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SUMMARY:Quasirandom Groups\, Minimally Almost Periodic Groups and Ergodic 
 Ramsey Theory - Bergelson\, V (Ohio State University)
DTSTART:20140630T103000Z
DTEND:20140630T112000Z
UID:TALK53241@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:According to the definition introduced by T. Gowers in 2008\, 
 a finite group G is called D-quasirandom for some parameter D\, if all non
 -trivial unitary 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-quasirandom for 
 a large value of D. Answering a question posed by L.\nBabai and V. Sos\, G
 owers have shown that\, in contrast with the more familiar "abelian" situa
 tion\, qusirandom groups can not have large product-free subsets.\nThe goa
 l of this lecture is to discuss the connection between the combinatorial p
 henomena observed in quasirandom groups and the ergodic properties of the 
 minimally almost periodic groups (these were introduced in 1934 by J. von 
 Neumann as groups which do not admit non-constant almost periodic function
 s). 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 rec
 ent results obtained in joint work with T. Tao and in the work of T. Austi
 n.\n
LOCATION:Seminar Room 1\, Newton Institute
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