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:
 April 25, 2022 Maria Gerasimova (Münster) The firefighter problem on infinite groups and graphs
 May 9, 2022 Gil Goffer (Weizmann Institute of Science) Is invariable generation hereditary?
 May 23, 2022 Raphael Appenzeller (ETH Zürich) Axiomatics of Λtrees
 May 30, 2022 Lara Beßmann (Münster) Is the rightangled building associated to a universal group unique?
 June 27, 2022 Alice Kerr (Oxford) Product set growth in mapping class groups
Abstract: We will discuss the Firefighter model, that is a deterministic, discretetime model of the spread of a fire on the vertices of a graph. In the Firefighter model, a fire erupts on some finite set X and in every time step all vertices adjacent to the fire catch fire as well (burning vertices continue to burn indefinitely) . At turn n we are allowed to protect f(n) vertices so that they never catch fire. We will discuss two different questions in this setting the firecontainment problem and the fireretainment problem. The classical firefighter problem, also known as the firecontainment problem, asks how large should f(n) be so that we will eventually contain any initial fire. The fireretainment problem asks how large should f(n) be for saving only a “sufficient” portion of the graph. We will be mainly interested in the asymptotic behaviour of f in relation with the geometry of the graph, focusing on Cayley graphs. The growth rates of these functions are nice quasiisometric invariants of groups. We will discuss the results about these invariants for different classes of groups. This is a joint work with G. Amir, R. Baldasso and G.Kozma.
Abstract: We will discuss the notion of invariably generated groups, with various motivating examples. We will then see how hyperbolic groups and small cancellation theory are used in answering the question in the title, which was asked by Wiegold and by KantorLubotzkyShalev. This is a joint work with Nir Lazarovich.
Abstract: Trees from graph theory and real trees both satisfy some notions of being connected and having no cycles. These notions can be brought under the common axiomatic framework of Λtrees, where the ordered abelian group Λ is Z for discrete and R for real trees. We will introduce and discuss the axioms and their independence. We will then give a construction of a Λtree which parallels the construction of the hyperbolic plane.
Abstract: A universal group is a subgroup of the group of type preserving automorphisms of a rightangled building and hence associated to this building. A question is then if this universal group can act chambertransitively and with compact open stabilisers on a different rightangled building of the same type. We answer this question and define two universal groups associated to different rightangled buildings which are isomorphic as topological groups.
Abstract: A standard question in group theory is to ask if we can categorise the subgroups of a group in terms of their growth. In this talk we will be asking this question for uniform product set growth, a property that is stronger than the more widely understood notion of uniform exponential growth. We will see how considering acylindrical actions on hyperbolic spaces can help us, and give a particular application to mapping class groups.