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 217/218 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 The results concerning RAAGs are joint work with Carl Zürcher, based on previous unpublished joint work with Amos Nevo and Michah Sageev.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