**Bielefeld-Münster Seminar**

Date: 3 August 2016

Venue: University of Münster, Einsteinstraße 62

The talks will be in lecture hall M6 (building opposite the main building). Tea will be served SR0 (main building) during the breaks.

### Schedule

10:15 | Christoph Hilmes |

Ends of group pairs | |

11:15 | Coffee break |

11:45 | Dawid Kielak |

Actions of Out(F_{n}) on RAAGs | |

12:45 | Lunch break |

14:00 | Emilio Pierro |

Quantities associated to the subgroup lattice of a finite group | |

15:00 | Coffee break |

15:30 | Patrick Wegener |

Hurwitz action in finite and affine Coxeter systems | |

16:30 | End the of seminar |

### Abstracts

#### Christoph Hilmes

*Ends of group pairs*

The Bass-Serre theory shows that a finitely generated group splits as a non-trivial amalgam or HNN-extension iff it acts on a tree without a global fixpoint. In this talk we explore a generalization of this result from 1995 by M. Sageev: A finitely generated group is semi-splittable iff it acts essentially on a CAT(0) cube complex.

#### Dawid Kielak

*Actions of Out(F*

_{n}) on RAAGsWe will discuss some rigidity phenomena occurring within the family of outer automorphism groups of right-angled Artin groups. We will focus on Out(F_{n}), and more specifically on homomorphisms with Out(F_{n}) as the domain, and investigate recent progress in the study of such homomorphisms.

#### Emilio Pierro

*Quantities associated to the subgroup lattice of a finite group*

We begin by discussing the Möbius function of a finite group, G. This function is primarily used to determine enumerative functions associated to G, such as the number of ordered generating pairs of elements of G. We illustrate this method in the specific case of the small Ree groups by using their natural 2-transitive permutation representation and also give some results on the generation and asymptotic generation of the small Ree groups. Finally, we will describe the connection between the Möbius function and the topology of the subgroup lattice regarded as a simplicial complex.

#### Patrick Wegener

*Hurwitz action in finite and affine Coxeter systems*

In joint work with B. Baumeister, T. Gobet and K. Roberts we classified the elements of a finite Coxeter system with transitive Hurwitz action. I will shortly review the main results of this work. Afterwards I will explain the situation for affine Coxeter systems.