BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Random rigidity in the free group - Danny Calegari (Cambridge)
DTSTART:20120228T141500Z
DTEND:20120228T151500Z
UID:TALK36030@talks.cam.ac.uk
CONTACT:24872
DESCRIPTION:If G is a group\, and [G\,G] is its commutator subgroup\, the\
 ncommutator length of an element w (denoted cl(w)) is the least number of\
 ncommutators in G whose product is w\; and the stable commutator length sc
 l(w)\nis the limit of cl(w^n)/n as n goes to infinity. Stable commutator l
 ength is\nrelated to bounded cohomology and quasimorphisms\, but is notori
 ously\ndifficult to calculate exactly\, or even to approximate. However\, 
 we show\nthat in a free group F of rank k a random word w of length n (con
 ditioned to\nlie in [F\,F]) has scl(w) = log(2k-1) n / 6 log(n) + o(n / lo
 g(n)) with high\nprobability. The proof combines elements from ergodic the
 ory and\ncombinatorics. This is joint work with Alden Walker.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
END:VEVENT
END:VCALENDAR