Senior Speakers:

Uri Bader: Higher property T, Banach representations and applications

Gromov conjectured that the L^p-cohomology of simple groups vanishes below the rank. Farb conjectured a fixed point property for actions of lattices in such groups on CAT(0) cell complexes of dimension lower than the rank. Both conjectures follow from a new cohomological vanishing result, which could be seen as a Banach version of higher property T. In my talk I will survey the subject and put the new contribution in context.

Based on a joint work with Saar Bader, Shaked Bader and Roman Sauer.

Stephen Cantrell: Manhattan manifolds and growth indicator functions

Suppose that a group G acts nicely on a collection of hyperbolic metric spaces (X_1,d_1),…,(X_n,d_n). It is natural to try to compare these actions simultaneously. That is, given x in G what should we expect the vector of displacements (d_1(o_1,x . o_1),…, d_n(o_n,x . o_n)) to look like? (Here o_1,…,o_n are fixed base points for X_1,…X_n). In this talk we’ll discuss how to address this question by studying growth indicator functions and Manhattan manifolds.

This is based on joint work with Eduardo Reyes and Cagri Sert.

Valentina Disarlo: The model theory of the curve graph 

The curve graph of a surface of finite type is a graph that encodes the combinatorics of isotopy classes of simple closed curves. It is a fundamental tool for the study of the geometric group theory of the mapping class group. In 1987 N.K. Ivanov proved that the automorphism group of the curve graph of a finite surface is the extended mapping class groups. In the following decades, many people proved analogue results for many "similar" graphs, such as the pants graph, the arc graph, etc. In response to the many results, N.V. Ivanov formulated a metaconjecture. which asserts that any "natural and sufficiently rich" object associated to a surface has automorphism group isomorphic to the extended mapping class group. In this talk, I will present a joint work with Thomas Koberda (Virginia) and Javier de la Nuez Gonzalez (KIAS) where we provide a model theoretical framework for Ivanov’s metaconjecture and we conduct a thorough study of curve graphs from the model theoretic point of view, with particular emphasis in the problem of interpretability between different "similar" geometric complexes. In particular, we will prove that the curve graph of a surface of finite type is w-stable. This talk does not assume any prior knowledge in model theory.

Kasia Jankiewicz : Topological complexity of graph braid group

Abstract: Graph braid groups are the fundamental groups of configuration spaces of particles in a graph. Topological complexity is the measure of discontinuity of the motion planning problem. In this talk I will discuss those notions. I will also describe a nonpositively curved cube complex associated to each graph braid group and how it can be used to compute its topological complexity. This is joint work with Kevin Schreve.

Dawid Kielak: Virtual fibering and Poincaré duality

I will talk about the problem of recognizing when a manifold admits a finite cover that fibers over the circle, with emphasis on the case of hyperbolic manifolds in odd dimensions. I will survey the state-of-art, and discuss the role that group theory plays in the problem. Finally, I will discuss a recent result that sheds light on the analogous group-theoretic problem, that is, virtual algebraic fibering of Poincaré-duality groups. The final theorem is joint with Sam Fisher and Giovanni Italiano. 

Robert Kropholler: Dehn functions of subgroups of hyperbolic groups

Abstract: Hyperbolic groups are characterised by having a linear Dehn function. This property does not pass to finitely presented subgroups by work of Brady. This opens the question of what Dehn functions of finitely presented subgroups of hyperbolic groups can be. In this talk I will detail what is known and give an example where we give an explicit computation of an upper bound. This is joint work with Claudio Llosa Isenrich and Ignat Soroko.

Volodymyr Nekrashevych: Geometry of orbits and amenability

We will discuss how the asymptotic geometry of labeled orbital (a.k.a. Schreier) graphs can be used to prove finiteness conditions such as amenability and Liouville property for the associated groups. As an example, I will describe a joint result with N. Matte Bon and T. Zheng showing the Liouville property for iterated monodromy groups of locally expanding maps of spaces of Ahlfors-regular conformal dimension less than 2. We will also discuss some open problems in this direction.

