# Abstracts for Arithmetic Groups and 3-Manifolds, May 16-20, 2022

Alternatively have a look at the program.

## Homology growth and (non)fibering

Posted in
Speaker:
Boris Okun
Affiliation:
University of Wisconsin-Milwaukee/MPIM
Date:
Mon, 16/05/2022 - 09:30 - 10:30

Suppose a group $$G$$ has a finite $$K(G,1)$$ space $$X$$, and suppose we have a sequence of deeper and deeper regular finite sheeted covers of $$X$$, so that the corresponding sequence of normal subgroups intersect at $$\{1\}$$.  What can we say about homology of these covers? Rationally, the answer is given by the celebrated Lück Approximation theorem: the normalized Betti numbers of the covers limit to the $$\ell^2$$-Betti numbers of $$G$$.

## Extremal hyperbolic manifolds and the Selberg trace formula

Posted in
Speaker:
Bram Petri
Affiliation:
Jussieu
Date:
Mon, 16/05/2022 - 11:00 - 12:00

Virtual talk.

## Thin part of the arithmetic orbifolds

Posted in
Speaker:
Mikolaj Fraczyk
Affiliation:
University of Chicago
Date:
Mon, 16/05/2022 - 13:30 - 14:30

Virtual talk.

## Length, Stable Commutator Length, and Hyperbolic Geometry

Posted in
Speaker:
Cameron Rudd
Affiliation:
Urbana-Champaign
Date:
Mon, 16/05/2022 - 14:45 - 15:45

Geodesic length and stable commutator length give geometric and topological notions of complexity for nullhomologous elements of the fundamental group of a hyperbolic manifold. The ratio of these complexity measures is a sort of geometric-topological isoperimetric ratio called the stable isoperimetric ratio. In this talk, I will discuss this ratio and describe how it relates to different aspects of the geometry and topology of hyperbolic manifolds.

## Rigid meromorphic cocycles for orthogonal groups

Posted in
Speaker:
Michael Lipnowski
Affiliation:
McGill University
Date:
Mon, 16/05/2022 - 16:00 - 17:00

Virtual talk.

## Betti numbers of arithmetic locally symmetric spaces

Posted in
Speaker:
Jean Raimbault
Affiliation:
Université Paul Sabatier, Toulouse
Date:
Tue, 17/05/2022 - 09:30 - 10:30

The cohomology of arithmetic groups, or equivalently of the associated locally symmetric spaces, is an object of interest in number theory, topology and group theory. Its behaviour is constrained quite strongly by the volume; in this talk I will present a very general result about this obtained in joint work with Mikolaj Fraczyk and Sebastian Hurtado.

## Torsion homology and regulators of Vignèras isospectral manifolds

Posted in
Speaker:
Aurel Page
Affiliation:
INRIA, Université de Bordeaux
Date:
Tue, 17/05/2022 - 11:00 - 12:00

Virtual talk.

## Kleinian surface groups and filling links

Posted in
Speaker:
William Stagner
Affiliation:
Rice University
Date:
Tue, 17/05/2022 - 14:30 - 15:30

Virtual talk.

## Eisenstein cocycles and elliptic Dedekind sums

Posted in
Speaker:
Wong Tian An
Affiliation:
University of Michigan-Dearborn
Date:
Tue, 17/05/2022 - 16:00 - 17:00

Virtual talk.

## Profinite recognition of fibring

Posted in
Speaker:
Dawid Kielak
Affiliation:
University of Oxford
Date:
Wed, 18/05/2022 - 09:30 - 10:30

A number of remarkable recent results in profinite rigidity use a theorem of Friedl and Vidussi that connects fibring of 3-manifolds with non-vanishing of twisted Alexander polynomials. I will discuss how a similar connection can be exhibited also in setting different from that of 3-manifolds. The talk is based on joint work with Sam Hughes.

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