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Symplectic Geometry and PhysicsGeometry of Lagrangian SubmanifoldsApril 14 - 18, 2003Organizing Committee:
Mark Gross
(University of California at San Diego)
IntroductionLagrangian submanifolds have classically played an important role in symplectic geometry. Recently their role has been expanded beyond that of their use in understanding symplectic diffeomorphisms. For example, conjecturally special lagrangian submanifolds play a central role in understanding the structure of Calabi-Yau 3-folds and in mirror symmetry (Strominger-Yau-Zaslow). Also conjecturally they play a central role in understanding the relation between certain Gromov-Witten type invariants and knot invariants (Gopakumar-Vafa). Although there has not been definitive progress on the construction of special lagrangian fibrations, the topological picture is much better understood (Gross, W.D. Ruan). From the point of view of existence theory for special lagrangian cycles, it has been shown that one can formulate a variational problem for volume and develop much of the necessary machinery (Schoen-Wolfson). In two dimensions the critical points of this variational problem can also be obtained, in some interesting cases, by the methods of completely integrable systems (Helein-Romon, Joyce). Recently geometric flow techniques, in particular, mean curvature flow, have been applied to lagrangian submanifolds (Thomas-Yau, M-T Wang) to construct special lagrangians in special cases. These lead to general conjectures about the nature of solutions of lagrangian mean curvature flow. This workshop aims at exploring the new applications of lagrangians in symplectic and Kähler geometry, with particular emphasis on techniques for construction. Among the topics to be explored are:
SpeakersMina Aganagic (Harvard University)Jim Bryan (University of British Columbia, Vancouver) Adrian Butscher (University of Toronto at Scarborough) Mark Gross (University of California at San Diego) Mark Haskins (Johns Hopkins University) Frederic Helein (Ecole Normale Supérieure, Cachan, France) Anton Kapustin (Caltech / USC) Albrecht Klemm (Humboldt University, Berlin) Alexei Kovalev (Cambridge University) Naichung Conan Leung (University of Minnesota, Twin Cities) Ai-Ko Liu (University of California at Berkeley) Chiu-Chu (Melissa) Liu (Harvard University) Yong-Geun Oh (University of Wisconsin) Tommaso Pacini (Massachusetts Institute of Technology) Alexander Polishchuk (Boston University) Weiyang Qiu (Harvard University) Pascal Romon (Universite de Marne-la-Vallee) Wei-Dong Ruan (University of Illinois at Chicago) Rick Schoen (Stanford University) Richard Thomas (Imperial College, London, UK) Gang Tian (Massachusetts Institute of Technology) Mu-Tao Wang (Math) Pelham Wilson (Cambridge University) Marco Zambon (University of California at Berkeley) Eric Zaslow (Northwestern University) Ilia Zharkov (Duke University) Contact Us:Institute for Pure and Applied Mathematics (IPAM) |
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