Joint Mathematics Colloquium ICMAT-UAM-UC3M-UCM

The dynamical view on gradient invariants of groups

Clara Löh
(Universität Regensburg)

31 May 2024 ,12:00
Aula 520, Departamento de Matemáticas, UAM - Streaming

For a residually finite group, on the one hand, one can study the asymptotic behaviour of group invariants along
systems of finite index subgroups, normalised by the index. For example, this leads to Betti number gradients,
torsion homology gradients, and rank gradients. On the other hand, the profinite completion provides a dynamical
system of the group. One may thus ask, to which extent gradient invariants can be described in terms of invariants
of such dynamical systems.
In this talk, I will give a non-technical introduction to this dynamical approach and how the dynamical view can
help calculating gradient invariants.