Thomas Hameister (University of Chicago)

Motivated by questions in relative Langlands and relative endoscopy, we study generalized Hitchin systems associated to symmetric spaces. We will use two new techniques in invariant theory, the regular quotient and the parabolic cameral cover, in an effort to describe the geometry of such systems. As corollaries of these results, we describe Hitchin fibers over a generic locus of the Hitchin base for several classical symmetric spaces. This work is joint with B. Morrissey.