Virtual Northern German Group Theory Colloquium 2021

Date: Friday 12th November 2021

We start at 2.30 pm, the virtual room can be entered from 2 pm on.
If you have questions about the programme, then please contact Rebecca Waldecker (rebecca.waldecker[at]mathematik.uni[minus]halle.de).
If you have technical questions, then please contact Marco Lotz.



Tentative programme, will be updated frequently! There are abstracts further below.

• 2.30 - 3.10 pm: Nick Gill "On Cherlin's conjecture"
  


• coffee break


• 3.30 – 3.50 pm: Paula Hähndel
  Finite Simple Groups Acting with Fixity 4 -- Update


• 4 – 4.20 pm: Olga Varghese
  Automatic continuity for Artin groups


• coffee break


• 5 pm – 5.20 pm: Matthias Neumann-Brosig
  Calculating the Frattini subgroup of a polycyclic group


• 5.30 – 5.50 pm: Paula Lins
  The braided Thompson's group F and R_infty property

Abstract for Nick Gill's talk: In this talk I will discuss a conjecture concerning finite groups that arose in model theory. This conjecture concerns how finite groups act homogeneously on finite relational structures. Here you should think of a "relational structure" as being something like a hypergraph whose edges can be different colours and different lengths, and you should think of "homogeneity" as being a very strong symmetry condition. Some deep model theory tells us that such actions can be used to organise finite permutation groups into natural families in a very strong way. We will discuss this organising principle, and we will discuss some of the many interesting group theory questions that it throws up.

The short talks will be given by Paula Hähndel, Olga Varghese, Matthias Neumann-Brosig and Paula Lins.

Abstract for Paula Hähndel's talk
Finite Simple Groups Acting with Fixity 4 -- Update:
In my talk I will discuss group actions with fixity 4, in particular the most recent developments towards a full classification of all finite simple groups that act with fixity 4. This is part of a project initiated by Kay Magaard, currently worked on jointly with Barbara Baumeister, Patrick Salfeld and Rebecca Waldecker.

Abstract for Olga Varghese's talk
Automatic continuity for Artin groups:
The conjecture we address says that any abstract group homomorphism from a locally compact Hausdorff group into an Artin group is continuous, i. e. all Artin groups are lcH-slender. We use the clique-cube complex C_Gamma associated to the Artin group A_Gamma to reduce the automatic continuity conjecture to Artin groups where the defining graphs are complete. Under mild algebraic conditions on small parabolic subgroups of A_Gamma we show that if all special complete subgroups A_\Delta of A_Gamma are lcH-slender, then A_Gamma is lcH-slender.

Abstract for Matthias Neumann-Brosig's talk
Calculating the Frattini subgroup of a polycyclic group:
We present a novel, practical method to determine the Frattini subgroup of a polycyclic group. This method is based on new theoretical investigations about complements and module strucure of elementary abelian sections in polycyclic groups. We have implemented our method in GAP and include a discussion of this implementation. Joint work with Bettina Eick.

Abstract for Paula Lins' talk
The braided Thompson's group F and R_infty property:
A group automorphism Phi of Gamma induces the action g*x= gxPhi(g)^-1 on Gamma. The orbits of such action are called Reidemeister classes. One says that Gamma$ satisfies the R_infty property if all its automorphisms have infinitely many Reidemeister classes. In this talk, we discuss the property R_infty of groups and the fact that the braided Thompson's group F satisfies this property. This is joint work with Yuri Santos Rego and Altair de Oliveira-Tosti.