Diophantine approximation and product of linear forms

Vortrag von Dr. Nicolas de Saxcé

Datum: 25.02.19  Zeit: 14.00 - 15.00  Raum: 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.