I will talk about a joint work with O. Glorieux. Let G be a semisimple, real linear, connected Lie group and Γ a Zariski dense, discrete subgroup of G. Let A be a maximal torus, K be a maximal compact subgroup and M be the centralizer of A in K. When G = PSL(2, R), the right action by multiplication of A on Γ\G identifies with the action of the geodesic flow on Γ\ . It is well known that this flow is topologically mixing on its non-wandering set. When Γ\G/M is non compact of infinite volume and G of higher real rank, what can we say about the right action of one parameter subgroups of A acting by right multiplication on Γ\G/M? First, I will give an example in higher rank of space of Weyl chambers and introduce in this situation the Weyl chamber flows I study. I will then state our result with Olivier Glorieux, a necessary and sufficient condition for topological mixing. Basing myself on the previous example, I will explain the geometric situation in higher rank. Lastly, I will give the main ideas behind our proof.
Donnerstag, den 7. Februar 2019 um 12:45 Uhr, in INF205, SR3 Donnerstag, den 7. Februar 2019 at 12:45, in INF205, SR3
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Dr. Anna Wienhard