# Growth of groups and algebras

24.11.2022 16:15

It has been very fruitful, since Gromov's seminal paper, to view infinite groups as geometric objects: if a group has a finite generating set, it may be seen as a metric space by declaring two elements to be at distance 1 if they differ by a generator. This immediately leads to geometric invariants of groups, the prominent one being volume growth, the number of group elements in a ball of given radius. By comparison, "geometric algebra theory" is still in its infancy.

In my talk, I will strive to show how algebras, and dynamical systems, play a crucial role in understanding growth phenomena in groups. I will review what is known and unknown about volume growth, and in particular

- what do restrictions on the volume growth (e.g. polynomial) entail on the group's structure?

- which kinds of growth behaviour are possible? in particular, under natural conditions on the group's algebraic properties?

### Lieu

Bâtiment: Conseil Général 7-9

Room 1-15

### Organisé par

Section de mathématiques### Intervenant-e-s

Laurent BARTHOLDI, Universität des Saarlandesentrée libre