String-Math Seminar: A taste of microlocal Hodge theory

Seminar | September 16 | 2-3 p.m. | 402 LeConte Hall

 Michael McBreen, University of Toronto

 Department of Mathematics

The nonabelian Hodge correspondence gives a diffeomorphism between the moduli of flat connections and the moduli of higgs bundles on a smooth Riemann surface. The two moduli, however, are completely different as algebraic varieties. Thus natural structures on one side of the correspondence, such as Hitchin's integrable system, become rather mysterious on the other side.

I will discuss joint work with Zsuzsanna Dancso and Vivek Shende, which defines a 'microlocal model' of the correspondence in a neighborhood of a singular fiber of the Hitchin system. In particular, we prove a conjecture of Hausel and Proudfoot relating the weight and perverse filtrations on either side of this microlocal correspondence.