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K-State Today

October 9, 2014

Math lecture today about character varieties, nested Hilbert schemes

By Reta McDermott

Tony Pantev, University of Pennsylvania, will present "Character Varieties and Nested Hilbert Schemes" as part of the Mathematics Department Colloquium 53rd William J. Spencer Lecture at 2:30 p.m. Thursday, Oct. 9, in 101 Cardwell Hall.

The abstract for the lecture is:

I will describe a novel framework for computing the topology of character varieties of fundamental groups of punctured Riemann surfaces. This framework merges techniques and constructions from algebraic geometry, topology, algebraic combinatorics, and mathematical physics. The main tool is to use the spectral correspondence and an appropriate version of geometric engineering to identify the refined parabolic stable pair theory of certain stacky Calabi-Yau threefolds with a generating series for enumerative invariants of nested Hilbert schemes on surfaces. Combined with a wall-crossing formula for parabolic ADHM sheaves this formalism gives an effective algorithm for computing Poincare polynomials of the moduli of tamely ramified parabolic Higgs bundles and of the corresponding character variety. Through a field theory limit this verifies a recent conjecture of Hausel, Letellier, and Rodriguez-Villegas. This is a joint work with W.-Y.Chuang, E.Diaconescu, and R.Donagi.

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