4th Meeting - Münster, 30th April 2026
Local organizers: Sam Shepherd and Robin J. Sroka.
Location and directions:
This meeting takes place at the Conference Centre of Cluster of Excellence "Mathematics Münster" at the University of Münster. All talks are scheduled in Seminar Room SRZ 216/217 on the second floor of the Seminarraumzentrum (SRZ), Orléans-Ring 12, 48149 Münster. For precise location and travel directions, please click HERE.
Registration:
No registration is needed to participate in this event.
Schedule:
13:00, Arrival
13:30-14:30, Thor Wittich (University of Osnabrück)
The Spherical Hopf Algebra
In spherical geometry, classical work of Sah shows that polytopes can be assembled into a commutative Hopf algebra, now called Sah algebra. In joint work with Klang, Kuijper, Malkiewich and Mehrle, we study this Hopf algebra from a homotopical point of view and show that the Hopf algebra structure also exists on the level of cohomology theories. We will hide most of the homotopy theory by rephrasing pretty much everything in terms of group cohomology, so do not worry about your homotopical background!
14:30-15:00, Conference Picture & Coffee Break
15:00-16:00, Stefanie Zbinden (University of Bonn)
Relating different notions of non-positive curvature
The study of non-positive curvature in groups is a major theme in geometric group theory, and there are now many competing definitions. In this talk, we take the perspective of studying the large-scale behaviours of geodesics, and compare the primary classes of groups that arise in this study, namely acylindrically hyperbolic and Morse local-to-global groups. We then show that Morse local-to-global groups are characterised by a compactness condition on its Morse boundary.
16:00-16:30, Coffee Break
16:30-17:30, Elia Fioravanti (Karlsruhe Institute of Technology)
Generators for automorphisms of special groups
Given a family F of finitely generated groups, do all groups in F have "tame" automorphisms, or can there be "wild" examples? More concretely, is Out(G) finitely generated for all groups G in the family F? Rips and Sela showed in the 90s that Out(G) is finitely generated for all Gromov-hyperbolic groups G, while Baues and Grunewald showed in the 00s that Out(G) is arithmetic over Q (and hence finitely generated) for all virtually polycyclic groups G. This essentially exhausts our limited understanding of general phenomena of this kind, with the structure of automorphisms of non-positively curved groups remaining a fundamental open problem. I will discuss the recent result that Out(G) is finitely generated for all (cocompact) special groups of Haglund and Wise. This is already new for most finite-index subgroups of right-angled Artin and Coxeter groups.
17:30, Discussion and Dinner
3rd Meeting - Bonn, 31st October 2025
Local organisers: Sam Hughes and Lawk Mineh.
Registration
No registration is needed to participate in this event.
Location
The event will happen in the "Lipschitz-Saal". This is in the Mathematical Institute, Endenicher Allee 60. This is a 10-to-15 minute walk from the Hauptbahnhof, or a five minute bus ride (604, 605, 606, 607) and a one minute walk.
Schedule
13:00: Arrival
13:30: Laura Ciobanu
On equations in free-by-cyclic groups
For a group or semigroup or ring G, solving equations where the coefficients are elements in G and the solutions take values in G can be seen as akin to solving systems of linear equations in linear algebra, Diophantine equations in number theory, or more generally, polynomial systems in algebraic geometry.
In this talk I will present some work in progress (with Bob Gray and Alex Levine) on the decidability of solving equations in free-by-cyclic groups, with or without constraints.
14:30: Break
15:00: Anthony Genevois
Towards a stringy geometry
After a general introduction to coarse geometry and lamplighter graphs, I will explain how a coarsification of the topological notion of local cut point can be used in order distinguish, up to quasi-isometry, some wreath products of groups (and more generally some lamplighter graphs).
16:00: Break
16:30: Amandine Escalier
Quantitative measure equivalence and graph products
Measure equivalence was introduced by Gromov in the 90’s. Although presented as a measure theoretical analogue of quasi-isometry, measure equivalence sometimes crushes two groups with very different geometries to a same equivalence class. A quantitative version of measure equivalence was thus introduced: it aims at specifying how close the two equivalent actions are.
In this talk we will focus on the behaviour of graph products under quantitative measure equivalence. Through this study, we will highlight the links between the latter notion and geometric properties. This is joint work with Camille Horbez.
17:30: Dinner and discussion
2nd Meeting - Münster, 25th April 2025
Local organizers: Sam Shepherd and Robin J. Sroka.
