Activités 2005-2006 2004-2005 2003-2004

2005-2006

Mini-course at Université Louis-Pasteur (Strasbourg) on Universal Floer theory

June 2005

Course at Stanford University on the Cluster complex and Universal Floer theory

Fall 2005

Workshop on cluster homology and polymanifolds theory

IAS, Princeton - October 10-14 2005

Organized with Octav Cornea, Helmut Hofer, François Lalonde and Katrin Wehrheim

On the new Cluster complex introduced by Cornea-Lalonde and Hofer's new polymanifolds theory

2004-2005

Informal Special Semester on Symplectic Geometry and Topology

15 septembre -23 décembre 2004

September 15-December 23 2004

organized with Octav Cornea

calendrier des conférences

calendar of conferences

Casim Abbas (Michigan State) November 22-26 novembre

Sylvia Anjos (IST, Lisbonne) November 7-13 novembre

Frédéric Bourgeois (Université Libre de Bruxelles)
November 1-5 novembre

Anne-Laure Biolley (Toronto) November 8-10 novembre

Yasha Eliashberg (Stanford) November 10-13 novembre

Misha Entov (Haifa)
October 10-17 octobre

Viktor Ginzburg (California at Santa Cruz)
November 10-13 novembre

Richard Hind (Notre Dame) November 9-12 novembre

Yael Karshon (Toronto) November 10-12 novembre

Ely Kerman (Urbana Champaing)
November 8-15 novembre

Chiu-Chu (Melissa) Liu (Harvard) November 6-13 novembre

Dusa McDuff (Stony Brook) November 4-9 novembre

Martin Pinsonnault (Toronto) November 2-9 novembre

Yongbin Ruan (Wisconsin at Madison)
November 7-11 novembre

Paul Seidel (Chicago)
November 5 novembre

Jean-Claude Sikorav (ENS Lyon) November 5-13 novembre

Andrei Teleman (Aix-Marseille) December 5-12 décembre

Kathrin Wehrheim (Princeton) November 7-13 novembre

Jean-Yves Welschinger (ENS Lyon)
November 1-10 novembre

Séminaire de géométrie et topologie

(organisé par Olivier Collin) - UQÀM-

Centre interuniversitaire de recherches en géométrie et topologie (CIRGET)
11h00 vendredi / Friday 11 a.m. salle/room PK-5115
Pavillon Président-Kennedy

2003-2004

Séminaire de Mathématiques Supérieures (SMS)
sous la direction de  François Lalonde

43eme édition

MORSE THEORETIC METHODS IN NONLINEAR ANALYSIS AND IN SYMPLECTIC TOPOLOGY

21 juin - 2 juillet 2004

Organisateurs : Octav Cornea (Montréal) et Paul Biran (Tel Aviv)

The talks at this meeting centered on Morse theoretical techniques which can be used to solve difficult analytic problems as well as problems in symplectic topology and in robotics.The key tool in modern symplectic topology is Floer homology and related techniques and this constituted a recurring theme for the lectures given. Some of the topics discussed (in particular by Hofer, Schwarz, Cornea and Polterovich) were presented publicly for the first time at the ASI. As well many of the talks of different speakers were strongly interrelated which contributed to the overall quality and strength of the ASI itself.

Alberto ABBONDANDOLO (Scuola Normale Superiore)

The Morse complex for infinite dimensional manifolds

Paul BIRAN (Tel-Aviv University)

Lagrangian Geometry and Topology Morse theory

Ralph COHEN (Stanford University)

Morse theory, Graphs, and Loop spaces

Octav CORNEA (Université de Montréal)

Homotopical methods in Morse-Floer theory

Michael FARBER (Tel-Aviv University)

Topology of robot motion planning

Kenji FUKAYA (University of Kyoto)

Floer homology of Lagrangian submanifolds

Helmut HOFER (Courant Institute)

The analytic background of Symplectic Field Theory

Marek ISYDOREK (Technical University of Gdansk)

The Conley index in Hilbert spaces with applications

Yong-Geun OH (University of Wisconsin at Madison)

Chain level Floer theory and geometry of Hamiltonian diffeomorphism group

Leonid POLTEROVICH (Tel-Aviv University)

Floer homology and symplectic dynamics

Matthias SCHWARZ (University of Leipzig)

Lectures on Floer-homological methods in symplectic geometry

Claude VITERBO (École Polytechnique - Palaiseau)

Generating functions and applications

In the first week Helmut Hofer talked about the foundations of symplectic field theory - this is one of the major new "machines" in symplectic topology whose development has been pursued by Hofer, Eliashberg and Givental for a number of years now. The origins of symplectic field theory lie in Floer's machinery but it goes much beyond that both in applications as well as in complexity. Hofer's lectures were therefore extremely timely. Matthias Schwarz presented his recent proof for a result of Viterbo relating the Floer homology of the cotangent bundle and the string topology of the zero section of this bundle. This notion of string topology has been recently introduced by Chas and Sullivan with a purely topological motivation and the fact that this notion fits perfectly with the quantum product in Floer theory is quite remakable.

Michael Farber discussed applications to robotics. Paul Biran described efficient methods to use Floer homology in the monotone case to prove results concerning the topological structure of Lagrangian submanifolds. Leonid Polterovich showed how to relate this symplectic topology to dynamics and geometric group theory methods. Octav Cornea presented higher order Floer type invariants and applications.
This was an intense first week with lectures of the highest order of interest for specialists as well as for beginners in the field. The second week continued as strongly:

Claude Viterbo talked about generating functions techniques, Alberto Abbondandolo discussed Morse theory in Hilbert spaces, Kenji Fukaya talked about a new version of his $A^{\infty}$ machinery (developed with Oh and Ono) and applications, some of which overlapped with applications obtained by different methods by Cornea jointly with Lalonde and mentioned in the first week. Marek Izydorek lectured on his approach to the infinite dimensional Conley index and Yong-Geun Oh presented his recent spectral invariant techniques and chain level Floer methods. Finally, Ralph Cohen described his topological approach to string topology and itspotential implications for symplectic topology.