Seminar: Group rings and dimensions; SS 2026

Prof. Dr. Clara Löh / Franziska Hofmann / Malena Wasmeier

News

Organisational meeting: Wed, Feb 4, 2026; 9:15, M 101.
This seminar will be held in English. The written report can be in English or German. The handouts should be in English.

Seminar: Group rings and dimensions

Group rings combine the multiplicative structure of a group with a base ring. They appear naturally in many algebraic and topological situations. Despite their simple definition, even basic questions about group rings (e.g., on the existence of non-trivial zero divisors) easily lead to surprising challenges.

In this seminar, we will study elementary algebraic properties of group rings and learn about embeddings of group rings into rings with better algebraic properties. In particular, we will discuss the Kaplansky conjectures, the von Neumann dimension, and the Atiyah conjecture.

Time/Location

Wednesday, 8:30--10:00, M104

Material

LaTeX template for handouts: .tex, .pdf
LaTeX template for reports: .tex, .pdf
Admin and preparation
Hints on writing mathematical texts (in German)
More such hints
Small print on slide talks

Prerequisites

Most of the talks will be accessible with basic knowledge on groups, rings, and modules. Some of the talks benefit from experience in analysis, topology or homological algebra.

Formalities/Credits

See the commented list of courses.

Last Change: January 19, 2026.