Speaker：Tim Burness（University of Bristol，UK）

Time：2023-3-23, 17:00

Location：Zoom ID: 856 490 7913  (Pwd: XMUmath)

Abstract:

Let G be a permutation group on a finite set. The fixed point ratio of an element x in G, denoted fpr(x), is the proportion of points fixed by x. Fixed point ratios have been studied for many decades, finding a wide range of applications. In this talk, I will introduce fixed point ratios and I will survey some of the main results, with a focus on the case where G is (almost) simple and primitive. I will also highlight a number of interesting applications, from problems concerning bases for permutation groups to questions on the generation and random generation of finite groups.