Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## Diophantine approximation and product of linear forms

Dr. Nicolas de Saxcé talk

**Date:** 25.02.19 **Time:** 14.00 - 15.00 **Room:** ETH HG G 43

Fix a one-parameter diagonal flow a_t on the space of unimodular lattices in R^d, and consider its conjugates L^{-1}a_tL, where L is chosen randomly on a subvariety M of SL(d,R). Under some algebraicity condition on M, we shall give a formula for the rate of escape of the orbit L^{-1}a_tL.Z^d and describe the shape of the lattice, for t large and almost every L. Finally, we shall give some applications to diophantine approximation on manifolds.