We'll describe a method for coloring the vertices of the rooted binary tree to obtain a collection of maximal subgroups of Thompson's group V. We'll also formulate a conjecture about the structure of all maximal sugroups of V. This is ongoing work with Jim Belk, Collin Bleak, and Martyn Quick.

TBA

It has been known by work of Carter-Keller and Tavgen since the 90s that classical matrix groups G defined over rings R of algebraic integers are boundedly generated by root elements (think elementary matrices). Work by Kedra-Gal has further shown that if a finite collection of conjugacy classes generates G, then it boundedly generates G. Also, it was shown in the case of G=SL_n by Morris that there is a bound (for bounded generation) only depending on the number of conjugacy classes (and not the classes themselves) that are taken as a generating set and by Kedra-Libman-Martin that the bound is actually linear in the number of conjugacy classes, if R is a principal ideal domain. In this talk, I explain a method to generalize the latter result to arbitrary rings of algebraic integers and all classical matrix groups by using G\"odels Compactness theorem. We demonstrate this in the case of Sp_4(R) and also explain (if time allows) how the general behavior for most classical groups is actu

This talk will be a gentle introduction to a theory of group actions on combinatorial-geometric structures that has been developed over the last years in joint work with several coauthors. Our main motivation comes from the study of arrangements of hypersurfaces, a nowadays classical field that was spurred by work by Arnol'd, Brieskorn and Deligne from the Seventies on arrangements of linear hyperplanes, configuration spaces and Artin groups of finite type. A hallmark of the classical theory is the strong interaction between geometry, algebra and combinatorics. In this talk, I will start by illustrating how the quest for a combinatorial framework for the general theory of arrangements of hypersurfaces motivates the development of a new theory of group actions on partially ordered sets with geometric structure. Then I will outline the basics of our theory, illustrated by examples and sample results as well as, in true "Oberseminar" spirit, some of the main open problems.

Garside groups and Artin groups are two generalizations of braid groups. We show that weak Garside groups of finite type and FC-type Artin groups are Helly, hence equip these groups with a particular nonpositive-curvature-like (NPC) structure. Such structure shares many properties of a CAT(0) structure and has some additional combinatorial flavor. We shall explain this NPC structure in more detail and discuss new results on the topology and geometry of these groups which are immediate consequences of such structure. This is joint work with D. Osajda.

In the theory of Coxeter groups, Coxeter elements have always played an important role. This talk will focus on one particular property of Coxeter elements. Given a finite irreducible Coxeter group (W,S) and a Coxeter element c in W, it is a classical result that the centralizer of c in W is cyclic. Here, we will discuss the extension of this result to infinite irreducible Coxeter groups. This is joint work with P. Wegener.