Universität Wien

250059 VO Geometric and asymptotic group theory (2011W)

4.00 ECTS (2.00 SWS), SPL 25 - Mathematik

Details

Sprache: Englisch

Prüfungstermine

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

  • Dienstag 11.10. 10:00 - 12:00 Seminarraum
  • Dienstag 18.10. 10:00 - 12:00 Seminarraum
  • Dienstag 25.10. 10:00 - 12:00 Seminarraum
  • Dienstag 08.11. 10:00 - 12:00 Seminarraum
  • Dienstag 15.11. 10:00 - 12:00 Seminarraum
  • Dienstag 22.11. 10:00 - 12:00 Seminarraum
  • Dienstag 29.11. 10:00 - 12:00 Seminarraum
  • Dienstag 06.12. 10:00 - 12:00 Seminarraum
  • Dienstag 13.12. 10:00 - 12:00 Seminarraum
  • Dienstag 10.01. 10:00 - 12:00 Seminarraum
  • Dienstag 17.01. 10:00 - 12:00 Seminarraum
  • Dienstag 24.01. 10:00 - 12:00 Seminarraum
  • Dienstag 31.01. 10:00 - 12:00 Seminarraum

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

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.

Art der Leistungskontrolle und erlaubte Hilfsmittel

Presentation or test.

Mindestanforderungen und Beurteilungsmaßstab

Prüfungsstoff

Literatur

Zuordnung im Vorlesungsverzeichnis

MALV, MGEV

Letzte Änderung: Mo 07.09.2020 15:40