Mathematics Colloquia and Seminars

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Gromov's work in the mid-eighties on holomorphic curves in symplectic manifolds has since led to the development of many geometrical ("hard") results in a theory once considered "soft." In the late eighties, Floer develop a symplectic invariant, now known as Floer homology, which counts certain holomorphic curves. This invariant has proved to be quite useful; for example, it was used in the proof of the Arnold Conjecture for Hamiltonian dynamics. Contact geometry is the odd-dimensional analog to symplectic geometry. Despite the similarities between the two fields, only recently have "hard" results emerged using Floer-type counts of holomorphic curves. I will survey some of these results, including a computation (joint with M. Hutchings) which conjecturally recovers Seiberg-Witten-Floer homology, a useful tool in four-manifold theory.

3:45 Refreshments will be served before the talk in 551 Kerr Hall