TBA

• Giovanni Italiano (University of Oxford)

Room: Aula Dini

Small cancellation theories and what they are good for

• Macarena Arenas (ICMAT)

Room: Aula Dini

Arithmetic locally symmetric spaces and geodesic immersions

• Leone Slavich (Università di Genova)

Room: Aula Dini We address the problem of classifying commensurability classes of totally geodesic immersion between finite volume, arithmetic, locally symmetric spaces and show how these correspond to morphism between algebraic groups defined over the rationals. We'll also show how the relation between the arithmetic invariants of the spaces encodes information about the geometric properties of the immersion, and construct a few interesting examples. If time allows, we will discuss how these results could hopefully be applied to the construction of non-arithmetic complex hyperbolic manifolds. Joint work with M. Belolipetski, K. Bogachev and A. Kolpakov

Finiteness properties of automorphism groups

• Naomi Andrew (Laboratoire de Mathématiques d’Orsay)

Room: Aula Dini Groups encode symmetries, and their automorphism groups encode the symmetries of the group themselves. So we can ask when "nice" properties of a group imply "nice" properties of its automorphisms. On the positive side, mapping class groups, GL(n,Z) and Out(F_n) are all finitely presented (in fact a stronger property: Type VF), and this can be analysed geometrically, using spaces built from actions of the original group. On the other hand, the Baumslag–Solitar group BS(2,4) is finitely presented, yet its outer automorphism group is not even finitely generated (and there is also a geometric explanation for this). I will discuss some new results in this area.

TBA

• Alice Merz (HUN-REN Rényi Alfréd Matematikai Kutatóintézet)

Room: Aula Dini

Small cancellation theories and what they are good for (part II)

• Macarena Arenas (ICMAT)

Room: Aula Dini

TBA (part II)

• Giovanni Italiano (University of Oxford)

Room: Aula Dini

TBA (part III)

• Giovanni Italiano (University of Oxford)

Room: Aula Dini

Small cancellation theories and what they are good for (part III)

• Macarena Arenas (ICMAT)

Room: Aula Dini

Almost planar finitely presented groups

• Joseph MacManus (University of Bristol)

Room: Aula Dini Following Benjamini-Schramm, a graph is called 'almost planar' if it can be drawn in the plane such that every edge crosses at most a bounded number of edges, and a finitely generated group is called an 'almost planar group' if its Cayley graphs are almost planar graphs. Despite being a relatively well-studied class, the only known examples of such groups are those which virtually admit a planar Cayley graph. Recently, it was conjectured by Georgakopoulos-Papasoglu that these are indeed the only examples, suggesting a robust rigidity result. In this talk, I will contextualise and report progress on this conjecture, settling it within the class of finitely presented groups. This talk is based on joint work with John Mackay and Davide Spriano.

Bounded cohomology, the Hausdorff property, and ultraproducts

• Alexis Marchand (Instytut Matematyczny Polskiej Akademii Nauk)

Room: Aula Dini (Joint work with Piotr Nowak.) Bounded cohomology is a functional-analytic variant of group cohomology. Despite its many connections with geometry and topology, it can be a mysterious object. This talk will be about the property of bounded cohomology being Hausdorff. We will explain how this property can be read in asymptotic cohomology, yet another cohomology theory that was introduced recently to study stability properties of groups. This makes use of ultraproduct techniques invented by Bader and Sauer in the context of property (T), and that we will explain.

Contact Surgery Numbers and Contact Surgery Distance

• Monika Monika (Uniwersytet Warszawski)

Room: Aula Dini A celebrated theorem of Ding and Geiges states that every connected, oriented, closed 3-manifold equipped with a cooriented contact structure can be obtained by contact surgery along a Legendrian link in the standard tight contact 3-sphere. This naturally leads to complexity measures for contact 3-manifolds: the contact surgery number and the contact surgery distance. The contact surgery distance between two contact 3-manifolds is the minimum number of contact surgeries required to pass from one to the other, while the contact surgery number of a contact 3-manifold is precisely its distance from the standard tight contact 3-sphere. In this talk, I will discuss joint work in which we compute contact surgery numbers for contact structures on the real projective 3-space and the 3-torus. If time permits, I will also discuss bounds on the contact surgery distance in terms of the corresponding smooth surgery distance.

Simultaneous Conjugacy In Thompson's Group V

• Luna Elliott (University of Manchester)

Room: Aula Dini Thompson’s group $ V $ was the first known finitely presented infinite simple group. The ordinary conjugacy problem in $ V $ was first solved by Higman and later given a uniform combinatorial treatment, via reduced closed abstract strand diagrams, by Belk–Matucci. The simultaneous (or $ k $-simultaneous) conjugacy problem asks whether, given two $ k $-tuples $ (g_1,\dots,g_k) $ and $ (h_1,\dots,h_k) $ of elements of a group $ G $, there exists a single conjugator $ c\in G $ such that $ c^{-1}g_ic=h_i $ for every $ i $. This problem had remained open for $ V $. In this talk we solve the simultaneous conjugacy problem in $ V $. We exhibit a decision procedure that, given any two $ k $-tuples, determines whether a common conjugator exists and, when one does, produces such an element. The method extends previously existing algorithms and uses the results of Bleak-Bowman-Gordon-Graham-Hughes-Matucci-Sapir on centralisers together with a careful analysis of the possible ways their dynamical data can be simultaneously matched under a single conjugating transformation. Joint work with Gemma Crowe.

Linear volume bounds for drilling and filling

• Gabriele Viaggi (Università di Pisa)

Room: Aula Dini There are two important operations that one can perform on a finite volume hyperbolic 3-manifold. One can drill out a simple closed geodesic and one can Dehn fill a cusp. It is a well-known phenomenon that all drillings and most fillings give back a hyperbolizable 3-manifold whose volume is larger for the first operation and smaller for the second. How can we bound the volume change in terms of the relevant geometric parameters (such as the lengths of the geodesic or of the filling slope)? After reviewing the global picture and the known results, I will describe some new (completely local) linear bounds.

Complete classification of the Dehn functions of Bestvina–Brady groups

• Jeronimo Garcia Mejia (University of Warwick)

Room: Aula Dini Introduced by Bestvina and Brady in 1997, Bestvina–Brady groups form an important class of examples in geometric group theory and topology, known for having unusual finiteness properties. In this talk, I will focus on the Dehn functions of finitely presented Bestvina–Brady groups. The Dehn function of a group is a fundamental quasi-isometry invariant that, very roughly speaking, measures how difficult it is to fill loops by discs in spaces associated to the group. After reviewing known results, I will present a classification of the Dehn functions of Bestvina–Brady groups. This talk is based on joint work with Yu-Chan Chang and Matteo Migliorini.