Differential Geometry Seminar: Harmonic Z/2 spinors and wall-crossing in Seiberg-Witten theory

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

 Aleksander Doan, Stony Brook

 Department of Mathematics

The notion of a harmonic Z/2 spinor was introduced by Taubes as an abstraction of various limiting objects appearing in compactifications of gauge-theoretic moduli spaces. I will explain this notion and discuss an existence result for harmonic Z/2 spinors on three-manifolds. The proof uses a wall-crossing formula for solutions of generalized Seiberg-Witten equations in dimension three, a result itself motivated by Yang-Mills theory on Riemannian manifolds with special holonomy $G_2$. The talk is based on joint work with Thomas Walpuski.