Seminar: Decision problems in groups; WS 2023/24

Prof. Dr. Clara Löh / Matthias Uschold / Franziska Hofmann


Seminar: Decision problems in groups

Many group-theoretic problems look deceivingly simple, but turn out to be algorithmically unsolvable: The algorithmic unsolvability of these problems has far-reaching consequences for other fields; e.g., many decision problems in geometry and topology can be reduced to such undecidable problems in group theory and thus are also algorithmically undecidable.

In this seminar, we will introduce the language of Turing machines, (un)decidability, and classical undecidable problems. Moreover, we will learn the basics on presentation of groups and group-theoretic constructions. We will then combine both aspects and study the (un)decidability of various problems in group theory. Conversely, we will also study certain special classes of groups in which several of the problems do have algorithmic solutions.

Several talks will also be suitable for students in the Lehramt Gymnasium track.


Wednesday, 8:30--10:00, M101



Basic group theory.

This seminar is suitable for Bachelor/Master students with an interest in group theory and algorithmic (un)solvability; several talks will also be suitable for students in the Lehramt Gymnasium track. This seminar could be the starting point for a project under my supervision (e.g., bachelor/master thesis, Zulassungsarbeit).


See the commented list of courses.

Last Change: June 17, 2023.