250059 VO Geometric and asymptotic group theory (2011W)
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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