Thematic Programme 20012002
Groups and Geometry





I  GROUPS, TOPOLOGY AND DIFFERENTIAL GEOMETRY
Throughout the 20th century there has been a remarkably fruitful interplay between group theory and the geometry and topology of lowdimensional manifolds. The study of 3manifolds 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 3dimensional topology have been fundamental in motivating many exciting developments in geometric group theory: actions on Rtrees, wordhyperbolic 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.
Organizer: Steven Boyer (UQAM)
This workshop will focus on recent progress on various open topological and geometric classification problems as well as some of the newer research directions. There will be four 50 minute talks per day, leaving plenty of time for informal discussions amongst the participants.
Participants will include:
M. Boileau (Universite Paul Sabatier), D. Calegari (Harvard University), A. Casson (Yale University), D. Cooper (University of California at Santa Barbara), M. Culler (University of Illinois at Chicago), D. Gabai, (California Instsitute of Technology), C. McA. Gordon (University of Texas at Austin), S. Kerchoff (Stanford University), M. Lackenby (University of Oxford), D. Long (University of California at Santa Barbara), J. Luecke (University of Texas at Austin), Y. Moriah (Technion), J. Porti (Universitat Autonoma de Barcelona), A. Reid (University of Texas at Austin), H. Rubinstein (University of Melbourne), P. Shalen (University of Illinois at Chicago), Y.Q. Wu (University of Iowa), X. Zhang (State University of New York at Buffalo).
WE ARE VERY SORRY! BECAUSE OF LIMITED SPACE, WE CANNOT ACCEPT ANYMORE REGISTRATIONS ! For more information, please call Louis Pelletier at pelletl@CRM.UMontreal.ca or at (514) 3432197
Michel Boileau (Universite Paul Sabatier) "Geometrisation of 3dimensional
orbifolds"
Martin Bridson (University of Oxford) "Nonpositively curved spaces
and hyperbolic groups"
Ruth Charney (Ohio State University) "The geometry of Coxeter and Artin
groups"
Benson Farb (University of Chicago) "A crash course on the geometry of
groups"
Peter Shalen (University of Illinois at Chicago) "Representations of
3manifold groups"
For any further information, please contact Louis Pelletier at pelletl@CRM.UMontreal.ca or at (514) 3432197
WE ARE VERY SORRY! BECAUSE OF LIMITED SPACE, WE CANNOT ACCEPT ANYMORE REGISTRATIONS ! For more information, please call Louis Pelletier at pelletl@CRM.UMontreal.ca or at (514) 3432197
WORKSHOP
ON GEOMETRIC GROUP THEORY
July 913, 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 UrbanaChampaign), M. Kapovich (University of Utah), O. Kharlampovich (McGill University), J. McCammond (Texas A & M), A. Myasnikov (CCNY), P. Papazoglou (Universite ParisSud), M. Sapir (Vanderbilt University), M. Sageev (Technion), Z. Sela (Hebrew University).
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 SeibergWitten 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 4manifolds, just to name a few. Not concentrated completely on 4dimensions, 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 (MaxPlanckInstitut 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).
Registration
From a differentialgeometric pointofview, infinitedimensional 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 infinitedimensional Lie groups becomes a fundamental problem in areas of mathematics as diverse as hydrodynamics and symplectic topology. Another wide class of infinitedimensional Lie groups is formed by loop groups, KacMoody 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 lowdimensional geometry and topology and in quantum field theory. Infinitedimensional 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 pseudodifferential and Fourier integral operators.
The purpose of this miniprogram 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
WORKSHOP
ON THE GEOMETRY OF INFINITEDIMENSIONAL LIE GROUPS
November 26, 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 (CNRSLuminy), 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
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 Dmodules and perverse sheaves. Geometry intervenes in a crucial fashion in the proof of such results as the KazhdanLusztig conjecture, the construction of canonical bases for representations, and the work of BeilinsonDrinfeld 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.
C/O Louis Pelletier
Centre de recherches mathématiques
Universite de Montréal
C.P. 6128, Succursale Centreville,
Montréal (Québec)
CANADA H3C 3J7Fax: (514) 3432254
Email: 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).
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 SaintAubin (Université de Montréal) : "KacMoody
algebras"
WINTER SCHOOL ON COMPUTATIONS IN COXETER GROUPS
January 2128, 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 skiresort 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!
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 (BarIlan), 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. MakarLimanov (Wayne State), L. MoserJauslin (*) (Bourgogne), M. Miyanishi (Osaka), P. CassouNogues (Bordeaux), V. Popov (MIEM) , A. Sathaye(Kentucky), G. Schwarz (Brandeis), D. Wright, M. Zaidenberg (Grenoble , D. Zhang (Singapore)
(*) to be confirmed
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. MoserJauslin, V. Popov, Y. Sanderson, R J. Shank, N. Thiery, W. van der Kallen (*), E. Vinberg (*).
(*) to be confirmed
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 ladic 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 Dmodules, 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 oneday workshop in honour of Robert Langlands.
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
ALGEBRAIC TRANSFORMATION GROUPS
June 1015, 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 (CergyPontoise), C. Woodward (Rutgers).
Registration
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. Centreville
Montréal (Québec), CANADA H3C3J7
Email: ACTIVITES@CRM.UMontreal.CA
World Wide Web: http://www.CRM.UMontreal.CA/geometry
INFORMATION
(514) 3432197
activites@CRM.UMontreal.CA
Last modifications: May 24, 2002
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