Advanced Seminar on Group Theory

Lehrstuhl für Algebra und Zahlentheorie

Sommersemester 2021

Where & When:
The usual time is Wednesday 14:30 till 16:00 online using Webex.
Advanced topics in group theory are discussed in short series of talks and guest lectures.
Prof. Dr. Benjamin Klopsch & Margherita Piccolo & Moritz Petschick

Thompson's groups(programme)

In the 1960’s Richard Thompson defined three groups nowadays denoted T, F and V that have remarkable properties, e.g.: They are finitely presented, but have unsolvable word problem, T and V are simple, F has property FP and is torsion-free. All three groups, as well as numerous generalisations, are still subject to much research.
Wednesday 21.04.21
Andoni Zozaya
Standard Hausdorff dimension in profinite R-analytic groups
The study of the Hausdorff dimension in the context of countably based profinite groups has been a fruitful area since it was introduced in the 90s. In this talk, we will introduce a natural Hausdorff dimension in the setting of profinite R-analytic groups, where R is a pro-p domain. We will show its main properties, as well as some recent results for profinite Fp[[t]]-analytic groups. This is joint work with Dr. González-Sánchez.
Wednesday 28.04.21
Margherita Piccolo
Wednesday 05.05.21
Martina Conte
More on F
Wednesday 12.05.21
Iker de las Heras
Wednesday 19.05.21
Nadja Hempel
Wednesday 26.05.21
Moritz Petschick
The conjugacy problem in F
Wednesday 02.06.21
Benjamin Klopsch
Commensurability and Thompson's groups
Wednesday 09.06.21
No seminar
Wednesday 16.06.21
Karthika Rajeev
Reidemeister numbers of the group F

Cohomology of profinite groups(programme)

After an introductory talk that explains how to define the theory of cohomology of groups in the setting of profinite groups, we turn to selected cohomological topics. In particular, we study the cohomology of uniform pro-p groups and the relation between the cohomology groups of discrete groups to those of their profinite completions (Cohomological goodness).
Wednesday 23.06.21
Pablo Cubides Kovacsics
Cohomology of Profinite Groups
Wednesday 30.06.21
Cohomology of Uniform Pro-p Groups - a Lemma of Serre
Wednesday 07.07.21
Margherita Piccolo
Cohomology of Uniform Pro-p Groups - a Theorem of Lazard
Wednesday 14.07.21
Martina Conte
Cohomological Goodness
Wednesday 21.07.21
Programme discussion for next semester
Friday 30.07.21
Giada Serafini
Configuration spaces and braids on graphs
Farley and Sabalka have given a method for computing presentations for braid groups on graphs by studying the corresponding configuration spaces of points on those graphs. In particular, this method relies on discrete Morse theory and on the fact that any graph must be sufficiently subdivided before applying it. We present a new and easier method for computing presentations for braid groups on graphs as follows. The idea is to define a kind of normalized configuration space and a cubical complex associated to it such that there is a homotopy equivalence between the fundamental group of the whole configuration space on the graph and the fundamental group of the cubical complex on the same graph. In this way, we are able to compute presentations for the braid groups on graphs by looking at the 2-skeleton of this cubical complex instead of studying the entire configuration space of n points on the graph.