Szego Seminar/Third Year Examination: "Winning Sets of Schmidt-Type Games"

Abstract: The first part of this talk will introduce the so called Banach-Mazur game on the interval [0, 1] and study the topological properties of a winning set. For us, a winning set is a subset of the unit interval which can guarantee a victorious player, regardless of the strategy that the other player adopts. By using metric properties of [0, 1], we will then define the Schmidt game, a particular case of the game above. Again, the aim will be to examine the size of a winning set for the game, but now in terms of its Hausdorff dimension.

Host: Christopher Felder