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SUMMARY:I.D. Shkredov (Steklov Mathematical Institute\, Russia)
DTSTART:20200602T180000Z
DTEND:20200602T182500Z
DTSTAMP:20260423T011239Z
UID:CANT2020/23
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2020/23/
 ">Growth in Chevalley groups and some applications</a>\nby I.D. Shkredov (
 Steklov Mathematical Institute\, Russia) as part of Combinatorial and addi
 tive number theory (CANT 2021)\n\n\nAbstract\nGiven a Chevalley group ${\\
 mathbf G}(q)$ and a parabolic subgroup \n$P\\subset {\\mathbf G}(q)$\, we 
 prove that for any set $A$ there is a certain growth of $A$\nrelatively to
  $P$\, namely\, either $AP$ or $PA$ is much larger than $A$. Also\,\nwe st
 udy a question about intersection of $A^n$ with parabolic subgroups $P$\nf
 or large $n$. We apply our method to obtain some results on a modular form
  of\nZaremba's conjecture from the theory of continued fractions and make 
 the first\nstep towards Hensley's conjecture about some Cantor sets with H
 ausdorff\ndimension greater than $1/2$\n
LOCATION:https://researchseminars.org/talk/CANT2020/23/
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