Daniel
Turaev
Berlin
Visibly Pushdown Languages in Groups
Group Theory and Friends  📅
Institute
Head
Laura Ciobanu
Organizer
Laura Ciobanu
Description
This seminar is organized by the Applied Algebra Group at TU Berlin. It covers topics in group theory and related areas.
Usual time
roughly every second week (day/time vary by talk)
Usual venue
NOT_SET
Number of talks
16
Comment
Irregular scheduling: the seminar meets roughly every second week, with day of week and start time varying by talk and semester. The location also varies by talk; many meetings are in MA 366, but MA 650 and ER 164 also appear. Occasionally other on-campus rooms (e.g., MA 001, EN 058) and off-site events (e.g., at the University of Potsdam) appear on the page. The page may list related external events (e.g., EGGG, MATH+ colloquium, Diskrete Mathematik/Geometrie Seminar); these are not series defaults.
June 2026
May 2026
Susan
Hermiller
University of Nebraska
Subgroups of the group of dyadic piecewise linear homeomorphisms of the real line
Abstract.
The group of dyadic orientation-preserving piecewise linear (PL) homeomorphisms of the unit interval is called Thompson's group F, and the question of which groups are - or cannot be - subgroups of F has yielded many interesting results. In this talk I'll discuss the question of what groups can or cannot be subgroups of Aut(F) (the automorphism group of F), and more particularly subgroups of an index 2 subgroup of Aut(F) that is isomorphic to a group of dyadic PL homeomorphisms of the real line. This is joint work with Conchita Martinez-Perez.
Islam
Foniqi
Berlin
The submonoid and rational subset membership problems for Artin groups
Abstract.
We demonstrate that the submonoid membership problem and the rational subset membership problem are equivalent in Artin groups. Both problems are undecidable in a given Artin group if and only if the group embeds the right-angled Artin groups of rank 4 over a path or a square; and this can be characterized using only the defining graph of the Artin group. These results generalize those of Lohrey and Steinberg for right-angled Artin groups. Moreover, both decision problems are decidable for a given Artin group if and only if the group is subgroup separable.
Marius
Streiff
Heidelberg
Conjugation in T-RAAGs and graph products of groups
Abstract.
Twisted right-angled Artin groups (T-RAAGs) and graph products of groups are two natural generalizations of right-angled Artin groups (RAAGs). The question arises, which nice geometric and algorithmic properties of right-angled Artin groups still hold for T-RAAGs and graph products of groups. In this talk, I will present a geometric solution to the conjugacy problem in T-RAAGs and use it to compute the conjugator length function of T-RAAGs. If time permits, I will also give an outlook on the question how centralizers can be described in both graph products of groups and T-RAAGs using the quasi-median and median structure of their Cayley graphs.
April 2026
Simon
Andre
Paris
On the Tarski problem for hyperbolic groups in the presence of torsion
Abstract.
Following his resolution of a famous problem of Tarski concerning elementary equivalence of non-abelian free groups, Sela gave a complete classification of torsion-free hyperbolic groups up to elementary equivalence. I will recall the necessary definitions, outline Sela's classification and explain some of the new difficulties encountered when elements of finite order are allowed, in particular the existence of pathological morphisms from surface groups to hyperbolic groups with torsion.
Corentin
Bodart
Oxford
Subgroup membership and formal languages
Abstract.
The intersection of Geometric Group Theory and Formal Language Theory has been fruitful in the last 50 years. I'll start by recalling some of the key results in the area, such as the Muller-Schupp theorem on groups with context-free Word Problem and Lehnert's conjecture on groups with co-context-free Word Problem. In joint work with André Carvalho and Carl-Fredrik Nyberg-Brodda, we have been looking at similar languages related to another decision problem in groups: Subgroup Membership. I'll explain the toolbox we have been developing, apply it to examples and non-examples, and highlight some open problems along the way.
January 2026
Jan Moritz
Petschick
Uni Bielefeld
Maximal subgroups in branch groups
Abstract.
Branch groups are groups whose subgroup structure resembles a rooted tree. Among many other intriguing properties, they contain examples of groups with unusual restrictions on their maximal subgroups. In this talk, I will provide an account of what is known about maximal subgroups of branch groups and present some recent results.
Matthew
Konefal
Loughborough, UK
Definability in Theories Based on Free Group and Free Monoid Equations
Abstract.
Equations in the free group and free monoid have long been studied together. I’ll outline their history and properties, comparing facets of their two theories. Each can be studied by adapting techniques developed for the other. After demonstrating this, we’ll focus on definability in theories whose atoms are free group equations. Tools for establishing nondefinability in this setting are due to group theorists and model theorists, yet have the appearance of word-combinatorial lemmas. The tools - combined - yield characterisations of definability, the free monoid analogues of which seem more elusive. I'll end discussing length abstractions and length constraints, which link equations to weak arithmetics. Naturally, more definability questions result, including major open problems.
December 2025
Leon
Pernak
Uni Saarland
Quadratic equations in wreath products of abelian groups
Abstract.
One of the strongest results that one can hope for when studying decidability questions in groups is the decidability of equations - is there an algorithm that, if we feed it a group equation, tells us if the equation has or does not have a solution in a given group? I will discuss this problem in the setting of wreath products of abelian groups. In particular, I will explain how to prove that the problem is decidable for quadratic equations, using techniques and intuitions inspired by commutative algebra. This is joint work with Ruiwen Dong and Jan-Philipp Wächter.
November 2025
Kevin
Li
FU Berlin
On higher coherence of RAAGs
Abstract.
A group is called coherent if every finitely generated subgroup is finitely presented. It is a classical result of Droms that a RAAG is coherent if and only if the defining graph is chordal. I will explain its proof and our attempt to generalise it to higher coherence. Ongoing joint work with Luis Jorge Sánchez Saldaña.
October 2025
Mireille
Soergel
TUB
Dual Artin groups
Abstract.
In 1998 when considering a new approach to the word and conjugacy problem in Braid groups, Birman-Ko-Lee introduce a new presentation for the braid group. This is now referred to as the dual presentation. Such dual presentations can be defined for all Artin groups. I will introduce standard and dual Artin groups and talk about some open conjectures.
Tamara
Imanuel
Das Konjugationsproblem in RAAGs: Theorie und Algorithmus
Sobhi
Massalha
TUB
Sentences over Random Groups
Abstract.
Around 2013, a natural conjecture by Julia Knight anticipated that given a first order sentence, its truth value over a random group in the few relators model, is equivalent to its truth value over non-abelian free groups. Our work extends the framework of this conjecture to random groups in the Gromov Density Model, at optimal density d<1/2. We prove the conjecture for sentences that belong to the Boolean algebra of universal sentences, as well as for sentences of minimal rank with arbitrary number of quantifiers, for random groups of density d<1/2. In this talk, we will present our results and, as time permits, outline the key strategies and ideas involved in the proofs.
Alex
Levine
University of East Anglia
The Diophantine problem in Thompson's group F
Abstract.
We discuss equations in groups, and when there exists an algorithm that can decide if a given system of equations admits a solution. We mention some recent work on Thompson's groups F and T. Based on joint work with Luna Elliott.
Nico
Waldau
TU Berlin
Tits-Alternative für hyperbolische Gruppen
January 2025
Jan Moritz
Petschick
Uni Bielefeld