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)
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.