Topology of Wild Character Varieties
Tony Pantev (U. Penn)

Wild character varieties parametrize monodromy representations of flat meromorphic connections on compact Riemann surfaces. They are classical objects with remarkable geometric and topological properties. In the past twenty years new insights from algebraic geometry lead to precise conjectures on the topological structure and complexity of character varieties. I will recall some of these conjectures and will sketch a strategy for approaching them. In particular I will describe recent joint works with Chuang, Diaconescu, Donagi, and Nawata in which we use dualities in geometry and physics to extract cohomological invariants of wild character varieties from enumerative Calabi-Yau geometry and refined Chern-Simons invariants of torus knots.