Model Theory Meets Geometric Group Theory
Model Theory meets GGT is a week-long conference aimed at bringing together young researchers in the areas of Model Theory and Geometric Group Theory. These two areas exhibit a rich interplay, and the mini-courses and research talks will be aimed to display topics in this intersection. Furthermore, there will be a lightning talks session in which all participants are encouraged to give a brief introduction to their own research and interests, so as to foster even more interaction between the participants.
Speakers
Mini courses:
Research Talks:
Crash Course on Model Theory:
Titles and Abstracts
Mini Courses:
Simon André: On the Tarski problem for free and hyperbolic groups
In the 1940s, Tarski posed the following question, known as the Tarski problem: are non-abelian free groups elementarily equivalent? This problem remained open for a long time and was finally solved by Sela using tools from geometric group theory (see also the work of Kharlampovich and Myasnikov). Then, Sela generalized his work to torsion-free hyperbolic groups (in the sense of Gromov) and gave a classification of the finitely generated groups that have the same elementary theory as a given torsion-free hyperbolic group. In this minicourse, I will discuss this classification and present partial generalizations to hyperbolic groups possibly with torsion, and to larger classes of groups (such as acylindrically hyperbolic groups).
Montse Casals: On the model theory of right-angled Artin groups
In this minicourse, we will discuss the problem of classification of groups up to universal and elementary equivalence. In the first lecture, we will review two classical examples, namely abelian and nilpotent groups; in the second one, we will characterise models of the universal theory from algebraic and geometric points of view. In the last lecture, we will center on the classification of right-angled Artin groups up to their universal and elementary theories.
Thomas Koberda: Studying surfaces with model theory
Mapping class groups of surfaces are central objects of study in geometric group theory. Curve graphs of surfaces are crucial combinatorial and geometric tools for investigating mapping class groups. In my minicourse, I will discuss how ideas from model theory can be used to study curve graphs, and approach the Ivanov Metaconjecture, which says that the automorphism group of any "natural" complex associated to a surface should be precisely the extended mapping class group of the surface. I will also discuss applications of model theory to the problem of classifying virtual injections between mapping class groups.
Research Talks:
Laura Ciobanu: Group equations, constraints and interpretability
In this talk I will discuss group equations with non-rational constraints, a topic inspired by the long line of work on word equations with length constraints. I will present work with Alex Evetts and Alex Levine establishing the decidability of equations with length, abelian or context-free constraints in virtually abelian groups. This contrasts the fact that solving equations with abelian constraints is undecidable for (non-abelian) right-angled Artin groups and hyperbolic groups with ‘large’ abelianisation (joint work with Albert Garreta), where interpretability can be used to encode arithmetic.
Jonathan Fruchter: Homological Torsion and Word Maps on Free Groups
In 2010, Perin and Sklinos proved that nonabelian free groups are homogeneous: elements that are indistinguishable from a first-order perspective lie in the same automorphic orbit. A long-standing, similar-spirited question, posed independently by Gelander, Lubotzky, and Shalev, asks whether two elements of a nonabelian free group that induce the same probability measure on every finite group (roughly speaking, behave identically in every finite quotient) must be related by an automorphism. This question remains very open, with only a few specific cases shown to be true.
In this talk, I will present a positive answer to this question for a new family of elements. The proof relies on showing that, similar to the case of hyperbolic 3-manifold groups, every graph of free groups amalgamated along cyclic subgroups contains prescribed torsion in the abelianization of some finite-index subgroup, unless it is a free product of free and surface groups (joint work with Dario Ascari).