Piotr Nowak: TBA

Damian Osajda: Systolic groups, exactly

Abstract: We prove that a class of systolic complexes (that is, complexes with a simplicial non-positive curvature) satisfy Yu's property A, a coarse geometric property implying e.g. coarse embeddability into a Hilbert space. It follows that groups acting properly on such complexes are exact, or equivalently, boundary amenable. As a consequence, groups from a class containing all large-type Artin groups, as well as all finitely presented graphical C(3)-T(6) small cancellation groups are exact. We use the Špakula-Wright combinatorial criterion for proving Property A. This is joint work with Martín Blufstein, Victor Chepoi, and Huaitao Gui.

Stefan Witzel: Building lattices

When studying S-arithmetic groups one is naturally led to considering their action as lattices on symmetric spaces and buildings. In low dimension (at most 2) lattices on buildings exist, that are not arithmetic. They share certain features with their arithmetic cousins,

but have striking differences as well. Examples are lattices on products of trees as studied by Burger, Mozes and Wise. I will speak about lattices on buildings that are not products. The talk is based on joint work with Jean Lécureux and Thomas Titz Mite. 

Abdul Zalloum: Construction of actions on hyperbolic and injective spaces and walls

I will discuss a construction that starts with a set S, a collection of walls W on S (i.e., a collection of bi-partitions of S), and equivariantly produces a range of geodesic metric spaces whose type is determined by the combinatorics of W. I will then describe various applications of this construction, such as constructing globally stable cylinders for residually finite hyperbolic groups, establishing equivariant quasi-isometric embeddings of the curve complex into finite products of quasi-trees, and constructing universal hyperbolic spaces for many classes of groups. I will also discuss some applications related to counting and growth problems in mapping class groups. The main theorems to be discussed are joint with Petyt and Spriano.

Junior Speakers:

Shaked Bader: Applications, Banach representations and higher property T

Gromov conjectured that the L^p-cohomology of simple groups vanishes below the rank. Farb conjectured a fixed point property for actions of lattices in such groups on CAT(0) cell complexes of dimension lower than the rank. Both conjectures follow from a new cohomological vanishing result, which could be seen as a Banach version of higher property T. In my talk I will give some details of the proof of the result above. Based on a joint with Saar Bader, Uri Bader and Roman Sauer.

Motiejus Valiunas: Means on groups and the degree of commutativity

Given a finite group G, one can count the proportion of pairs of elements in G that commute -- giving a number, denoted dc(G), behaviour of which has been studied since the 1960s.  To make sense of this for infinite groups G, one needs to define some sort of a nice measure or a mean on G.  In this talk, I will explain how such means -- more specifically, finitely additive probability means that give the "correct" answer for cosets of subgroups -- can be constructed.  As an application of these methods, one can define dc(G) for any group G, and show that dc(G) > 0 if and only if G is finite-by-abelian-by-finite.

This is joint work with Armando Martino.

Federica Bertolotti: Isoperimetric Inequalities in subgroups of direct products of free groups

In this talk, I will discuss how a subgroup H can be embedded into a direct product of groups when the factors belong to a fixed class, such as free groups. A key aspect is how the finiteness properties of H constrain its structure. Bridson, Howie, Miller, and Short showed that if the factors are free (or surface) groups and H is of type F)n, then H must be virtually a direct product. On the other hand, Kuckuck proved that if H is of type F_{n-1}, then it is virtually isomorphic to the kernel of a map F_m x ... x F_m -> Z^r. A well-known example of such groups is given by the Stallings-Bieri groups SB_n, defined as kernels of maps F_2 x ... x F_2 -> Z. I will focus on isoperimetric inequalities for groups arising as kernels of homomorphism F_m x ... x F_m -> Z^r. In particular, we will see that there is a uniform polynomial bound on their Dehn functions, answering a question posed by Dison. This is joint work with Ascari, Italiano, Llosa Isenrich, and Migliorini.

