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CATEGORIES:Geometric Group Theory (GGT) Seminar
SUMMARY:Geometric results on linear actions of reductive L
ie groups for applications to homogeneous dynamics
- Rodolphe Richard (Cambridge)
DTSTART;TZID=Europe/London:20181019T134500
DTEND;TZID=Europe/London:20181019T144500
UID:TALK112471AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/112471
DESCRIPTION:Several problems in number theory when reformulate
d in terms of homogeneous dynamics involve the stu
dy of limiting distributions of translates of alge
braically defined measures on orbits of reductive
groups. The general non-divergence and linearizati
on techniques\, in view of Ratner's measure classi
fication for unipotent flows\, reduce such problem
s to dynamical questions about linear actions of r
eductive groups on finite-dimensional vector space
s.\n\nWe will limit ourselves to the treatment of
the archimedean place (i.e. over the field of real
numbers)\, taken from the eponymous article https
://arxiv.org/abs/1305.6557 (Ergodic Theory and Dyn
amical Systems (this month issue)).\n\nWe will add
ress these finite-dimensional problems\, namely: i
n which directions does the trajectory of a bounde
d subset get arbitrarily small\, or stay bounded.
This involves the geometry of the concerned real a
lgebraic groups (Mostow decomposition\, convexity
arguments on the associated symmetric spaces)\, an
d some representation theory.\n\nThe problem treat
ed and the methods used give an example of the rel
evance\, in homogeneous dynamics\, of the notion o
f stability (in the Mumford sense) taken in an arc
himedean context and in an arithmetic context.
LOCATION:CMS\, MR13
CONTACT:Richard Webb
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