MathematicsSeminar |
Rocky Mountain Algebraic Combinatorics Seminar
Upcoming Seminars Schedule
Synchronization, diagonal structures, and the Hall--Paige conjecture
Peter Cameron
University of St Andrews
I will begin by telling you some of the story of synchronization, an investigation of permutation groups that has its origins in automata theory and semigroup theory; this work is mainly with João Araújo, along with several others.
Synchronizing permutation groups are primitive, so it is natural to look at (a simplified form of) the O'Nan-Scott classification of primitive groups. One of the types we have to deal with is diagonal type. The problem has been almost completely solved for these; this uses the solution of the celebrated Hall-Paige conjecture concerning perfect mappings in groups by Stewart Wilcox, Anthony Evans and John Bray. This analysis prompted a closer look at diagonal type. The wreath products and affine groups preserve well-known geometric or combinatorial structures; such structures are not so well understood for diagonal type. With Rosemary Bailey, Cheryl Praeger and Csaba Schneider, I have just managed to find a beautiful characterisation of the combinatorial structures that diagonal groups preserve, which is not even written down yet; but if the proof is still standing by the time of the talk I will tell you about it.
Online via Zoom, Meeting at 3:30pm, talk starting 4.00pm
This is a joint Denver U / UC Boulder / UC Denver / U of Wyoming / CSU seminar that meets biweekly. Anyone interested is welcome to join us at a local restaurant for dinner after the talks.