Spectral Theory and Discrete Subgroups in Higher Rank 1: Invariant Differential Operators

These two talks provide an overview of recent results regarding the interplay between spectral theory and discrete subgroups of higher-rank Lie groups, with a particular focus on Anosov subgroups.

The first talk examines the joint spectrum of invariant differential operators on higher-rank symmetric spaces, generalizing the spectrum of the Laplace operator in rank one. The discussion will cover embedded eigenvalues and the "bottom" of the joint spectrum, illustrating how a precise understanding of this bottom yields refined counting estimates for regular subgroups.

(Joint work with Lasse Wolf and Chris Lutsko)