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SUMMARY:Simple groups\, characteristic covering numbers and tensor product
  growth of representations - Aner Shalev (Hebrew University of Jerusalem)
DTSTART:20220728T130000Z
DTEND:20220728T135000Z
UID:TALK176579@talks.cam.ac.uk
DESCRIPTION:I will present two recent joint works with Michael Larsen and 
 Pham Tiep. The first shows that short products of words (in disjoint varia
 bles) which are not an identity of&nbsp\;any (non-abelian) finite simple g
 roup are surjective on ALL finite simple groups. This is carried&nbsp\;out
  in a more general framework of characteristic collections of groups\, and
  may be regarded&nbsp\;as a generalization of work by Guralnick\, Liebeck\
 , O'Brien\, Tiep and me (2018)\, which in turn&nbsp\;extends the Odd Order
  Theorem.\nThe second part of the talk will focus on representations of fi
 nite simple groups\, exploring related&nbsp\;growth phenomena. It is motiv
 ated by the theory of approximate subgroups\, which establishes&nbsp\;3-st
 ep growth phenomena for simple groups of Lie type of bounded rank. We repl
 ace products of&nbsp\;subsets by tensor products of representations\, and 
 establish stronger 2-step growth results also&nbsp\;in unbounded rank.
LOCATION:Seminar Room 1\, Newton Institute
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