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Topology/Geometry Seminar

Compactness for generalized Seiberg-Witten equations

Boyu Zhang (Princeton)

Location:  Hill 525
Date & time: Tuesday, 06 November 2018 at 4:00PM - 4:50PM

Abstract:  The Seiberg-Witten equation can be generalized to higher-rank vector bundles with a hyperKahler moment map. Examples among these are the Kapustin-Witten equations, Vafa-Witten equations, Seiberg-Witten equations with multiple spinors, and the ADHM equations. Witten, Haydys, and Doan-Walpuski have proposed several conjectures about the gauge theories from these equations, and the conjectures suggest that they will reflect topological information of the base manifold beyond the Yang-Mills and Seiberg-Witten equations. The analytic difficulty of establishing gauge theories based on generalized Seiberg-Witten equations is the lack of compactness. It was proved by Taubes and Haydys-Walpuski that solutions to many of these equations satisfy certain compactness properties described by Z/2-harmonic spinors. In this talk, we will discuss some recent progress on the compactness problems for generalized Seiberg-Witten equations.

Some of the works presented in the talk are in collaboration with Thomas Walpuski.

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