Decision problems in groups

Decision problems in groups

Semester
WiSe 2023 / 24

Lecturer
Clara Löh/Matthias Uschold/Franziska Hofmann

Type of course (Veranstaltungsart)
Seminar

German title
Entscheidungsprobleme in Gruppen

Contents
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.

Recommended previous knowledge
Basic group theory is sufficient.

Time/Date
Wed 8:30--10:00

Location
M 101

Course homepage
https://loeh.app.ur.de/teaching/decsem_ws2324
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration

Organisational meeting/distribution of topics: Mo, 17.07., 12:15, PHY 5.0.20
Registration for course work/examination/ECTS: FlexNow

Course work (Studienleistungen)

Presentation: Giving a seminar talk of roughly 90 minutes

Examination (Prüfungsleistungen)

Detailed written report of the seminar talk

Modules
BSem, MV, MSem, LA-GySem

ECTS
4.5

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