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:
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