Title: Derangements and random matrices over finite fields
Speaker: Jason Fulman - University of Southern California
Abstract: An element of the symmetric group on n symbols is called a derangement if it has no fixed points, and a classical result in combinatorics and probability is that for n > 1, the proportion of derangements is at least 1/3. A vast generalization was conjectured by Boston and Shalev, stating that for any transitive action of a finite simple group G on a set X of size greater than 1, the proportion of derangements is bounded away from 0 by an absolute constant. This was proved by Fulman and Guralnick, and in this talk we describe how random matrices over finite fields were essential to the proof. We also discuss motivations for the study of derangements.
