Hello everyone,

Today in seminar we are very happy to have Jeff Meyer joining us from Cal State - San Bernadino. His title and abstract are below. The link for seminar is the same: https://meet.google.com/frv-bgow-byi

Title: Systoles of Arithmetic Manifolds Speaker: Jeff Meyer, Cal State San Bernardino Date: Mar 10, 2021 Time: 3:30 PM Room: Virtual

Abstract: Pick your favorite compact space. How short is the shortest closed loop on it? Now look at your favorite cover of this space. Did that loop unwrap to a longer loop? These are systole questions. The systole of a manifold is the minimal length of a non-contractible closed loop. Systoles in arithmetic manifolds have many fascinating relationships with deep problems in number theory, such as Lehmer’s Mahler measure problem. In recent years, there have been numerous papers studying systoles, their bounds, and their growth up covers as you vary the underlying manifolds. In this talk, I will discuss interesting systole problems, survey known results, and present recent work with collaborators Sara Lapan and Benjamin Linowitz.

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Neil R. Hoffman Assistant Professor Department of Mathematics 523 Math Science Building Oklahoma State University Stillwater, OK 74078-1058 405-744-7791 http://math.okstate.edu/people/nhoffman