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 Dr. Sathaye
Talks:
 24.10.2022 Jeffrey Carlson (Imperial College London) Equivariant formality of isotropy actions and products of spheres
 31.10.2022 Konstantin Andritsch (ETH Zürich) Bounded Cohomology and Bounded Acyclicity of groups acting on Cantor sets
 14.11.2022 José Pedro Quintanilha (University of Bielefeld) An introduction to Sigmainvariants
 5.12.2022 François Thilmany (UC Louvain) Using hyperbolic Coxeter groups to construct highly regular expander graphs
 12.12.2022 Mireille Soergel (ETH Zürich) A generalized DavisMoussong complex for Dyer groups
Abstract: For beststudied class of homogeneous spaces G/H with G > H compact, connected Lie groups, those for which rank(G) = rank(H), it is well known that the standard left ("isotropy") action of H on G/H is equivariantly formal, meaning every rational cohomology class on G/H lifts to a class in Borel Hequivariant cohomology.
Moving to the case rank(G)  rank(H) = 1, we give a characterization of pairs (G,H) such that the isotropy action is equivariantly formal, via a sequence of reductions ending with pairs such that G/H has the rational homotopy type of a product of spheres. The irreducible such pairs are for the most part already classified in works of Kramer, Wolfrom, and BletzSiebert, which require only mild extension to handle the cases we asre interested in and then reduce the entire problem to a verification of finitely many cases. This work is joint with Chen He.
Abstract: Bounded Cohomology is a functionalanalytic analogue of ordinary cohomology. There are various applications in different fields from rigidity theory, actions on the circle up to the geometry of manifolds. However, although bounded cohomology can be very useful, the problem lies in calculating it since it is in general very hard to compute.
I will talk about recent developments in calculating bounded cohomology of discrete groups. In particular, I am going to elaborate on the bounded acyclicity, meaning the vanishing of bounded cohomology with real coefficients in nontrivial degree, of the full homeomorphism group of the Cantor set and Thompson's group V.
Abstract: The features of a group being finitely generated or finitely presented are wellknown to be, respectively, the n=1 and n=2 cases of the property F_{n}: a group G is said to be of type F_{n} if it admits a K(G,1) with finite nskeleton. Towards the end of the last century, the question of when such finiteness conditions descend to subgroups of G led to the discovery of the homotopical Sigmainvariants Σ^{n}(G) and their homological counterparts Σ^{n}(G;A) (for A a ZGmodule). Intuitively, Σ^{n}(G) can be thought of as the set of group homomorphims χ : G → R for which G is "of type F_{n} in the direction of χ", with the classical property F_{n} being equivalent to 0 ∈ Σ^{n}(G).
In my talk I will give an introduction to the theory of Sigmainvariants, with particular focus on Σ^{1}, mentioning some of their applications in group theory and topology. If time permits I will also say a few words on the more recent efforts to extend these notions to locally compact groups.
Abstract: A graph X is defined inductively to be (a_{0}, . . . , a_{n−1})regular if X is a_{0}regular and for every vertex v of X, the sphere of radius 1 around v is an (a_{1}, . . . , a_{n−1})regular graph. A family F of graphs is said to be an expander family if there is a uniform lower bound on the Cheeger constant of all the graphs in F.
After briefly (re)introducing Coxeter groups and their geometries, we will describe how they can be used to construct very regular polytopes, which in turn can yield highly regular graphs. We will then use the superapproximation machinery, whenever the Coxeter group is hyperbolic, to obtain the expansion of these family of graphs. As a result, we will obtain interesting infinite families of highly regular expander graphs, some of which are related to the exceptional groups. The talk is based on work joint with Conder, Lubotzky and Schillewaert.
Abstract: One common feature of Coxeter groups and rightangled Artin groups is their solution to the word problem. I will introduce Dyer groups, as a class of groups sharing this feature. Which other properties do Dyer groups share with Coxeter groups and rightangled Artin groups? I will give a first answer to this question. Finally I hope to explain how to construct actions of Dyer groups on CAT(0) spaces that extend those of Coxeter groups on Davis–Moussong complexes and those of rightangled Artin groups on Salvetti complexes.