Alternatively have a look at the program.

## Homology growth and (non)fibering

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

Virtual talk.

## Thin part of the arithmetic orbifolds

Virtual talk.

## Length, Stable Commutator Length, and Hyperbolic Geometry

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

Virtual talk.

## Betti numbers of arithmetic locally symmetric spaces

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

Virtual talk.

## Kleinian surface groups and filling links

Virtual talk.

## Eisenstein cocycles and elliptic Dedekind sums

Virtual talk.

## Profinite recognition of fibring

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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