Inhyeok Choi: Metric WPD of pseudo-Anosov maps and quasimorphisms 

Recently, Bowden-Hensel-Webb introduced the notion of fine curve graph as an analogue of the classical curve graph. They used this to construct nontrivial quasi-morphisms (in fact, infinitely many independent ones) on Homeo_0(S). Their method crucially uses independent pseudo-Anosov conjugacy classes, whose existence follows from the WPD property of pseudo-Anosov mapping classes on the (classical) curve graph. In this talk, I will explain an analogue of the WPD property of pseudo-Anosov maps acting on the fine curve graph. If time allows, I will explain how this is related to constructing quasi-morphisms on Homeo_0(S). 

Francesco Fournier-Facio: The Boone-Higman Conjecture for Aut(F_n)

The Boone-Higman conjecture predicts that every finitely presented group with solvable word problem embedg s into a finitely presented simple group. I will survey what is (not) known about this conjecture, and the central role that is played by twisted Brin-Thompson groups. Then I will present a Boone-Higman embedding for Aut(F_n), which is joint work with Jim Belk, James Hyde and Matt Zaremsky. If time permits, I will touch on the higher finiteness properties of these simple groups, which is joint work with Peter Kropholler, Robbie Lyman and Matt Zaremsky.

Alice Kerr: Stable subgroups in graph products 

Stable subgroups of finitely generated groups were introduced by Durham and Taylor as a generalisation of quasiconvex subgroups of hyperbolic groups. They also nicely coincide with many other classes of subgroups: in the general case they are the hyperbolic Morse subgroups, in mapping class groups they are the convex cocompact subgroups, and in right-angled Artin groups they are the purely loxodromic subgroups. In this talk we will extend this to a characterisation of the stable subgroups of graph products with infinite vertex groups. This is joint work with Sahana Balasubramanya, Marissa Chesser, Johanna Mangahas, and Marie Trin. 

Monika Kudlinska: Conjugacy separability in unipotent suspensions

A group is conjugacy separable if the conjugacy class of every element is closed in the profinite topology. We prove that free-by-cyclic groups with unipotent and polynomially growing monodromy are conjugacy separable. Along the way, we show that double cosets of cyclic subgroups are separable and cyclic subgroups satisfy the Wilton--Zalesskii property. Our methods involve constructing vertex fillings and p-quotients. This is based on joint work with Francois Dahmani, Sam Hughes, and Nicholas Touikan. 

Corentin Le Bars: Boundary theory and affine buildings

I will survey some recent works about groups acting on (possibly exotic) affine buildings and show how Furstenberg's boundary theory and random walks can be used to derive structural properties (like Tits alternatives for such groups) as well as rigidity results.  

Marco Linton: Coherence of group pairs

A group is coherent if all its finitely generated subgroups are finitely presented. In 2023, Jaikin-Zapirain and I confirmed that one-relator groups are coherent by proving a criterion for coherence of groups of cohomological dimension two. In this talk I will explain how to generalise this criterion to group pairs of cohomological dimension two and show how it can be used to prove that one-relator products of coherent locally indicable groups (of arbitrary dimension) are coherent. This is joint work with Andrei Jaikin-Zapirain and Pablo Sánchez-Peralta.

Francesco Milizia: Minimal volume entropy of mapping tori of 3-manifolds 

The volume entropy of a Riemannian manifold is the exponential growth rate of metric balls in its universal cover; in particular, it is related to the growth rate of the fundamental group. By letting the metric vary, one obtains the "minimal volume entropy", which turns out to be not only an invariant of the smooth or topological structure, but a homotopy invariant. After an introduction about the minimal volume entropy, I will talk about its relation with other invariants and I will present a result which says that the minimal volume entropy of mapping tori over 3-manifolds is zero. This is joint work with Giuseppe Bargagnati, Alberto Casali and Marco Moraschini.