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

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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.