T&G: Donghao Wang (SCGP), Seidel's spectral sequence and monopole Floer homology

Tue, 17/05/202218:00-19:00
The algebraic topology of a finite dimensional manifold is detected by Morse theory using a real valued Morse function, while the symplectic topology of a K ̈ahler manifold can be probed by a holomorphic Morse function using Picard-Lefschetz theory. The first viewpoint has been successfully generalized to the infinite dimensional case by Floer in late 1980s producing powerful invariants in both low dimensional topology
and symplectic topology.
This talk is a progress report in attempt to generalize the second idea to one particular infinite dimensional example – the Seiberg-Witten equations, following the proposals of Haydys and Gaiotto-Moore-Witten. In particular, we will outline an alternative proof to Seidel’s spectral sequence for Lagrangian Floer cohomology, which may help us approach this infinite dimensional problem.