**Bielefeld-Münster Seminar**

Date: 13 July 2018

Venue: University of Münster, Einsteinstraße 62

The talks will be in room SR0 in the main building. Tea will be served in the same room during the breaks.

### Schedule

10:00 | Olga Varghese |

Coherence in graph products | |

11:00 | Coffee break |

11:30 | Jeroen Schillewaert |

On exceptional homogeneous compact geometries of type C_{3} | |

12:30 | Lunch break |

14:00 | Sophiane Yahiatene |

Coxeter transformations of extended Weyl groups | |

15:00 | Coffee break |

15:30 | Eduard Schesler |

Sphericity of complexes associated to spherical buildings | |

16:30 | End the of seminar |

### Abstracts

#### Olga Varghese

*Coherence in graph products*

A groups G is coherent if every finitely generated subgroup of G is finitely presented. We prove that many graph products are coherent.

#### Jeroen Schillewaert

*On exceptional homogeneous compact geometries of type C*

_{3}Tits introduced geometries of Coxeter type, which locally are buildings.

Flag-transitive finite geometries of type C_{3} have been classified by Aschbacher and Yoshiara. Such a geometry is either a building, or it is isomorphic with the Neumaier geometry on seven points. In the compact connected case a similar classification has been obtained by Kramer and Lytchak, such a geometry is either covered by a building, or it is isomorphic to one of two exceptional geometries. We will provide a uniform construction for these two exceptional geometries using composition algebras and show their simple connectedness.

#### Sophiane Yahiatene

*Coxeter transformations of extended Weyl groups*

Extended Weyl groups occur in various branches of mathematics, for example in representation theory of finite dimensional algebras and in singularity theory. There, the Coxeter transformations play an important role in understanding the underlying structures. After a short motivation and necessary definitions, we will present important properties and state some open problems and also progress in solving them.

#### Eduard Schesler

*Sphericity of complexes associated to spherical buildings*

Every spherical building Δ admits a canonical CAT(1)-metric d
such that every apartment Σ of Δ is isometric to the
unit sphere S^{dim(Δ)} with respect to d.
Hence for any point p ∈ Σ we can define the hemisphere
H_{p} ⊂ Σ centered at p.
Let ρ_{Σ,C}: Δ → Σ be the canonical
retraction with respect to some chamber C of Σ.
We formulate a conjecture concerning the sphericity of the subspace ρ^{-1}_{Σ,C}(H_{p}) ⊂ Δ
and present some known and some new affirmative results for that conjecture.

### Connections

There is an ICE connection leaving in Bielefeld at 8:22 and arriving in Münster at 9:22. There is also a local train connection leaving in Bielefeld at 7:59 and arriving in Münster at 9:17.

The following busses go from Münster station to Coesfelder Kreuz in the relevant period:

- line 1 (platform B1) from 9:21 to 9:36,
- line R64 (platform C3) from 9:27 to 9:40,
- line 34 (platform C3) from 9:30 to 9:46,
- line 13 (platform B1) from 9:31 to 9:48,
- line R63 (platform C3) from 9:43 to 9:54.