## 6:30 pm — 9:00 pm

## Monday, 23^{rd} Nov 2020

**
Schedule (Zoom): **

18.30-19.30: William Hautekiet

19.30-20.00: Break

20.00-21.00: Florian Breuer

# Dr William Hautekiet

(Faculté des Sciences, Université libre de Bruxelles)
*Automorphism groups of transcendental field extensions*

It is well-known that the Galois group of an (infinite) algebraic field extension is a profinite group. When the extension is transcendental, the automorphism group is no longer compact, but has a totally disconnected locally compact structure (TDLC for short). The study of TDLC groups was initiated by van Dantzig in 1936 and then restarted by Willis in 1994. In this talk some of Willis' concepts, such as tidy subgroups, the scale function, flat subgroups and directions are introduced and applied to examples of automorphism groups of transcendental field extensions. It remains unknown whether there exist conditions that a TDLC group must satisfy to be a Galois group. A suggestion of such a condition is made.

# Prof. Florian Breuer

(School of Mathematical and Physical Sciences, The University of Newcastle)
*Realising general linear groups as Galois groups*

I will show how to construct field extensions with Galois groups isomorphic to general linear groups (with entries in various rings and fields) from the torsion of elliptic curves and Drinfeld modules. No prior knowledge of these structures is assumed.