Universität Wien

250116 VO Computational Group Theory (2024S)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik
ON-SITE
Moodle
Mo 27.05. 16:45-18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock

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Details

Language: English

Lecturers

Classes (iCal) - next class is marked with N

Monday 04.03. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Monday 11.03. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Monday 18.03. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Monday 08.04. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Monday 15.04. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Monday 22.04. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Monday 29.04. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Monday 06.05. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Monday 13.05. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Monday 03.06. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Monday 10.06. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Monday 17.06. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Monday 24.06. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

Algorithms and techniques for computations in infinite, finitely presented groups.
Topics include:
* Stallings' folding and related free group algorithms
* Reidemeister-Schreier Algorithm for computing a presentation of a subgroup.
* Todd-Coxeter coset enumeration
* Rewriting systems and the Knuth-Bendix Algorithm
* Finite state automata and Automatic Groups
We will also introduce free software tools to do the above computations, including GAP, SAGE, KBMAG.

Assessment and permitted materials

Oral exam.

Minimum requirements and assessment criteria

Pass the oral exam.

Examination topics

Contents of the course.

Reading list

D. B. A. Epstein, D. F. Holt, and S. E. Rees, The use of Knuth-Bendix methods to solve the word problem in automatic groups, J. Symbolic Comput. 12 (1991), no. 4-5, 397–414, Computational group theory, Part 2.

David B. A. Epstein and Derek F. Holt, Computation in word-hyperbolic groups, Internat. J. Algebra Comput. 11 (2001), no. 4, 467–487.

Derek F. Holt, Bettina Eick, and Eamonn A. O’Brien, Handbook of computational group theory, Discrete Mathematics and its Applications (Boca Raton), Chapman & Hall/CRC, Boca Raton, FL, 2005.

Ilya Kapovich and Alexei Myasnikov, Stallings foldings and subgroups of free groups, J. Algebra 248 (2002), no. 2, 608–668.

Association in the course directory

MALV

Last modified: Th 07.03.2024 10:06