Location and directions:
This meeting takes place at the Conference Centre of Cluster of Excellence "Mathematics Münster" at the University of Münster. All talks are scheduled in Seminar Room SRZ 216/217 on the second floor of the Seminarraumzentrum (SRZ), Orléans-Ring 12, 48149 Münster. For precise location and travel directions, please click HERE.
Registration:
No registration is needed to participate in this event.
Schedule:
13:00-14:00, Kevin Li (University of Regensburg)
A combination theorem for homological properties of groups
I will present an axiomatic combination theorem that applies to several properties of groups, such as: finiteness properties, vanishing of $\ell^2$-Betti numbers, vanishing of $\mathbb{F}_p$-homology growth, and the algebraic cheap rebuilding property. The latter implies vanishing of torsion homology growth and is satisfied by elementary amenable groups. Joint with Clara Löh, Marco Moraschini, Roman Sauer, and Matthias Uschold.
14:00-15:00, Tobias Hartnick (Karlsruhe Institute of Technology)
Approaches to Patterson-Sullivan measures for RAAGs
We discuss four different constructions which all yield the unique conformal density of probability measures on the boundary of a free group: The Patterson-Sullivan construction, spherical measures, Gibbs measures and Hausdorff measures. We then discuss how these constructions generalize to more general classes of groups with good normal forms, in particular to right-angled Artin groups (RAAGs). The emphasis will be on the interactions between methods from geometric group theory, symbolic dynamics, automata theory and ergodic theory. The results concerning RAAGs are joint work with Carl Zürcher, based on previous unpublished joint work with Amos Nevo and Michah Sageev.
15:00-15:30, Conference Picture & Coffee Break
15:30-16:30, Lawk Mineh (University of Bonn)
Separability of products in groups
Determining the closed subsets of groups with respect to the profinite topology has become an common theme in geometric group theory. Most often, subgroups are the main focus of such a study, but more complex subsets are also important to consider. We give an overview of what is known about the separability of products of subgroups, their applications, and discuss how this property behaves with respect to group extensions.
16:30-17:30, Ilaria Castellano (Heinrich-Heine University Düsseldorf)
Totally disconnected locally compact groups, accessibility and Euler-Poincaré characteristic
In the first part of the talk I will illustrate how the classical notion of accessibility for finitely generated groups carries over to the realm of compactly generated totally disconnected locally compact (= t.d.l.c.) groups. Then, by means of a new notion of Euler-Poincaré characteristic, I will discuss an accessibility result in the t.d.l.c. framework, under the assumption of rational discrete cohomological dimension = 1.
17:30-open end, Dinner
1st Meeting - Bonn, 17th January 2025
Local organisers: Sam Hughes and Lawk Mineh
The event will happen in the "Zeichensaal". This is in the Natural Sciences building on Wegelerstraße 10. This is approximately a twelve minute walk from the Hauptbahnhof, or a five minute bus ride (604, 605, 606, 607) and a two minute walk.
14:00 - 14:55
Stefan Witzel (Justus-Liebig-Universität Gießen)
Finiteness properties of locally compact groups
A discrete group G is of type F_n if there exists a universal free G-CW-complex with cocompact n-skeleton. While a non-discrete group does not admit a universal free G-CW complex, various extensions of the properties F_n to non-discrete groups have been proposed. I will discuss some of these properties, related problems, and give some examples.
15:00 - 15:55
Ursula Hamenstädt (Rheinische Friedrich-Wilhelms-Universität Bonn)
A Z-structure for the mapping class group
A Z-set for a finitely generated group is the boundary of a compactification of the group which allows to study the group cohomology, however it is defined in purely point-set topological terms. We show that the mapping class group of a surface of finite type admits a Z-set.
15:55 - 16:30
Break
16:30 - 17:30
Claudio Llosa Isenrich (Karlsruher Institut für Technologie)
The Boone--Higman Conjecture for groups acting on locally finite trees
Motivated by embedding results, such as the Higman Embedding Theorem, in 1974 Boone and Higman conjectured that a finitely generated group has solvable word problem if and only if it embeds in a finitely presented simple group. This is now known as the Boone--Higman Conjecture. While it has recently been confirmed for many interesting classes of groups, including hyperbolic and virtually special groups, it remains wide open in general. In this talk I will present a new method for proving the Boone--Higman Conjecture for groups acting on locally finite trees. As a consequence, we can verify the Boone--Higman Conjecture for many new classes of groups, including all (finitely generated free)-by-cyclic groups and all Baumslag--Solitar groups, solving it in two cases that have been raised explicitly by Belk, Bleak, Matucci and Zaremsky. This is joint work with Kai-Uwe Bux and Xiaolei Wu.
17:30 - late
Discussion session over dinner