Tea Seminar of our groupPlace and time:

Inhalt:
In this seminar, guests and members of our group present their research, or topics of interest to us. Presently we use a hybrid format for the seminar (inperson and zoom). In case you are interested, please contact Linus Kramer.
Talks:
 22.04.2024 Ilaria Castellano (Bielefeld) Invariants of t.d.l.c. groups acting on locally finite buildings
 29.04.2024 Hendrik Van Maldeghem (Gent) Generalised dualities and Segre varieties.
 06.05.2024 Anna Cascioli (Regensburg) Profinite rigidity and amenability
 27.05.2024 Linde Lambrecht (Gent) Exploring spherical buildings of type F_{4} as pointline geometries
 03.06.2024 (SR0) Rebecca Waldecker (Halle) Two perspectives on finite simple groups
 24.06.2024 Kevin Klinge (Karlsruhe) ΣInvariants and nilpotent groups
 08.07.2024 Đorđe Mitrović (Auckland) Graph Growth of Permutation Groups
Abstract: Given a totally disconnected locally compact group G that has a sufficiently transitive action on a locally finite building Δ, we aim to investigate some invariants of G and uncover the relation to the analogue invariants of the type W of Δ. In particular, we will talk about the rational discrete cohomological dimension and the number of ends of G. Work in progress with Bianca Marchionna and Thomas Weigel, Università di Milano Bicocca.
Abstract: Jacques Tits generalised the notion of a "polarity" in order to describe all embeddable polar spaces. We further extend it to the notion of "generalised duality". We use it to classify and describe all geometric hyperplanes of a Segre geometry, which is the direct product of two arbitrary projective spaces. This result, in turn, can be applied to Segre varieties over arbitrary fields and we obtain an explicit list of all geometric hyperplanes that are not induced by a projective hyperplane. Among them are socalled black hyperplanes, which are embedded long root geometries of type A, and we will mention some special features about those.
Abstract: Given a finitely generated, residually finite group G, we ask which properties can be detected from the set of its finite quotients, encoded in its profinite completion. After investigating recent advances in the context of profinite rigidity, we will focus on the interplay between profinite completions and the notion of amenability. We will see, following a construction by S. Kionke and E. Schesler, that amenability is not a profinite invariant by using tools related to automorphisms of rooted trees.
Abstract: In this talk we dive into the world of pointline geometries related to spherical buildings of type F_{4}. These turn out to be parapolar spaces of rank 3 with some extra properties. They differ from the other exceptional spherical buildings by the fact that they are not determined by only a field, but one also needs a quadratic alternative division algebra over this field. This makes them a bit harder to tackle and therefore they are omitted by several authors. After a short introduction, we will discuss some analogs of recent results about other exceptional spherical buildings. In particular, we will discuss subgeometries, domestic collineations and kangaroos.
Abstract: We talk about the Classification of Finite Simple Groups from (at least) two perspectives: Where does it come from? How is it applied? What is special about this big result, both in terms of its origin and proof and in terms of what we can learn about how mathematical work changed during that time?
Abstract: The classical Σinvariant can be used to determine finiteness properties of kernels of maps onto abelian groups. I will present an analogue invariant that allows us to consider maps onto nilpotent groups instead. A main tool will be partial orders on groups and a possible application is to characterise groups that fibre algebraically. This is based on my doctoral thesis and on ongoing joint work with Sam Fisher.
Abstract: Let X be a finite connected graph and let G be a vertextransitive group of automorphisms of X. The pair (X, G) is locallyL if the group induced by the action of the stabiliser Gv on the neighbourhood of a vertex v is permutation isomorphic to L. Using this language, a classical theorem of Tutte states that for locallyA3 and locallyS3 pairs, G grows linearly with V(X). More generally, given a transitive permutation group L, we are interested in determining the growth of G as a function of V(X) for locallyL pairs (X,G). We present new results on this topic and highlight an exciting connection with the study of eigenspaces of graphs over finite fields.