Title: Cohomology of the moduli of Higgs bundles
Abstract: The moduli space of Higgs bundles and Hitchin's integrable system lie at the crossroads of mathematical physics, representaton theory, and geometry. In this talk, we focus on the structure of cohomology for the moduli of Higgs bundle from the viewpoints of the non-abelian Hodge theorey, hyper-Kähaler geometry, and mirror symmetry. We will discuss recent progress on the P=W conjecture and Hausel-Thaddeus' topological mirror symmetry conjecture. Based on joint work with Mark de Cataldo and Davesh Maulik.