Professor Bridson will deliver a lecture titled 'Symmetry through shadows: Chasing infinite groups through their finite actions'. An abstract and biography can be found below.

Abstract:

There are many situations in geometry or elsewhere in mathematics where it is natural or convenient to explore infinite groups of symmetries via their actions on finite objects. But how hard is it find these finite manifestation and  to what extent does the collection of all such actions determine the infinite group? 

In this colloquium, I will sketch some of the rich history of  such problems and then describe some of the great advances in recent years. I'll describe pairs of distinct groups that have the same finite images and I'll sketch the proof of some "profinite rigidity results", ie theorems showing that in certain circumstances one can identify an infinite group if one knows its set of finite images. 

We'll pay particular attention to groups that arise in 3-dimensional geometry and topology.

Short Biography: Martin Bridson is the Whitehead Professor of Pure Mathematics at Oxford and President of the Clay Mathematics Institute. He is renowned for his work in geometry, topology, and group theory.

Born in the Isle of Man, he was an undergraduate at Oxford and a graduate student at Cornell (PhD1991). He subsequently held faculty positions at Princeton, Geneva, and Imperial College London. He has also been a visiting professor at  Stanford and the EPFL.

His honours include the LMS Whitehead Prize (1999), AMS Steele Prize (2020), and the Royal Society's Wolfson Research Merit Award (2012). A Fellow of the Royal Society (2016), the American Mathematical Society (2015), and Academia Europeae (2020), he was an Invited Speaker at the International Congress of Mathematicians in 2006 and a Plenary Speaker at the European Congress of Mathematics in 2024.