Time:
10:00-11:30 November 21 (Thursday)
10:00-11:30 November 22, 2024 (Friday)
16:00-17:30 December 11, 2024 (Wednesday)
10:00-11:30 December 12, 2024 (Thursday)
10:00-11:30 December 16, 2024 (Monday)
10:00-11:30 December 18, 2024 (Wednesday)
Venue: MCM610
Title: Ratner's measure rigidity theorem for semisimple ambient groups
Abstract: I will give a series of lectures to explain some details of the proof of Ratner's measure rigidity theorem when the ambient group is semisimple. This is the most important and difficult case in Ratner's proof.
In the first lecture, I will give a general introduction to Ratner's theorem. I will mention several important applications of Ratner's theorem to number theory, and some important related works. I will also mention recent developments on its effective versions.
In the second lecture, I will explain the proof of measure rigidity for probability measures invariant and ergodic under a semisimple subgroup (due to Einsiedler). The proof is relatively simple and contains some important ideas appearing in Ratner's proof.
In the remaining three lectures, I will focus on Ratner's proof. I will explain the most important ideas and arguments in the proof. I will more or less follow the following paper by Ratner:
On measure rigidity of unipotent subgroups of semisimple groups. Acta mathematica, 165:229–309, 1990.
