Differential Geometry Seminar: Classification of Nahm Pole Solutions to the KW Equations on $S^1\times \Sigma \times \mathbb R^+$

Seminar | April 22 | 3:10-4 p.m. | 939 Evans Hall

 Siqi He, Simons Center for Geometry and Physics (Stony Brook)

 Department of Mathematics

We will discuss Witten’s gauge theory approach to Jones polynomial by counting solutions to the Kapustin-Witten(KW) equations with singular boundary conditions over 4-manifolds. We will give a classification of solutions to the KW equations on $S^1\times\Sigma\times \mathbb R^+$ with $\Sigma$ a Riemann surface. We prove that all solutions to the KW equations over $S^1\times\Sigma\times \mathbb R^+$ are $S^1$ direction invariant and we give a classification of the KW monopole over $\Sigma\times R^+$ based on the Hermitian-Yang-Mills type structure of KW monopole equation. This is based on joint works with Rafe Mazzeo.