Speaker: Michael Bleher，Heidelberg University

Inviter: Prof. Siqi He (MCM)

Title: Haydys-Witten instantons and the gauge theoretic approach to Khovanov Homology

Language: Chinese

Time & Venue: 2024.07.03 15:00-16:00 Zoom ID: 3329836068 Password: mcm1234

Abstract: The Haydys-Witten equations are gauge theoretic partial differential equations on five-dimensional Riemannian manifolds that are equipped with a non-vanishing vector field. Conjecturally, their solutions on M^5=IR×W^4 determine the Floer differential in a gauge-theoretic approach to homological knot invariants. In this talk, I will provide a brief overview of this ‘instanton Floer theory of four-manifolds’ and then focus on a ‘decoupled’ version of the Haydys-Witten equations that emerges in the geometric setup for knot invariants. Since the latter exhibit a Hermitian Yang-Mills structure, these results may offer novel insights into the conjectured relationship to knot invariants.