Speaker: Omri Solan (Hebrew University)

Title: Limits of compact diagonal orbits in the lattice space

Abstract:

The diagonal subgroup $A<SL_n(\RR)$ acts on the space of lattices. The compact $A$-orbits are classified using a number theoretic construction. We will discuss the following limit phenomenon:
What are the possible limits of $A$-invariant measures on compact $A$-orbits?

We prove that any ergodic A-invariant measure can rise as an ergodic component. To this end, we will use both dynamical properties of Hecke operators and a number theoretic construction. The talk is based on a joint work with Yuval Yifrach.