Pure Maths Colloquium: Scott Harper

Studying generating sets for groups has led to many interesting and surprising results. For instance, every finite simple group can be generated by just two elements. In fact, Guralnick and Kantor, in 2000, proved that in a finite simple group every nontrivial element is contained in a generating pair, a property known as \(3/2\)-generation. This answers a 1962 question of Steinberg. This talk will be a survey of several lines of current research that are motivated by this result. In particular, I will discuss recent progress towards a complete classification of the finite \(3/2\)-generated groups, work with Tim Burness on the stronger notion of uniform domination (which has a close connection with bases for permutation groups), and work with Casey Donoven on analogous results for infinite groups related to Thompson’s group \(V\).