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Symplectic Geometry and PhysicsSymplectic Geometry and Physics Workshop I: Symplectic GeometryMarch 24 - 28, 2003Organizing Committee:
Denis Auroux
(Massachusetts Institute of Technology)
IntroductionSymplectic manifolds play a central role in modern topology. Most notably, the revolution initiated by Seiberg-Witten invariants and the results of Taubes, Kronheimer, Mrowka, Fintushel and Stern have made the study of four-dimensional symplectic manifolds a central topic of low dimensional smooth topology. Fundamental results on the topology of symplectic manifolds have also been obtained by M. Gromov, Y. Eliashberg, R. Gompf, D. McDuff, D. Salamon and G. Tian, among many others. Their works have allowed the subject to mature into one of the most exciting parts of modern mathematics. More recently, the existence result obtained by Donaldson for symplectic Lefschetz pencil structures on symplectic manifolds has opened a completely new direction in low dimensional symplectic topology, followed by work of Auroux and Katzarkov on the topology of 4-dimensional symplectic manifolds viewed as finite ramified coverings of CP2. These results allow one, in principle, to classify symplectic 4-manifolds using combinatorial data in certain groups (mapping class groups or braid groups respectively). They also make the study of four-dimensional symplectic manifolds accessible to methods from algebraic geometry. The following research directions are particularly active at the moment and are indicative of the topics that this workshop aims to focus on: 1. J-holomorphic curves, Gromov-Witten invariants and quantum cohomology. 2. Lagrangian Floer homology and the homological mirror symmetry conjecture. 3. Applications of Seiberg-Witten invariants in symplectic topology. 4. Monodromy invariants of symplectic Lefschetz pencils or branched covering maps, and their relation to other invariants (Seiberg-Witten, Gromov-Witten, Lagrangian Floer homology). 5. Characteristic properties of symplectic Lefschetz fibrations (singular fibers, irreducibility properties, holomorphicity criteria, ...) 6. Geometry and topology of symplectomorphism groups; symplectic capacity theory and symplectic packing problems. 7. Contact topology: symplectic fillings, contact pencils, ... 8. Contact homology and symplectic field theory. SpeakersRonald Fintushel (MSU)Kenji Fukaya (Kyoto University) Emmanuel Giroux (Ecole Normale Superieure de Lyon, France) Mark Gross (UCSD / University of Warwick) Ko Honda (University of Southern California) Michael Hutchings (University of California at Berkeley) Eleny Ionel (University of Wisconsin) Dieter Kotschick (LMU Munich) Yi-Jen Lee (Princeton University) Naichung Conan Leung (University of Minnesota, Twin Cities) Tian-Jun Li (University of Minnesota) Paolo Lisca (University of Pisa) Yiming Long (Nankai Institute of Mathematics) Ignasi Mundet i Riera (University Polit. Catalunya) Lenny Ng (Stanford University) Kaoru Ono (Hokkaido University, Japan) Peter Ozsvath (Princeton University) Francisco Presas (Stanford University) Dietmar Salamon (ETH, Zurich) Vsevolod Shevchishin (Ruhr-University, Bochum, Germany) Ronald Stern (University of California at Irvine) Andras Stipsicz (Renyi Institute, Budapest) Stefano Vidussi (KSU) Contact Us:Institute for Pure and Applied Mathematics (IPAM) |
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