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CATEGORIES:Geometric Group Theory (GGT) Seminar
SUMMARY:Three dichotomies for connected unimodular Lie gro
ups. - David Hume (University of Oxford)
DTSTART;TZID=Europe/London:20191206T134500
DTEND;TZID=Europe/London:20191206T144500
UID:TALK134203AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/134203
DESCRIPTION:Using the Levi decomposition theorem\, Lie groups
are usually studied in two separate classes: semis
imple and solvable. Both these classes further div
ide into two subclasses with very different behavi
our: semisimple groups split into the rank 1 and h
igher rank cases\; while solvable groups divide in
to those of polynomial growth and those of exponen
tial growth.\n\nAmongst connected unimodular Lie g
roups\, let us say that G is "small" if it shares
a cocompact subgroup with some direct product of a
rank one simple Lie group and a solvable Lie grou
p with polynomial growth. Otherwise\, we say G is
"large". We present three strong dichotomies which
distinguish "small" and "large" groups\; which ar
e respectively algebraic\, coarse geometric\, and
local analytic in nature. As an application we wil
l show that Baumslag-Solitar groups admit a simila
r "small"/"large" dichotomy. This is part of a joi
nt project with John Mackay and Romain Tessera.
LOCATION:CMS\, MR13
CONTACT:
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