**Bielefeld-Münster Seminar**

Date: January 17, 2020

Venue: Bielefeld University

The talks will take place in V2-210. Coffee will be served in the same room during the coffee breaks.

### Schedule

10:00 Uhr | Dawid Kielak |

Fibring of manifolds and groups | |

11:00 Uhr | Coffee break |

11:30 Uhr | Herbert Abels |

Dense sub(semi)groups of Lie groups | |

12:30 Uhr | Lunch break |

14:00 Uhr | Josh Maglione |

Isomorphism of nilpotent groups via derivations | |

15:00 Uhr | Coffee break |

15:30 Uhr | Giles Gardam |

Leighton's theorem | |

16:30 Uhr | End the of seminar |

### Abstracts

#### Dawid Kielak

*Fibring of manifolds and groups*

I will discuss how one can use a little group homology to reprove and generalise statements about 3-manifolds fibring over the circle.

#### Herbert Abels

*Dense sub(semi)groups of Lie groups*

I am planning to present the recent joint result with E.B. Vinberg on dense subsemigroups of nilpotent Lie groups. I will put it into the context of other results and questions on dense sub(semi)groups of Lie groups. And I will explain why the question of density is the wrong question.

#### Josh Maglione

*Isomorphism of nilpotent groups via derivations*

By bringing in tools from multilinear algebra, we introduce a general method to aid in the computation of isomorphism for groups. Of particular interest are nilpotent groups where the only classically known proper nontrivial characteristic subgroup is the derived subgroup. This family of groups poses the biggest challenge to all modern approaches. Through structural analysis of the bi-additive commutator map, we leverage the representation theory of Lie algebras to prove efficiency for families of nilpotent groups. We report on joint work with Peter A. Brooksbank, Uriya A. First,and James B. Wilson.

#### Giles Gardam

*Leighton's theorem*

Leighton proved that any two finite graphs with the same universal cover have a common finite-sheeted cover. I will present a strengthening of this theorem proved in joint work with Daniel Woodhouse and independently by Sam Shepherd.