Seminar: Growth of Groups; WS 2026/27

Prof. Dr. Clara Löh / Franziska Hofmann / Malena Wasmeier

News

Organisational meeting: Tuesday, July 14, 2026; 12:00, M 201.
This seminar will be held in English. The written report can be in English or German. The handouts should be in English.

Seminar: Growth of Groups

No reasonable classification of finitely generated groups is possible. One attempt at structuring the universe of finitely generated groups is to sort groups by their "growth types". Examples of notions of growth of groups include the following:

Word-length growth measures the growth of balls in groups of growing radius with respect to the word-length;
subgroup growth counts the number of subgroups of growing (finite) index;
residual finiteness growth measures how difficult it is to detect non-triviality of elements by passing to finite quotients.

The growth of fundamental groups (a notion from algebraic topology) of manifolds leads to interesting group-theoretic applications in topology and geometry. Even though the above notions of growth are substantially different and not directly related, many intriguing parallels exist. For instance, the question of which classes of groups have polynomial word-length growth or polynomial subgroup growth leads to similar answers (and even, to a certain extent, to similar proof techniques).

In this seminar, we will study word-length growth, subgroup growth, and residual finiteness growth. We will illustrate these notions in concrete examples and learn how to approach the polynomial growth theorems. Moreover, we will discuss some basic applications in topology and geometry.

Time/Location

Friday, 8:30--10:00, M104

Material

tba

Prerequisites

Most of the talks will be accessible with basic knowledge on groups, rings, and modules. Some of the talks benefit from experience in topology or geometry.

Formalities/Credits

See the commented list of courses.

Last Change: June 19, 2026.