BPS states and the P=W conjecture

Abstract

A string theoretic framework is presented for the work of Hausel and Rodriguez-Vilegas as well as de Cataldo, Hausel and Migliorini on the cohomology of character varieties. The central element of this construction is an identification of the cohomology of the Hitchin moduli space with BPS states in a local Calabi-Yau threefold. This is a summary of several talks given during the Moduli Space Program 2011 at Isaac Newton Institute.