Abstract:

What do we mean when we say a set is small? In math, there are several different notions of "smallness", and different sets can be small in some ways and large in others. Determining whether a certain set is small in a specific sense is often a chore. We will discuss several games that characterize the notion of "smallness" for certain senses of the term: the Banach-Mazur game, Schmidt's game, McMullen's game, and a newer game called the Banach-Mazur-McMullen Game.