Floer theory in gauge theory and symplectic geometry

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DMS-0604890Yi-Jen LeeThe PI plans to continue pursuing her research in two directions: thefirst is a long program to relate the theories of Seiberg-Witten andOzsvath-Szabo. The second is a possible generalization of the PI'sprevious work on Floer-theoretic torsions to a Floer-theoretic analog of Chern-Simons perturbative invariants.This proposal showcases the recent fertile interactions betweenmathematics and high energy physics. Gauge-theoretic invariants,enumeratitve invariants of holomorphic curves, and Floer theory all have their origin in physics, yet have since yielded the most important recent results in the fields of low dimensional topology and symplectic geometry. The proposal deals with fascinating relations among these physics-inspired invariants, and their applications to topology."