Guest lecture on Ratner’s theorem and Mozes-Shah theorem

Speaker: Mengyang Wang (Chinese academy of sciences)

Time: 2025-10-30, 09:30-15:30
Location: 1610, SIMIS

Abstract:

Ratner’s theorem, which describes the rigidity of unipotent flows on homogeneous spaces, has played a significant role in various fields such as Diophantine approximation,counting rational points on algebraic varieties, and hyperbolic geometry since its introduction in the 1990s. In this talk, I will introduce Ratner’s theorem and, using linearization techniques, present a proof of the Mozes–Shah theorem. If time permits, I will also explain how the effective version of Ratner’s theorem can be applied to prove the Mozes–Shah theorem. You are more than welcome to attend.