Title: Badly approximable points on manifolds and unipotent orbits in homogeneous spaces
Speaker: Lei Yang (Sichuan University, China)
Abstract: We will study n-dimensional badly approximable points on manifolds. Given an smooth non-degenerate submanifold in R^n, we will show that any countable intersection of the sets of weighted badly approximable points on the manifold has full Hausdorff dimension. This strengthens a previous result of Beresnevich by removing the condition on weights and weakening the analytic condition on manifolds to smooth condition. Compared with the work of Beresnevich, we study the problem through homogeneous dynamics. It turns out that the problem is closely related to the study of distribution of long pieces of unipotent orbits in homogeneous spaces.