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Gromov-Witten invariants, representation theory, and geometry of KdV equationsGeometry/Topology
|Speaker:||Motohico Mulase, U.C. Davis|
|Start time:||Wed, Jan 4 2006, 4:10PM|
Gromov-Witten invariants are symplectomorphic invariants of a manifold. They are defined through cohomology theory of the space of all maps from an arbitrary Riemann surface into the symplectic manifold. Therefore, even GW invariants of a single point are non-trivial: they are the subject of the celebrated Witten-Kontsevich theory.
It has been conjectured that the generating function of Gromov-Witten invariants satisfy differential equations of KdV type. Most recently geometric reasons why the KdV should appear in this context have been proposed by two different groups: the Stockholm/Moscow group, and the Davis group led by Brad Safnuk. I will explain these two approaches, one through representation theory of symmetric groups, and the other through hyperbolic geometry of surfaces.