Speaker: Barak Weiss, Tel Aviv University
January 11, 2024 04:00 PM
- 05:00 PM
Abstract:
Let \nu be a Bernoulli measure on a fractal in Rd generated by a finite collection of contracting similarities with no rotations and with rational coefficients; for instance, the usual coin tossing measure on Cantor's middle thirds set. Let at = diag (et,..., et, e-dt), let U be its expanding horospherical group, which we identify with Rd, and let \bar \nu be the pushforward of \nu onto the space of lattices SLd+1(R)/SLd+1(Z), via the orbit map of the identity coset under U. In joint work in progress with Khalil and Luethi, we show that the pushforward of \bar \nu under at equidistributes as t tends to infinity, as do the pushforwards under more general one parameter subgroups. This generalizes a previous result of Khalil and Luethi. I will discuss some Diophantine applications and some probabilistic ideas used in the proof.