EVENT DETAILS AND ABSTRACT

Title: The P=W conjecture
Speaker: Davesh Maulik
Speaker Info: MIT
Brief Description:
Special Note:
Abstract:

Given a compact Riemann surface, nonabelian Hodge theory relates topological and algebro-geometric objects associated to it. Namely, complex representations of the fundamental group are in correspondence with algebraic vector bundles, equipped with an extra structure called a Higgs field. This gives a transcendental matching between two very different moduli spaces associated with the Riemann surface: the character variety (parameterizing representations of the fundamental group) and the Hitchin moduli space (parameterizing Higgs bundles). In 2010, de Cataldo, Hausel, and Migliorini proposed the P=W conjecture, which predicted that the Hodge theory of the character variety is determined by the topology of the Hitchin space, imposing surprising constraints on each side. In this talk, I will introduce the conjecture and review its recent proofs; time permitting, I will try to explain how this phenomenon relates to other geometric questions.