Rebecca Waldecker - Professorin für Algebra

Norddeutsches Gruppentheoriekolloquium

Date: Friday 12th November 2021

We start at

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.

- 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

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

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.

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.

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.

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.