANIFOLDS AND GROUP ACTIONS
August 20-24, 2001
Organizers: Ian Hambleton (McMaster), Ronnie Lee (Yale)
Recently there have been important break throughs in the study of the topology
of manifolds and related topics on group actions, especially in the area of
3- and 4- dimensional manifolds with new imput from the Seiberg-Witten theory
and symplectic topology. One of the main objects of this workshop is to describe
these new advances on the subject.
In addition, there also have been important developments in other areas:
For example there are the study of discrete group actions on Euclidean space
using control surgery theory, the generalization of Casson invariants from
SU(2) to SU(3), the study of Torelli group actions on the cohomology of moduli
spaces, the classification of topological group actions on 4-manifolds, just
to name a few. Not concentrated completely on 4-dimensions, our program will
also present these topics of high dimensional manifolds and related topics.
In fact, it is the design of the conference to bring about formal and informal
discussion between different perspectives, to compare questions, methods and
applications.
Participants will include:
R. Cohen (Stanford), S. Cappell (Courant Institute), J. Davis (Indiana),
A. Edmonds (Indiana), T. Farrell (SUNY at Binghamton), P. Feehan (Rutgers
University & Trinity College, Dublin), K. Froyshov (Harvard), R. Gompf (University
of Texas at Austin), C. Herald (University of Nevada at Reno), R. Kirby (UC
Berkeley), T. Leness (Florida International University), T. Li (Princeton),
M. Marcolli (Max-Planck-Institut für Mathematik, Bonn), M. McCooey (McMaster),
E. Miller (Polytechnic University of New York), J. Morgan (Columbia), L. Nicolaescu
(Notre Dame), P. Ozsvath (Princeton University), E. Pedersen (SUNY at Binghamton),
F. Quinn (Virginia Polytech Inst & State University), D. Wilczynski (Utah
State University at Logan), B. Williams (Notre Dame).
Abstracts
Schedule
Registration
INFINITE-DIMENSIONAL LIE GROUPS
October - November 2001
Organizers: Niky Kamran (McGill), Boris Khesin (Toronto)
From a differential-geometric point-of-view, infinite-dimensional Lie groups
arise as automorphism groups of various geometric structures on the manifolds,
such as a volume form, a foliation, a contact structure or a symplectic structure.
The study of these infinite-dimensional Lie groups becomes a fundamental problem
in areas of mathematics as diverse as hydrodynamics and symplectic topology.
Another wide class of infinite-dimensional Lie groups is formed by loop groups,
Kac-Moody groups, and more generally, by gauge groups on manifolds of arbitrary
dimension. The successes in the study of these groups have been immensely
fruitful both in low-dimensional geometry and topology and in quantum field
theory. Infinite-dimensional Lie groups are also fundamental in the theory
of integrable systems and their hierarchies. In this context, their action
becomes quite explicit on spaces of pseudo-differential and Fourier integral
operators.
The purpose of this mini-program will be to review some of the significant
recent developments in the above areas and to explore some of the important
open problems.
INTRODUCTORY LECTURES by V. Guillemin (MIT) and A.A. Kirillov (Pennsylvania)
October 29 - November 1, 2001
Registration
Schedule
WORKSHOP
ON THE GEOMETRY OF INFINITE-DIMENSIONAL LIE GROUPS
November 2-6, 2001
Participants will include:
A. Banyaga (Penn State), O. Bogoyavlenskij (Queen's), J. Harnad (CRM &
Concordia), J. Hurtubise (CRM), L. Jeffrey (Toronto), M. Kapranov (Toronto),
F. Lalonde (UdeM), J. Leslie (Howard), E. Meinrenken (Toronto), G. Misiolek
(Notre Dame), P. Olver (Minnesota), H. Omori (Tokyo), V. Ovsienko (CNRS-Luminy),
A. Pianzola (Alberta), M. Pinsonnault (UQAM), T. Ratiu (EPFL Lausanne), T.
Robart (Howard), C. Roger (Lyon 1), P. Slodowy (Hamburg), R. Wendt (Fields
Institute),(P. Winternitz (CRM), I. Zakharevich (Ohio State).
Registration
Schedule
II GROUPS AND ALGEBRAIC GEOMETRY
January - June 2002
The importance of algebraic geometry in representation theory,
has grown enormously during the past decades, with the arrival of such techniques
as D-modules and perverse sheaves. Geometry intervenes in a crucial
fashion in the proof of such results as the Kazhdan-Lusztig conjecture, the
construction of canonical bases for representations, and the work of Beilinson-Drinfeld
on the Geometric Langlands program. A number of deep connections have arisen
between the algebraic geometry and algebraic combinatorics, whose ramifications
extend all the way to mathematical physics and topology. A special emphasis
of the programme will be in graduate training, and a variety of short courses
will be organised, as well as graduate courses of a more introductory nature.
Funding is available for graduate students wishing to attend.
Some financial support to help defray living expenses is available for graduate
students. A request for funds must be accompanied by a reference letter from
the student's research director and a C.V.
