Fuglede-Kadison determinants over free groups and Lehmer’s constants (Fathi Ben Aribi, UC Louvain)

14.12.2021 10:30

The Fuglede-Kadison determinant associates a non-negative real number to any equivariant operator acting on the completion of a group algebra. This determinant is technical to define, difficult to compute, and admits connections with the Mahler measure and the hyperbolic volume.
In this project, we compute the Fuglede-Kadison determinants of an infinite family of operators over the free groups.
To do so, we relate the operators in question with random walks on Cayley graphs, which translates in counting closed paths on regular trees, following works of Bartholdi and Dasbach-Lalin.
As a consequence, we give a partial answer to a question of Lück as we establish new upper bounds on Lehmer’s constants for a large family of groups.
If time permits, we will mention further applications in constructing topological invariants from representations of braid groups.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Séminaire "Groupes et géométrie"

Organisé par

Section de mathématiques

Intervenant-e-s

Fathi Ben Aribi, UC Louvain

entrée libre

Classement

Catégorie: Séminaire

Mots clés: groupes et géométrie