Advanced Seminar on Group Theory

Lehrstuhl für Algebra und Zahlentheorie

Summer Semester 2021

Where & When:
The usual time is Wednesday 14:30 – 16:00. Until further notice, the seminar will be on-line via Webex. An invitation link will be shared in time.
Content:
Advanced topics in group theory are discussed in short series of talks and guest lectures.
Organizers:
Prof. Dr. Benjamin Klopsch
Moritz Petschick, Margherita Piccolo
See also:
Seminar on Model Theory
Oberseminar

Thompson’s groups (programme)

In the 1960's Richard Thompson defined three groups nowadays denoted by 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. Our plan is to follow the Introductory Notes on Richard Thompson's Groups [2] by Cannon, Floyd, and Parry, and afterwards to look at a selection of more recent results.

  1. Belk, J., Matucci, F. Conjugacy and dynamics in Thompson's groups. Geom. Dedicata 169, 239--261 (2014), arx:0708.4250
  2. Cannon, J. W., Floyd, W. J., Parry, W. R. Introductory notes on Richard Thompson's groups. Enseign. Math., II. Sér. 42, No. 3-4, 215-256 (1996).
  3. Röver, C. E. Abstract Commensurators of Groups Acting on Rooted Trees. Geom. Dedicata 94, 45--61 (2002).
Wednesday 21.04.21
online
Andoni Zozaya (University of the Basque Country)
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
online
Margherita Piccolo
F
Wednesday 05.05.21
online
Martina Conte
More of  F
Wednesday 12.05.21
online
Iker de las Heras
T
Wednesday 19.05.21
online
Nadja Hempel
V
Wednesday 26.05.21
online
Moritz Petschick
Solving the conjugacy problem in F (& T & V)
Wednesday 02.06.21
online
Benjamin Klopsch
Abstract Commensurators of Groups Acting on Rooted Trees
Wednesday 16.06.21
online
Karthika Rajeev
Reidemeister Numbers of 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).

  1. Grunewald, F., Jaikin-Zapirain, A., Zalesskii, P. A. Cohomological goodness and the profinite completion of Bianchi groups. Duke Math. J. 144, 53-72 (2008).
  2. Serre, J. P. Galois Cohomology. Springer-Verlag, Berlin (1997).
  3. Wilson, J. S. Profinite groups. Clarendon Press, Oxford (1998).
Wednesday 23.06.21
online
Pablo Cubides Kovacsics
Cohomology of Profinite Groups
Wednesday 30.06.21
online
Benjamin Klopsch
Cohomology of Uniform Pro-p   Groups - a Lemma of Serre
Wednesday 07.07.21
online
Margherita Piccolo
Cohomology of Uniform Pro-p   Groups - a Theorem of Lazard
Wednesday 14.07.21
online
Martina Conte
Cohomological Goodness
Wednesday 21.07.21
online
Discussion for next semester's seminar

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