Random Walks in Finite Groups

As the name declares, the theory of random walks in groups is somehow in the middle of group theory and probability theory. The central question is “how to generate a group efficiently?” In this seminar I will present the notions of diameter, mixing time and expander graphs, as well as some explicit constructions. The second part will be dedicated to the Bourgain-Gamburd Machine, a recent technique to show expansion in quasirandom groups.