This semester the IRTG Seminar will take place online.

#### Meeting: Thursday, July 9, 2020 at 2 p.m.

Time | Name | Title |
---|---|---|

14:00 - 14:40 | Carlo Sircana | Construction of number fields with solvable Galois group |

14:50 - 15:30 | Daniel Gromada | Gluing compact matrix quantum groups |

#### Abstracts of the meeting

**Carlo Sircana**

**Title:** Construction of number fields with solvable Galois group

**Abstract:** The celebrated Shafarevich’s theorem solves the inverse Galois problem over the rationals for solvable groups. However, the proof is far from being constructive. In this talk, we will present a strategy to construct fields with a given solvable Galois group up to a given discriminant bound. In particular, we will focus on the problems of such an algorithm and the solutions we have adopted in order to overcome them.

**Slides: Slides_Carlo_Sircana**

**Daniel Gromada**

**Title:** Gluing compact matrix quantum groups

**Abstract: **In the talk, we discuss certain construction procedure for compact matrix quantum groups – so called gluing and ungluing. First, we describe the concept of gluing for matrix groups and for finitely generated groups. Then we show how those concepts generalize to the quantum case. We present the main theorem of the talk, which states that, under certain assumptions, the gluing procedure can be reversed and we define the ungluing of quantum groups. Finally, we discuss some applications of this result. The talk is based on a recent preprint arXiv:2006.13656.

**Slides:** Slides_Daniel_Gromada