Victor Beresnevich

Badly approximable points: games, measures and dynamics

In this talk I will discuss a recent paper joint with Erez Nesharim and Lei Yang, in which we prove that the intersection of the sets of badly approximable points in R^n with any analytic non-degenerate curve is an absolute winning set. The method we develop in the paper exploits new and old ideas, which I will attempt to explain following a short introduction. In particular, I will explain the role of games and measures supported on fractals as well as techniques from homogeneous dynamics that we deploy in the proof.