Harmonic Z/2 spinors and wall-crossing in Seiberg-Witten theory
GAUGE-TOPOLOGY-SYMPLECTIC
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October 19, 2018 3:30 pm - 4:30 pm
Science Center 507
Address:
1 Oxford Street, Cambridge, MA 02138 USA
Speaker:
Aleksander Doan - Stony Brook
Abstract:
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.