SEMINAR: Groups and Combinatorics Seminar 16:00 Fri 23/03/2018: Michael Giudici (University of Western Australia)

Speaker: Prof. Michael Giudici (University of Western Australia)

Title: Bases for permutation groups and the Saxl graph

Time and place: 16:00 Friday 23/03/2018 in Weatherburn LT

Abstract: Let G be a permutation group on a set X. A base for G, is a subset B of X such that the pointwise stabiliser of the elements of B is trivial. There has been a large amount of recent research on the size of a base of a primitive permutation group, culminating with the recent proof of Pyber’s Conjecture. At the same time there has been a large amount of work devoted to finding the primitive groups with a base of size two. For such groups we can define the Saxl graph of G to be the graph with vertex set X and two elements are joined by an edge if they are a base. I will discuss some recent work with Tim Burness that investigates some of the properties of this graph.

Please come at 15:00 this Friday to meet our BPhil students over cake (which may go quickly).

All welcome.