Twisted spectral correspondence and torus knots -- Tony Pantev, March 15, 2019

I will explain how the cohomological invariants of twisted wild character varieties can be derived from enumerative Calabi-Yau geometry and refined Chern-Simons invariants of torus knots. I will describe a geometric approach for computing such topologies which is based on a spectral correspondence for meromorphic Higgs bundles with fixed conjugacy classes at the marked points. This construction is carried out for twisted wild character varieties associated to (l,lk-1) torus knots, providing a colored generalization of theorems of Hausel, Mereb and Wong and of Shende, Treumann and Zaslow. The talk is based on recent joint works with Chuang, Diaconescu, Donagi, and Nawata.