Thursday January 26, 14:05 (UK time), B3.02 Zeeman.

Zoom meeting

Davide Spriano (Oxford)

Combinatorial criteria for hyperbolicity

Abstract: Perhaps one of the most fascinating properties of hyperbolic groups is that they admit equivalent definitions coming from different areas of mathematics. In this talk, we will survey some interesting definitions, and discuss a new one that, perhaps surprisingly, was previously unknown, namely that fact that hyperbolicity can be detected by the language of quasi-geodesics in the Cayley graph. As an application, we will discuss some progress towards a conjecture of Shapiro concerning groups with uniquely geodesic Cayley graphs.

Thursday February 23, 14:05 (UK time), B3.02 Zeeman.

Zoom meeting

Saul Schleimer (Warwick)

From loom spaces to veering triangulations

Abstract: A ``loom space'' is a copy of $\mathbb{R}^2$ equipped with a pair of transverse foliations satisfying certain axioms. These arise as the link spaces associated to veering triangulations and also as the flow spaces of (drilled) pseudo-Anosov flows without perfect fits. Following work of Guéritaud, we prove a converse: namely, every loom space gives rise, canonically, to a locally veering triangulation. Furthermore, the realisation of this triangulation (minus the vertices) is homeomorphic to $\mathbb{R}^3$. I will sketch the proof, giving many pictures.

This is joint work with Henry Segerman.

Thursday March 2, 14:05 (UK time), B3.02 Zeeman.

Zoom meeting Slides

Malavika Mukundan (Michigan)

Dynamical approximation of entire functions

Abstract:Postsingularly finite holomorphic functions are entire functions for which the forward orbit of the set of critical and asymptotic values is finite. Motivated by previous work on approximating entire functions dynamically by polynomials, we ask the following question: given a postsingularly finite entire function $f$, can $f$ be realised as the locally uniform limit of a sequence of postcritically finite polynomials?

In joint work with Nikolai Prochorov and Bernhard Reinke, we show how we may answer this question in the affirmative.

Thursday March 9, 14:05 (UK time), D1.07 Zeeman.

Zoom meeting

Elia Fioravanti (MPIM Bonn)

Coarse cubical rigidity

Abstract: When a group $G$ admits nice actions on $\mathrm{CAT}(0)$ cube complexes, understanding the space of all such actions can provide useful information on the outer automorphism group $\mathrm{Out}(G)$. As a classical example, the Culler-Vogtmann outer space is (roughly) the space of all geometric actions of the free group $F_n$ on a $1$-dimensional cube complex (a tree). In general, however, spaces of cubulations tend to be awkwardly vast, even for otherwise rigid groups such as the hexagon RAAG. In an attempt to tame these spaces, we show that all cubulations of many right-angled Artin and Coxeter groups coarsely look the same, in a strong sense: they all induce the same coarse median structure on the group.

This is joint work with Ivan Levcovitz and Michah Sageev.

Thursday March 9, 15:05 (UK time), D1.07 Zeeman.

Zoom meeting

Nansen Petrosyan (Southampton)

Hyperbolicity and $L$-infinity cohomology

Abstract: $L$-infinity cohomology is a quasi-isometry invariant of finitely generated groups. It was introduced by Gersten as a tool to find lower bounds for the Dehn function of some finitely presented groups. I will discuss a generalisation of a theorem of Gersten on surjectivity of the restriction map in $L$-infinity cohomology of groups. This leads to applications on subgroups of hyperbolic groups, quasi-isometric distinction of finitely generated groups and $L$-infinity cohomology calculations for some well-known classes of groups such as RAAGs, Bestvina-Brady groups and $\mathrm{Out}(F_n)$. Along the way, we obtain hyperbolicity criteria for groups of type $FP_2(Q)$ and for those satisfying a rational homological linear isoperimetric inequality.

I will first define L-infinity cohomology and discuss some of its properties. I will then sketch some of the main ideas behind the proofs. This is joint work with Vladimir Vankov.