Topology Festival image

Topology Festival

May 7–10, 2010

Abstracts of Workshops

Nikolay Nikolov, Imperial College London

Profinite Groups and their Applications

Profinite groups arose first in number theory as the p-adic integers and infinite Galois groups. For group theorists they are a convenient tool to study asymptotic questions about families of finite groups in terms of topological and algebraic properties. In this talk I will introduce the basic properties of profinite groups and sketch some of their more striking applications in other fields of mathematics.

Daniel Wise, McGill University

Residual Finiteness and Subgroup Separability of Discrete Groups

The study of residual finiteness among combinatorial group theorists reached a high point in the 60’s, but it was subsequently kept on a mathematical back burner during the “small-cancellation era” in the 70’s and during the flowering of geometric group theory in the late 80’s and early 90’s. Nevertheless, among low-dimensional topologists, residual finiteness had retained a steady interest because it played a useful role and was often available. The pendulum swings to and fro, and there has been a resurgence of interest in residual finiteness among discrete group theorists in recent years.

I will survey some of the theorems and examples related to residual finiteness in combinatorial group theory, and will also focus on separable subgroups (which are subgroups that are “closed in the profinite topology”) and their utility in low-dimensional topology.