Date & Time 2:00-4:00pm June 23，June 25, June 29, July 1, July 6
10:00-12:00am July 8
Venue June 23，June 25, June 29, July 1 -- Room 1213, Beijing International Center for Mathematical Research, Resource Plaza
July 6, July 8 -- Room 1328, Beijing International Center for Mathematical Research, Resource Plaza
Abstract

In these notes we are going to look at the structure of incidence structures" which have ``large'' automorphism groups. Both of these terms need defining but we will come to that later. Many mathematical objects can be seen as incidence structures, especially geometrical objects. In this series of lectures the main focus will be on "linear spaces", these are structures which are, in some ways, most familiar in the sense that any two points uniquely determine a line. However, many results can be stated in a more general setting and in the first chapter I have tried to do this.

Much of the material will be concerned with setting out the necessary background to show how there is a chance of classifying those linear spaces which have line-transitive automorphism groups. Much of this material depends on permutation group theory and the classification of finite groups. The classification will be taken for granted though I have included a proof of the O'Nan-Scott Theorem. This is fundamental to examining the structure of the automorphism groups, with the variation due to Cheryl Praeger for the case of quasiprimitive groups. All these terms will be explained as we go on.