Haydys-Witten instantons and the gauge theoretic approach to Khovanov Homology
Michael Bleher
2024-07-03 15:00-16:00
ZOOM
Speaker: Michael Bleher (Heidelberg University)Time: 15:00-16:00 July 3, 2024 (Wednesday)
Venue: Online (Zoom ID: 3329836068 Password: mcm1234)
Title: Haydys-Witten instantons and the gauge theoretic approach to Khovanov Homology
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.
