January 13, 2021
TITLE: Line defects, UV-IR map and exact WKB
In this talk I’ll give an overview of the relations between class S theories and Hitchin systems, focusing on roles played by line defects in class S theories. Deforming onto the Coulomb branch triggers a UV-IR map for line defects, corresponding to a trace map for certain flat nonabelian connections over a Riemann surface. The UV-IR map admits a q-deformation, which corresponds to a quantum trace map embedding certain skein algebra into a quantum torus algebra. I’ll also briefly describe connections to exact WKB and a potential q-deformation thereof.