  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.
