Advanced Seminar on Group Theory

Lehrstuhl für Algebra und Zahlentheorie

Wintersemester 2022/23

Where & When:
The usual time is Tuesday in the morning in seminar room 03.73.
Advanced topics in group theory are discussed in short series of talks and guest lectures.
Prof. Dr. Benjamin Klopsch & Iker de las Heras & Luca Di Gravina

Research talks

Tue 18.10.22, 10:30-12:00
Seminar room 03.73
Matteo Pintonello
Abelian splittings of pro-p right angled Artin groups
Tue 20.12.22, 10:00-11:30
Seminar room 03.73
Anitha Thillaisundaram

Beauville structures for quotients of infinite Grigorchuk-Gupta-Sidki groups acting on the pn-adic tree

Groups of surfaces isogenous to a higher product of curves can be characterised by a purely group-theoretic condition, which is the existence of a so-called Beauville structure. Gul and Uria-Albizuri showed that quotients of the periodic Grigorchuk-Gupta-Sidki groups, GGS-groups for short, that act on the p-adic tree, admit Beauville structures. We extend their result by showing that quotients of infinite periodic GGS-groups, that act on the pn-adic tree, also admit Beauville structures for all primes p and positive integers n. This is joint work with Elena Di Domenico and Şükran Gül.

Bass-Serre theory (programme)

The goal of this seminar is to give an introduction to Bass-Serre theory, a branch of modern geometric group theory which studies structural properties of groups by exploiting their action on trees. See the programme for more details.

Main references:

  1. L. Ribes and P. Zalesskii, Pro-p trees and applications, in New Horizons in pro-p groups, Springer, 2000. link
  2. J.P. Serre, Trees, Springer, 1980. link
Tue 08.11.22, 10:30-12:00
Seminar room 03.73
Margherita Piccolo
Tue 15.11.22, 10:00-11:30
Seminar room 03.73
Lucia Morotti
Trees and free groups
Tue 22.11.22, 10:00-11:30
Seminar room 03.73
Iker de las Heras
Trees and amalgams
Tue 29.11.22, 10:00-11:30
Seminar room 03.73
Giada Serafini
Structure of a group acting on a tree I
Tue 06.12.22, 10:00-11:30
Seminar room 03.73
Daniel Echtler
Structure of a group acting on a tree II
Tue 13.12.22, 10:00-11:30
Seminar room 03.73
Thomas Smith

Amalgams and fixed points

Tue 10.01.23, 10:00-11:30
Seminar room 03.73
Djurre Tijsma

The tree of SL2 over a local field I

Tue 17.01.23, 10:00-11:30
Seminar room 03.73
Martina Conte

The tree of SL2 over a local field II

Tue 24.01.23, 10:00-11:30
Seminar room 03.73
Luca Di Gravina

Profinite graphs and pro-p trees

Tue 31.01.23, 10:00-11:30
Seminar room 03.73
Fabian Korthauer

Pro-p groups acting on pro-p trees