Radhika Gupta: Conformal dimension of Bowditch boundary of certain Coxeter groups
Quasi-isometry (QI) classification of finitely generated groups is an important problem in geometric group theory. When two Gromov hyperbolic groups are quasi-isometric, then they have homeomorphic visual boundaries. But the converse is not true. One tool to distinguish two hyperbolic groups with the same visual boundary is to show that the conformal dimension, which is an analytic QI invariant, of the two boundaries are different. In this talk, we consider a particular family of Coxeter groups that are hyperbolic relative to free abelian subgroups (CAT(0) with isolated flats). We give the first computation of bounds for the conformal dimension of the Bowditch boundary of a non-hyperbolic group. As a corollary, we show that there are infinitely many QI classes of groups in this family of Coxeter groups (which all have the same visual boundary by the work of Haulmark-Hruska-Sathaye). In the process, we also construct a CAT(-1) geometry for non-hyperbolic Coxeter groups in our family. This is joint work with Elizabeth Field, Robbie Lyman and Emily Stark.
Alice Kerr: Short loxodromics in graph products
Let G be a finitely generated group, with finite generating set S. Suppose G contains elements with some property that we’re interested in. Can we find an element with this property uniformly quickly in G? That is, with S as our alphabet, can we find a word of bounded length with this property, where the bound does not depend on S? We will discuss this question for graph products, where the elements we are looking for are ones with nice hyperbolic properties, such as loxodromic and Morse elements. We will also talk about consequences for the growth of these groups. This is joint work with Elia Fioravanti.
Jone Lopez De Gamiz Zearra: On subgroups of right-angled Artin groups
In this talk we will discuss subgroups of right-angled Artin groups (RAAGs for short). Although, in general, subgroups of RAAGs are known to have a wild structure, difficult finiteness properties and bad algorithmic behaviour, we will show that under certain conditions they have a tame structure. Firstly, we will discuss finitely generated normal subgroups of RAAGs and show that they are co-(virtually abelian). Secondly, we will recall results of Baumslag-Roseblade and Bridson-Howie-Miller-Short on subgroups of direct products of free groups and explain how they generalize to other classes of RAAGs.
Chloé Perin: Forking in the free group
Using the tools he developed for solving the Tarski problem, Sela was able to show that the first order theory of free groups is stable. This model theoretic notion indicates that the geometry induced by definable sets on these groups is well behaved. In particular, stability of the free group implies the existence of a nice forking independence relation, which coincides for example with algebraic independence when it is an algebraically closed field. In a joint work with Rizos Sklinos, we gave an algebraic and geometric interpretation of forking independence in the free group using Grushko and JSJ decompositions.
Organisers
Marco Amelio
Benjamin Brück
Zahra Mohammadi
Schedule
tba
Registration
Registration is open! Please register via this link.
The registration deadline is December 31, 2024.
If you require an invitation letter to support your visa application for attending the event, please email us at modeltheory.meets.ggt@gmail.com.
Financial support
There is limited funding for accommodation available that you can apply for when you register. The deadline to apply for accommodation funding is 30 November 2024.
You can also apply for the ASL Student Travel Awards to help cover your travel expenses. To apply for these travel awards, you must be (or become) an ASL member and submit your application at least three months in advance. For more details, please visit ASL Student Travel Awards .
Support and child care
Childcare is available free of charge for all conference participants.
Venue and Travel Information
The event takes place in room SRZ 216/217 on the second floor of the seminar building (Seminarraumzentrum, SRZ) next to the Faculty of Mathematics and Computer Science and the Cluster of Excellence Mathematics Münster.
University of Münster
Seminar Room Center (SRZ)
Orléans-Ring 12
48149 Münster
Germany
Directions can be found on openstreetmap , on the University of Münster campus map , and on the MM websites .
We have also collected practical information in a leaflet: Information for conference guests / Informationsblatt für Tagungsteilnehmer:innen [enIde]
Poster
You are welcome to download the poster and display it at your institution.
Sponsors
The conference is jointly supported by the Cluster of Excellence Mathematics Münster and the Collaborative Research Center 1442 Geometry: Deformations and Rigidity .
This event is also sponsored by the Association for Symbolic Logic (ASL) .
Contact
Please direct any inquiries to modeltheory.meets.ggt@gmail.com.