# 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
Zugehörigkeit:
University of Wisconsin-Milwaukee/MPIM
Datum:
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
Zugehörigkeit:
Jussieu
Datum:
Mon, 16/05/2022 - 11:00 - 12:00

Virtual talk.

## Thin part of the arithmetic orbifolds

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

Virtual talk.

## Length, Stable Commutator Length, and Hyperbolic Geometry

Posted in
Speaker:
Cameron Rudd
Zugehörigkeit:
Urbana-Champaign
Datum:
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
Zugehörigkeit:
McGill University
Datum:
Mon, 16/05/2022 - 16:00 - 17:00

Virtual talk.

## Betti numbers of arithmetic locally symmetric spaces

Posted in
Speaker:
Jean Raimbault
Zugehörigkeit:
Université Paul Sabatier, Toulouse
Datum:
Die, 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
Zugehörigkeit:
INRIA, Université de Bordeaux
Datum:
Die, 17/05/2022 - 11:00 - 12:00

Virtual talk.

## Kleinian surface groups and filling links

Posted in
Speaker:
William Stagner
Zugehörigkeit:
Rice University
Datum:
Die, 17/05/2022 - 14:30 - 15:30

Virtual talk.

## Eisenstein cocycles and elliptic Dedekind sums

Posted in
Speaker:
Wong Tian An
Zugehörigkeit:
University of Michigan-Dearborn
Datum:
Die, 17/05/2022 - 16:00 - 17:00

Virtual talk.

## Profinite recognition of fibring

Posted in
Speaker:
Dawid Kielak
Zugehörigkeit:
University of Oxford
Datum:
Mit, 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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