George Willis, University of Newcastle
“Classifying Symmetry”
Classifying types of symmetry has been an important theme in mathematics going back to the classification of the five Platonic solids. The more modern approach is to study symmetry groups, which encode the regularities of structures much as numbers encode their size, and an important part of this study is the classification of simple groups of various types.
The first part of the talk will survey some of the classifications that have been achieved in the past, including those of the frieze and crystallographic groups and the classifications of the simple finite groups and the simple connected Lie groups. Locally compact groups and why they are important will be described in genereal terms. The final part of the talk gives an overveiew of a current classification program, that of the simple totally disconnected, locally compact groups. It is only recently that it has seemed feasible to at least roughly classify these groups, and the talk will describe joint work with Pierre-Emmanuel Caprace and Colin Reid that separates simple groups into types according to their local structure.
Refreshments will be served in MC 5046 at 3:30 p.m. Everyone is welcome to attend.