Please send your application for financial aid to:
C/O Louis Pelletier
Centre de recherches mathématiques
Universite de Montréal
C.P. 6128, Succursale Centre-ville,
Montréal (Québec)
CANADA H3C 3J7
Fax: (514) 343-2254
E-mail: activites@CRM.UMontreal.CA
AISENSTADT CHAIRS
There will be three series of lectures delivered under the auspices of
the Aisenstadt chair, by E. Frenkel (Berkeley), L. Lafforgue
(IHES) and G. Lusztig (MIT).
Conferences Program
GRADUATE COURSES
January - April 2002
Abram Broer (Université de Montréal) : "Hilbert
schemes of points and their applications"
Henri Darmon (McGill University) : "Automorphic
forms"
Eyal Goren (McGill University) : "Curves,
vector bundles on curves and their moduli"
Yvan Saint-Aubin (Université de Montréal) : "Kac-Moody
algebras"
More information
WINTER SCHOOL ON COMPUTATIONS IN COXETER GROUPS
January 21-28, 2002
Organizers: William Casselman
(UBC), Robert Bédard (UQAM), Fokko Du Cloux (Lyon I)
These short courses are designed to show how techniques from
computer algebra can be applied to effective computation in Coxeter groups.
This course will take place at the Far
Hills Inn , in the ski-resort town of Val Morin, about 150 km north of
Montreal. This charming inn will provide an intimate setting for the worshop.
The inn also offers many opportunities for various activities. What's more,
the inn's kitchens provide exquisite food! The lectures will begin on January
21, 2002 (Monday), and will end at lunch time on January 28, 2002 (Monday).
Accomodation at the Far Hills Inn is $130/person/night (double occupancy)
or $170/person/night (single occupancy), taxes and service included. The dollar
amounts are all in Canadian currency. This includes the room and three meals
per day. We will arrange for a shuttle to travel from Montreal to the Far
Hills Inn on Sunday, January 20, 2002, and back again on Monday, January 28,
2002. Please note that attendance at the workshop will be limited to approximately
40 participants, because of the limited number of rooms available at the Far
Hills Inn. We therefore encourage people to register
early!
More information
GROUP
ACTIONS ON RATIONAL VARIETIES
February 27 - March 3, 2002
Organizer: Peter Russell (McGill)
The workshop will focus on recent developments in automorphisms
of affine spaces and related algebraic varieties with simple topology, in
particular exotic affine spaces (algebraic varieties homeomorphic to an affine
space).
Participants will include:
T. Asanuma (Toyama), T. Bandman (Bar-Ilan), D. Daigle (Ottawa),
A. Van den Essen (*) (Nijmegen), G. Freudenburg (Southern Indiana), M. Gizatullin
(UTFSM), R. Gurjar (*) (Tata), I. Dolgachev (*) (Michigan), J. Winkelmann
(*) (Bochum), S. Kaliman (Miami), K. Masuda (Himeji), F. Knop (*) (Rutgers),
M. Koras, H. Kraft (Basel), L. Makar-Limanov (Wayne State), L. Moser-Jauslin
(*) (Bourgogne), M. Miyanishi (Osaka), P. Cassou-Nogues (Bordeaux), V. Popov
(MIEM) , A. Sathaye(Kentucky), G. Schwarz (Brandeis), D. Wright, M. Zaidenberg
(Grenoble , D. Zhang (Singapore)
(*) to be confirmed
Program
Registration
INVARIANT THEORY
April 8 - April 19, 2002
Organizers: David Wehlau (Queen’s), Eddy Campbell (Queen’s)
(the meeting will be held at Queen’s University, in
Kingston)
The first week will be devoted to introductory lectures aimed
at graduate students by Professors P. Fleischmann (Kent), H. Kraft (Basel),
G. W. Schwarz (Brandeis) and Harm Dersksen (MIT). The second week will be
devoted to a workshop on Invariant Theory. Other invited speakers include:
M. Brion (*), B. Broer, C. De Concini (*), L. Helminck , M. Hunziker, G. Kemper,
N. Kechagias, F. Knop, P. Littelmann , L. Moser-Jauslin, V. Popov, Y. Sanderson,
R J. Shank, N. Thiery, W. van der Kallen (*), E. Vinberg (*).
(*) to be confirmed
Invariant
Theory Web Site
For more information
CONCENTRATION PERIOD ON THE LANGLANDS PROGRAMME
FOR FUNCTION FIELDS
April - May 2002
Organizers: Henri Darmon (McGill), Jacques Hurtubise (CRM)
The last few years have seen spectacular new results in the
Langlands programme over function fields, both in characteristic zero and
in characteristic p. The aim of this period is to provide an overview of some
essential techniques in the area, as well as new results.
April 2002: Short courses for graduate students on
topics including the classical Hitchin systems, étale and l-adic sheaves,
as well as a survey of the number theoretic Langlands programme.
