Homological Mirror Symmetry and Higgs-Coulomb Correspondence in Abelian GLSMs

Explore a 58-minute lecture on Homological Mirror Symmetry delivered by Chiu-Chu Melissa Liu from Columbia University at the University of Miami. Delve into the Higgs-Coulomb Correspondence and Wall-Crossing in Abelian Gauged Linear Sigma Models (GLSMs). Examine the input data of GLSMs, including GIT quotients of complex vector spaces and G-invariant polynomial functions. Discover how the Higgs-Coulomb correspondence connects GLSM invariants, relating virtual counts of Landau-Ginzburg quasimaps to Mellin-Barnes type integrals. Investigate the correspondence when the gauge group is an algebraic torus and learn how it can be applied to study the dependence of GLSM invariants on GIT stability conditions. Gain insights from Liu's joint work with Konstantin Aleshkin in this advanced exploration of mathematical physics concepts.