On Gromov's theorem on group growth
Hovedinnhold
Mauricio Godoy Molina, a PhD student in the Analysis group, will give a seminar on a self-selected topic.
Title: On Gromov's theorem on group growth
Abstract: One of the most celebrated results of M. Gromov is the characterization of finitely generated groups of polynomial growth as groups with a nilpotent subgroup of finite index, called almost nilpotent groups. The proof and some related results of this theorem have a strong "sub-Riemannian flavour". For example, the degree of the polynomial growth, given by the Bass-Milnor-Wolf formula, also known as Bass-Guivarch formula, is surprisingly similar to Mitchell's formula for the Hausdorff dimension of a sub-Riemannian manifold at a regular point.
The aim of this talk is to present the necessary definitions, to sketch the proof of Gromov's theorem from a sub-Riemannian point of view and to study some examples.
