Virtual homological torsion in low dimensionsMPIM

by Jonathan Fruchter (Universität Bonn)

Thursday Feb 12, 2026, 1:30 PM → 3:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Oberseminar Differentialgeometrie

A long-standing conjecture of Bergeron and Venkatesh predicts that in closed hyperbolic 3-manifolds, the amount of torsion in the first homology of finite-sheeted normal covers should grow exponentially with the degree of the cover as the covers become larger, at a rate reflecting the volume of the manifold. Yet no finitely presented residually finite group is known to exhibit such behaviour, and meaningful lower bounds on torsion growth are rare.

In this talk I will explain how a two-dimensional lens offers a clearer view of some of the underlying mechanisms that create homological torsion in finite covers, and how they might relate to its growth. If time allows, I will also discuss how these ideas connect to the question of profinite rigidity: how much information about a group is encoded in its finite quotients.