250059 VO Geometric and asymptotic group theory (2011W)
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Details
Language: English
Examination dates
Lecturers
Classes (iCal) - next class is marked with N
- Tuesday 11.10. 10:00 - 12:00 Seminarraum
- Tuesday 18.10. 10:00 - 12:00 Seminarraum
- Tuesday 25.10. 10:00 - 12:00 Seminarraum
- Tuesday 08.11. 10:00 - 12:00 Seminarraum
- Tuesday 15.11. 10:00 - 12:00 Seminarraum
- Tuesday 22.11. 10:00 - 12:00 Seminarraum
- Tuesday 29.11. 10:00 - 12:00 Seminarraum
- Tuesday 06.12. 10:00 - 12:00 Seminarraum
- Tuesday 13.12. 10:00 - 12:00 Seminarraum
- Tuesday 10.01. 10:00 - 12:00 Seminarraum
- Tuesday 17.01. 10:00 - 12:00 Seminarraum
- Tuesday 24.01. 10:00 - 12:00 Seminarraum
- Tuesday 31.01. 10:00 - 12:00 Seminarraum
Information
Aims, contents and method of the course
The course is on infinite random groups. These are groups obtained using a random choice of group relators. There are various models of random groups: combinatorial, topological, statistical, etc. The idea goes back to works of Gromov and Ol'shanskii.We will give an elementary account of the subject. First we introduce basic notions of geometric and asymptotic group theory such as van Kampen diagrams and Dehn's isoperimetric functions. Then we will proceed with a short discussion of small cancellation theory and Gromov's hyperbolic groups, and give a combinatorial proof of Gromov's small cancellation theorem stating that a graphical small cancellation group is hyperbolic.The main technical goal we pursue is Gromov's sharp phase transition theorem: a random quotient of the free group F_m is trivial in density greater than 1/2, and non-elementary hyperbolic in density smaller than this value. This refers to the density model of random groups, where the choice of group relators depends on the density parameter d with values between 0 and 1.
Assessment and permitted materials
Presentation or test.
Minimum requirements and assessment criteria
Examination topics
Reading list
Association in the course directory
MALV, MGEV
Last modified: Mo 07.09.2020 15:40