Abstract: In this talk, I will survey the P=W conjecture, which describes certain structures of the cohomology of the moduli space of Higgs bundles on a curve in terms of the character variety of the curve. I will then explain how certain symmetries of this cohomology, which are predictions of this conjecture, can be constructed using techniques from non-abelian Hodge theory in positive characteristic. Based on joint work with Mark de Cataldo, Junliang Shen, and Siqing Zhang.
Cohomology of the moduli of Higgs bundles via positive characteristic
01/26/2022 9:30 am - 8:30 pm