The PI plans to continue pursuing her research in two directions: the first is a long program to relate the theories of Seiberg-Witten and Ozsvath-Szabo. The second is a possible generalization of the PI's previous work on Floer-theoretic torsions to a Floer-theoretic analog of Chern-Simons perturbative invariants.
This proposal showcases the recent fertile interactions between mathematics 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."
