Random groups in number theory and topology
Speaker: Professor Nigel Boston (UCD)
Date: Wed 17th September 2008
Location: Mathematical Sciences Seminar Room
In a recent Inventiones paper Dunfield and Thurston compared fundamental groups of random 3-mainfolds and random discrete groups. Analogously, we develop a theory comparing certain random Galois groups and random p-groups. In particular, what is the probability that r relators chosen at random from a g-generator free group present a particular group? We make sense of and answer this question for p-groups. This leads to some mysterious mass formulae, some infinite groups that arise with nonzero probability, and applications to number theory.
(This talk is part of the K-Theory, Quadratic Forms and Number Theory series.)