Seminar: Decision problems in groups; WS 2023/24

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

News

The organisational meeting for this seminar: Mo, 17.07., 12:15, PHY 5.0.20
Registration: through the GRIPS registration form (before 24.07.2023, 10:00).
The schedule is now available.
This seminar will be held in English. The written report can be in English or German. The handouts should be in English.

Seminar: Decision problems in groups

Many group-theoretic problems look deceivingly simple, but turn out to be algorithmically unsolvable:

Given a presentation of a group, can we decide whether the resulting group is trivial, finite, cyclic?
Which order does a given element have?
Are two given elements conjugate?

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.

Time/Location

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

Material

Overview of all talks.
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

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).

Formalities/Credits

See the commented list of courses.

Last Change: June 17, 2023.