Differential Geometry Seminar

Speaker: 
Guangbo Xu (Texas A&M)
Topic: 
Compactness of instantons and the Atiyah-Floer conjecture

Abstract:
The Atiyah-Floer conjecture says that the instanton Floer homology of a three-manifold (constructed via gauge theory) agrees with a Lagrangian Floer homology (constructed via symplectic geometry) associated to a splitting of the manifold. Atiyah's heuristic argument of this conjecture relies on a compactness result for instantons in a certain adiabatic limit. I will present a proof of such a compact theorem for the case when the gauge group is $SO(3)$, as well as another compactness theorem related to bounding chains on the symplectic side.

Event Date: 
October 6, 2020 - 10:30am to 11:20am
Location: 
Online
Calendar Category: 
Seminar
Seminar Category: 
Differential Geometry