Regular Polytopes and Almost Simple Groups

Lecturer: Dimitri Leemans, University of Auckland, New Zealand 

Abstract: The aim of these lectures is to explain how several results in the past ten years have been obtained on abstract regular polytopes whose automorphism groups are almost simple  groups. These results have been obtained by first collecting experimental data, then analysing the data to elaborate conjectures and finally prove these conjectures. The lectures will  cover several aspects, namely:  algorithms to classify regular polytopes of a given group;  subgroup lattices of groups as a tool to bound the maximal rank of abstract regular polytopes; centralizers of involutions and abstract regular polytopes; abstract regular polytopes and transitive groups; permutation representation graphs, fracture graphs and 2-fracture graphs.