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SUMMARY:Subset products and applications - Aner Shalev (Hebrew University 
 of Jerusalem)
DTSTART:20200317T113000Z
DTEND:20200317T123000Z
UID:TALK140656@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:In the past two decades there has been intense interest in pro
 ducts of subsets in finite groups.<br> Two important examples are Gowers&#
 39\; theory of Quasi Random Groups and its applications by<br> Nikolov\, P
 yber\, Babai and others\, and the theory of Approximate Subgroups and the 
 Product Theorem <br> of Breuillard-Green-Tao and Pyber-Szabo on growth in 
 finite simple groups of Lie type of bounded rank\,<br> extending Helfgott&
 #39\;s work. These deep theories yield strong results on products of three
  subsets <br> (covering\, growth). What can be said about products of two 
 subsets?<br> <br> I will discuss a recent joint work with Michael Larsen a
 nd Pham Tiep on this challenging problem\, <br> focusing on products of tw
 o normal subsets of finite simple groups\, and deriving some applications.
  <br> The proofs involve algebraic geometry\, representation theory and co
 mbinatorics.  <br> <br>
LOCATION:Seminar Room 1\, Newton Institute
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