Aktuelles

Adventsseminar zur Algebra

Am Dienstag, den 16.12.2025 veranstaltet das Lehrgebiet Algebra im Seminarraum E408 (Gebäude 3) ein kleines Adventsseminar mit drei Vorträgen, zu denen Sie herzlich eingeladen werden:

10:00 - 11:00: Margherita Piccolo (FernUniversität in Hagen)

Quasi-semisimple profinite groups as profinite completions and their representation growth

Abstract: A profinite group is called quasi-semisimple if it is perfect and the quotient with its center is a semisimple profinite group, which is a cartesian product of finite non-abelian simple groups. The representation growth of such groups can be studied looking at the distribution of irreducible representations by means of a zeta function, that is a Dirichlet generating function. Under certain restrictions, the representation growth is polynomial with a wide range of growth. Moreover, given a profinite group, it is generally a difficult question to determine if it is, in fact, isomorphic to a profinite completion of a finitely generated abstract group. Kassabov and Nikolov introduced the concept of a frame to provide a criteria for a semisimple profinite group to be a profinite completion.

11:15 - 12:15: Adrian Baumann (HHU Düsseldorf)

Profinite solitude of arithmetic groups

Abstract: Profinite rigidity of various groups has been a central research interest in recent years. Profinite solitude asks a slight variation of this: If the profinite completions of two groups are commensurable, must the two groups themselves be commensurable? Arithmetic groups are a natural target for investigation of this property. In this talk, I will present some of my ongoing research on this matter through the use of Galois cohomology. All of this is joint work with Holger Kammeyer.

14:00 - 15:00: Nowras Otmen (Università di Padova)

Probabilistic identities, analytic groups and free constructions

Abstract: Profinite groups can be endowed with a probability measure, which allows one to investigate probabilistic questions in this class of topological groups. A particularly interesting instance is that of a group with a probabilistic identity, that is, when a group satisfies a word with positive probability. In this presentation, I will talk about the structural implications of satisfying a probabilistic identity in two classes of groups: analytic groups and fundamental groups of graphs of pro-p groups. This is joint work with Steffen Kionke, Tommaso Toti, Matteo Vannacci and Thomas Weigel.

Zum Abschluss des Seminars gibt es Tee, Kaffee und Plätzchen.