Event time:

Monday, February 6, 2023 - 4:00pm

Speaker:

Lam Pham

Speaker affiliation:

Brandeis University

Event description:

A well-known conjecture of Margulis predicts the existence of a uniform lower bound on the systole of any irreducible arithmetic locally symmetric space. In joint work with F. Thilmany, we proved that this conjecture is equivalent to a weak version of the Lehmer conjecture, a well-known problem from Diophantine geometry.

In joint work with M. Fraczyk, we recently established a uniform lower bound for simple Lie groups of higher rank conditional on a uniform lower bound on Salem numbers, a much weaker – but still open – problem. I will discuss these results and some tools used in the proofs and present additional results which highlight the structure of the bottom of the length spectrum.