Registration
The Langlands programme
for function fields - Short courses for graduate students
April 29 - May 14, 2002: The Langlands program for
function fields. A three week extended workshop, with the first two weeks
devoted to survey lectures for graduate students:
Week 1: Survey lectures on preliminary material:
stacks, chtoucas, perverse sheaves and D-modules, opers. Lectures by D. Ben
Zvi (Chicago), D. Goss (Ohio State), A.Polischuk (Boston), Ch. Sorger (Nantes),
K. Vilonen (Northwestern)
Registration
Week 2: Aisenstadt lectures given by L. Lafforgue
(IHES) and E. Frenkel (Berkeley), covering recent results in the Langlands
programme over function fields, in both characteristic 0 and characteristic
p. During the first two weeks, R. Langlands will also give a series of lectures.
Registration
The Langlands
programme for function fields - Schedule and abstracts
May 15: Special one-day workshop in honour of Robert Langlands.
Program
The concentration period is to be followed by the
2002 Canadian Number Theory Association conference.
COMPUTATIONAL LIE THEORY
May 27 - June 7, 2002
Organizers: William Casselman (UBC), Friedrich Knop (Rutgers)
This extended workshop is aimed at researchers interested
in explicit computations in Lie theory, in particular Coxeter groups. In addition
to the usual talks, there will also be several series of survey lectures,
suitable for graduate students, by M. Brion (Grenoble), M. Geck (Lyon), F.
Knop (Rutgers), P. Littelmann (Wuppertal), G. Olshanskii (*) (IITP), J. Stembridge
(Michigan). Professor G. Lusztig (MIT) will be delivering some of his Aisenstadt
lectures during the period of the conference.
Invited participants include:
D. L. Alvis (Indiana), A. Anatolievich Klyachko (Bilkent),
R. Bédard (UQAM), R. Bezrukavnikov (Chicago), S. Billey (MIT), M. Brion
(Joseph Fourier), I. Cherednik (North Carolina), F. du Cloux (Lyon I), M.
J. Dyer (Notre Dame), W. Fulton (Michigan) M. Geck (Lyon), M. Haiman (North
California, San Diego), G. J. Heckman (Nijmegen), A. G. Helminck (Carolina),
F. Knop (Rutgers), S. Kumar (North Carolina at Chapel Hill), P. Littelmann
(Bergische), R. MacPherson (IAS), J. McKay (Concordia), M. Noumi (Kobe), A.
Okounkov (California, Berkeley), G. Olshanski (Moscow), E. M. Opdam (Amsterdam),
A. Ram (Wisconsin), Y. B. Sanderson (William Paterson) T. A. Springer (Utrech),
J. R. Stembridge (Michigan), B. Sturmfels (California, Berkeley), P. Trapa
(Harvard), J. F. van Diejen (Chile), M. van Leeuwen (Poitiers), D. A. Jr Vogan
(MIT), N. R. Wallach (California, San Diego), G. Saunders Warrington (Harvard),
A. Zelevinski (Northeastern)
Registration
Program
ALGEBRAIC TRANSFORMATION GROUPS
June 10-15, 2002
Organizers: Abraham Broer (Montréal), Jim Carrell (UBC)
The purpose of the meeting is to bring together experts in
Algebraic Groups, Algebraic Geometry, Representation Theory and related areas,
especially those touching on: geometric methods in representation theory using
tools like equivariant cohomology and perverse sheaves; the Hilbert scheme
of points on a surface and its connection with the n!-conjecture in algebraic
combinatorics; equivariant versions of cohomology and Chow groups related
to flag manifolds and Schubert varieties; quantum cohomology and Schubert
calculus.
Invited participants include:
K. Behrend (UBC), A. Bertram (Utah), M. Brion (Grenoble),
V. Ginzburg (Chicago), M. Haiman (UCSD), G. Heckman (Nijmegen), A. Knutson
(Berkeley), B. Kostant (MIT), S. Kumar (North Carolina), L. Manivel (Grenoble),
E. Meinrenken (Toronto), I. Mirkovic (Massachusetts), H. Nakajima (Kyoto),
D. Peterson (UBC), E. Vasserot (Cergy-Pontoise), C. Woodward (Rutgers).
Registration
Program
ORGANIZING COMMITTEE
A. Broer (Montréal), S. Boyer (UQAM), J. Carrell (UBC)
W. Casselman (UBC), H. Darmon (McGill), I. Hambleton (McMaster)
J.Hurtubise (CRM), N. Kamran (McGill), B. Khesin (Toronto)
F. Knop (Rutgers), R. Lee (Yale), D. Wise (Brandeis & McGill)
Those wishing to participate in the above activities are
invited to write to:
Louis Pelletier
Centre de recherches mathématiques (CRM)
Université de Montréal
C.P. 6128, Succ. Centre-ville
Montréal (Québec), CANADA H3C3J7
E-mail: ACTIVITES@CRM.UMontreal.CA
World Wide Web: http://www.CRM.UMontreal.CA/geometry
INFORMATION
(514) 343-2197
activites@CRM.UMontreal.CA
Last modifications: May 24, 2002
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