Michael Bleher (Heidelberg) will speak in the differential geometry seminar, at 2pm on Monday 4th December. Michael’s title is “Haydys-Witten instantons in the gauge theoretic approach to Khovanov Homology” and his abstract is below.
The Haydys-Witten equations are partial differential equations in gauge theory, defined on five-dimensional Riemannian manifolds that are equipped with a non-vanishing vector field $v$. Conjecturally, their solutions on $M^5 = \mathbb{R} \times W^4$ 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 appears in the context of knot invariants. I will discuss conditions under which the full equations simplify to the decoupled form. Since the latter exhibit a Hermitian Yang-Mills structure, these results may offer novel insights into the conjectured relationship to knot invariants.