David Fisher “Arithmeticity, superrigidity, and totally geodesic submanifolds“ | The Vinberg Lecture

The Vinberg Lecture Series: Lecture 8 (March 23, 2022) _______ David Fisher (Indiana University Bloomington, USA) Title: Arithmeticity, superrigidity, and totally geodesic submanifolds Abstract: Arithmeticity of locally symmetric spaces is an old and important area of study in which Vinberg proved some central results. I will discuss the history of the area, some open questions and then focus on recent joint work with Bader, Miller and Stover. We prove that non-arithmetic real and complex hyperbolic manifolds cannot have infinitely many maximal totally geodesic submanifolds. The Vinberg Lecture: