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Siqi He: Lectures

January 11, 2018
TITLE: The extended Bogomolny equations and generalized Nahm pole solutions

ABSTRACT: We will discuss Witten’s gauge theory approach to Jones polynomial and Khovanov homology by counting solutions to some gauge theory equations with singular boundary conditions. When we reduce these equations to 3-dimensional, we call them the extended Bogomolny equations. We develop a Donaldson-Uhlenbeck-Yau type correspondence for the moduli space of the extended Bogomolny equations on Riemann surface Σ times R^+ with Generalized Nahm pole singularity at Σ × {0} with the stable SL(2,R) Higgs bundle. This is joint work with Rafe Mazzeo.