Harmonic Z/2 spinors and wall-crossing in Seiberg-Witten theory

Harmonic Z/2 spinors and wall-crossing in Seiberg-Witten theory

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Aleksander Doan, Stony Brook University
Fine Hall 314

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 to generalized Seiberg-Witten equations in dimension three, a result itself motivated by Yang-Mills theory on manifolds with exceptional holonomy. The talk is based on joint work with Thomas Walpuski.