Advanced Seminar on Group Theory

Lehrstuhl für Algebra und Zahlentheorie

Summer semester 2022

Where & When:
The usual time is Tuesday in the morning in seminar room 03.73.
Content:
Advanced topics in group theory are discussed in short series of talks and guest lectures.
Organizers:
Prof. Dr. Benjamin Klopsch & Margherita Piccolo & Moritz Petschick
Tue 05.04.22 10:30-12:00
Seminar room 03.73
Daniel Echtler
(Universität Regensburg)

The Hochschild-Serre spectral sequence in bounded cohomology

Bounded cohomology is a functional analytical variation of cohomolgy, where only uniformly bounded cochains are considered. This gives an invariant with applications in geometry and group theory. One very powerful tool of homological algebra to compute many forms of (co)homolgy are spectral sequences. In this talk we discuss some basics on spectral sequences and boundend cohomology, with the goal to introduce the Hochschild-Serre spectral sequence in bounded cohomology. If time permits, we will also discuss some applications, such as a version of the mapping theorem in bounded cohomology or a characterization of boundedly acyclic morphisms.
Tue 12.04.22 10:00-11:30
Seminar room 03.73
Luca Di Gravina
Möbius functions of groups
Tue 19.04.22 10:00-11:30
Seminar room 03.73
Iker de las Heras
Commuting probability of infinite groups
Tue 26.04.22 09:30-11:00
Seminar room 03.73
Eugenia Kochubinska
Gentle introduction to transformation semigroups
Tue 03.05.22 09:30-11:00
Seminar room 03.73
Eugenia Kochubinska
Gentle introduction to transformation semigroups: idempotents, nilpotents and their combinatorics

Totally disconnected locally compact groups (programme)

Totally disconnected locally compact (short tdlc) groups arise naturally as the quotients of locally compact groups by their identity component. The goal is to understand the theory of tidy subgroups and the scale function introduced by Willis, which gave a big impetus to the area.
  1. I. Castellano, An Introduction to totally disconnected locally compact groups, 2020. link
  2. R. G. Moeller, Structure theory of totally disconnected locally compact groups via graphs and permutations, Canad. J. Math. Vol. 54 (4), 795--827, 2002.
  3. P. Wesolek, An Introduction to totally disconnected locally compact groups, 2018. link
Tue 24.05.22 09:30-11:00
Seminar room 03.73
Margherita Piccolo
Introduction and van Dantzig's Theorem
Tue 07.06.22 09:30-11:00
Seminar room 03.73
Fabian Korthauer
Cayley-Abels Graphs
Tue 14.06.22 09:30-11:00
Seminar room 03.73
Iker de las Heras
Neretin Groups

Research talks

Tue 12.07.22 10:00-11:30
Seminar room 03.73
Jorge Fariña
Branch structures among (weakly) branch groups
In this talk, we examine branch structures for the class of weakly branch groups, which are well-studied subgroups of the full automorphism group of a regular rooted tree. In particular, we are interested in the cases when a weakly branch group is weakly branch over some derived subgroup, and, more generally, over a verbal subgroup.
Tue 19.07.22 10:30-11:30
Seminar room 03.73
Florian Felix
Universality of Integration in Non-Archimedean Fields
Wed 27.07.22 10:00–11:30
Seminar room 03.73
Alberto Cassella (Milano-Bicocca/Saragossa)
Can we put arrows in RAAGs?
In the realm of Geometric Group Theory, the family of right-angled Artin groups has gained more and more importance through the years. They generalize at the same time both free and free abelian groups, and moreover their combinatorial nature has led to proving important results. On top of that, they also have a rich geometric nature. But what happens if we put some arrows in the defining graph of a RAAG? During this seminar we will discuss the consequences of such decision and we will see the analogies and the differences between classical and oriented RAAGs. We will also briefly talk about the family of hypercubical groups, to which both RAAGs and oriented RAAGs belong. If time permits, we will also see some results related to the pro-2 completion of an oriented RAAG. Most of this is a joint work with S. Blumer, I. Foniqi, C. Quadrelli and T. Weigel.

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