The main aim of Mic Seminars is to bring together young mathematicians from different universities. It provides an informal context to share knowledge and ideas, and to build social networks within the different mathematical communities.
Speaker: Jessica Anzanello (Università degli Studi di Milano-Bicocca)
Title: On the proportion of derangements in finite transitive groups
Abstract: A derangement is a permutation with no fixed points. By a classical result of Jordan, any nontrivial finite transitive permutation group contains such elements. This fact has far-reaching applications and raises natural questions about the abundance and orders of derangements, which have been widely studied in recent years. In this talk, I will survey some of these problems and results, and I will discuss how combinatorial tools can be used to obtain simple formulas for the proportion of derangements in certain natural subgroups of the finite affine general linear group.