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 geometric models do we have; 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, when can we deduce that the groups are the same? Does geometry help? Can we see what the finite quotients are?
In this talk I’ll describe some of the major themes in the modern study of infinite groups, sketch the universe of finitely presented groups, and describe recent results concerning some of the above questions.
The talk will be followed by a reception in the Huxley Common Room (549) from 18:00.
Further information about Professor Bridson’s research can be found here.