Title: Simple groups, probabilistic methods and applications

Abstract: Group theory is used to study symmetry in a vast range of mathematical and physical systems, from the foundations of quantum physics to the intricacies of the Rubik's cube. The finite simple groups are the "atoms" in this theory, analogous to the primes in number theory, and they have been a central focus of interest for almost 200 years. An ambitious project to classify these fascinating objects was completed about 20 years ago and this monumental achievement has had a profound influence on group theory and its applications.

In this lecture, I will begin by discussing some of the history around simple groups and their central role in group theory. I will then highlight several more recent developments, where the power of the classification theorem has been combined with probabilistic methods to great effect. For example, I will explain the major impact of these ideas on the study of bases for permutation groups, which is a classical concept introduced in the 19th century, and I will conclude by presenting some recent results on the generation properties of finite groups.

 

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Although this event is free to attend we ask that you please book your place via the Eventbrite page here to allow us to monitor numbers.

Please note, the lecture will begin at 4pm, however we invite attendees to join us in Fry Atrium from 3.15pm for refreshments.