Alexei Miasnikov, McGill University

Abstract:
The Gromov-Hausdorff-Grigorchuk topology provide a very efficient way to measure similarity of finitely generated groups. Thus limits of free groups are obviously “free-like” groups, while limits of finite groups are “approximately finite” groups, etc. It turns out that this geometric similarity (on the level of the Cayley graphs) can be expressed also in model-theoretic terms (in the language of universal sentences), as well as in the language of algebraic –geometry (via the coordinate groups of irreducible varieties). In this talk I would like to go a bit further and discuss relations between some logic al, topological and algebraic invariants of a given group that naturally occur in this framework.