Short closed geodesics in higher rank arithmetic locally symmetric spaces

Abstract: A well-known conjecture of Margulis predicts that there is a uniform lower bound on the systole of any irreducible arithmetic locally symmetric space. Recently, in joint work with Mikolaj Fraczyk, we show that for simple Lie groups of higher rank, this conjecture is equivalent to a well-known conjecture in number theory: that Salem numbers are uniformly bounded away from 1. I will discuss our proof and some tools used, and some additional results which hold unconditionally and highlight the structure of the bottom of the length spectrum.

dynamical systemsnumber theory

Audience: general audience

New England Dynamics and Number Theory Seminar