The symmetries (automorphisms) of any mathematical object form a group, and arbitrary degrees of complexity can be encoded into finite group-presentations. So what can we say about the universe of all finitely presented groups; what flavours of mathematics should we use to organise and explore it; what monsters will we find; and can we encode arbitrarily monstrous behaviour into the subgroups of familiar groups such as SL(n,Z)?
If a mystery group has the same finite quotients as a group we know well, and we know that each finite subset of these groups injects into some finite quotient, must the groups be the same?
In this talk I’ll describe some of the major themes in the modern study of infinite groups, I’ll sketch the universe of finitely presented groups, and I’ll describe recent results concerning the last two questions.
About the Speaker:
Martin R Bridson has been the Whitehead Professor of Pure Mathematics at the University of Oxford since 2007. His research spans geometry, topology and group theory. His honours include the Whitehead Prize of the London Mathematical Society in 1999, the Forder Lectureship of the New Zealand Mathematical Society in 2005, a Senior Fellowship from the EPSRC, and Royal Society Wolfson Research Merit Awards in 2006 and 2012. In 2006, he was an invited speaker at the International Congress of Mathematicians in Madrid. He was an Abel Lecturer in 2010, a Schroedinger Lecturer in 2011, and has given many distinguished lecture series, including the Marker Lectures in 2009.
Bridson received a BA from the University of Oxford in 1986 and a PhD from Cornell University in 1991. He spent four years as an assistant professor at Princeton University and seven as a Fellow of Pembroke College Oxford, where he became a Reader and then Professor of Topology. From 2002 to 2007 he was Professor at Imperial College London.