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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Quasirandom Groups\, Minimally Almost Periodic Gro
ups and Ergodic Ramsey Theory - Bergelson\, V (Ohi
o State University)
DTSTART;TZID=Europe/London:20140630T113000
DTEND;TZID=Europe/London:20140630T122000
UID:TALK53241AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/53241
DESCRIPTION:According to the definition introduced by T. Gower
s in 2008\, a finite group G is called D-quasirand
om for some parameter D\, if all non-trivial unita
ry representations of G have dimension greater or
equal to D. For example\, the group SL(2\, F_p) is
(p-1)/2 quasirandom for any prime p. Informally\,
a finite group is quasirandom if it is D-quasiran
dom for a large value of D. Answering a question p
osed by L.\nBabai and V. Sos\, Gowers have shown t
hat\, in contrast with the more familiar "abelian"
situation\, qusirandom groups can not have large
product-free subsets.\nThe goal of this lecture is
to discuss the connection between the combinatori
al phenomena observed in quasirandom groups and th
e ergodic properties of the minimally almost perio
dic groups (these were introduced in 1934 by J. vo
n Neumann as groups which do not admit non-constan
t almost periodic functions). This connection will
allow us to give a simple explanation the dynamic
al underpinnings of some of the Gowers' results as
well as of the more recent results obtained in jo
int work with T. Tao and in the work of T. Austin.
\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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