Simple groups, fixed point ratios and applications

Abstract

The study of fixed point ratios is a classical topic in permutation group theory, with a long history stretching back to the origins of the subject in the 19th century. Fixed point ratios arise naturally in many different contexts, finding a wide range of applications. In this survey article we focus on fixed point ratios for simple groups of Lie type, highlighting some of the main results, applications and related problems.

arXiv comment50 pages; to appear in the proceedings of the program "Local representation theory and simple groups" (CIB, Lausanne 2016)