[Settfa] *Tomorrow* Tuesday 7 Oct, Peter J. Cameron

[David Bradley-Williams]

Tuesday, 7 October 2025 - 10:00 to 11:30
Place: IM, konírna

Speaker: Peter J. Cameron, University of St Andrews
Title: Graphs (and simplicial complexes) defined on groups

Abstract

My subject is graphs whose vertex set is a group and whose edges are 
defined in terms of the group operation, so that the graph is invariant 
under all automorphisms of the group. The classical example is the 
commuting graph of a group, defined by Brauer and Fowler in a seminal 
paper in 1955.

There has been a lot of work on this topic recently. My interests are 
mainly in how the theories of groups and graphs can help one another. 
Some of the questions I will address are

- finding new results about groups;
- characterising important classes of groups using graphs;
- recognising graphs obtained from groups and, if possible, 
reconstructing the groups;
- finding some beautiful graphs.

Recently I have widened the investigation to simplicial complexes 
defined on groups; I will present a small amount of new material and 
some open problems on this also.

For more information see the seminar web page at
https://www.math.cas.cz/index.php/events/seminar/6