Title: The Geometry of the Hitchin Fibration for Symmetric Spaces Abstract: 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 […]

Title: Why do cusp forms exist? Abstract:  I will begin this talk by reviewing the Eichler-Shimura isomorphism between the space of cusp forms of weight k and level N, and a certain cohomology group. Shimura called this cohomology group as parabolic cohomology. In the context of automorphic forms on higher groups, such a cohomology group takes the form […]