Title: Schmidt's game, badly approximable vectors and fractals.
Abstract: The main theme of the talk is playing Schmidt's game on a fractal play board. Schmidt's game, invented by W. M. Schmidt in 1966, is a powerful tool for determining the Hausdorff dimension of certain very “small” sets (i.e., meager sets of Lebesgue measure zero) in the n-dimensional Euclidean space. In particular the sets of badly approximable numbers, vectors and matrices. Recently, due to results in geometric measure theory, similar results can be obtained with respect to the Hausdorff dimension of the intersection of these sets and certain fractals. We shall define the badly approximable sets, Schmidt's game, explain what fractals we are considering and discuss the resuts. No prior knowledge in number theory nor geometric measure theory is assumed.