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 grouptheoretic 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 farreaching 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 grouptheoretic 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, 8:3010:00, M101
Material
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.