Featured Speaker: Siqing Zhang (SUNY at Stony Brook)

Title: Cohomological Non-Abelian Hodge Theorems in characteristic p.

Abstract: We introduce two cohomological incarnations of the Non-Abelian Hodge Theorem for curves in characteristic p. Using the first one, we show that, in arbitrary characteristics, the cohomology of the moduli space of Higgs bundles is independent of the degree, as long as it is coprime to the rank. A closer analysis of the results above shows that, over the complex numbers, the Galois conjugation action on the character variety preserves the perverse Leray filtration on the cohomology of the moduli space of Higgs bundles. Everything above is based on joint works with Mark de Cataldo, Davesh Maulik, and Junliang Shen.