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SUMMARY:Gabriel Conant (University  of Cambridge\, UK)
DTSTART:20200605T190000Z
DTEND:20200605T192500Z
DTSTAMP:20260423T011224Z
UID:CANT2020/67
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2020/67/
 ">Small tripling with forbidden bipartite configurations</a>\nby Gabriel C
 onant (University  of Cambridge\, UK) as part of Combinatorial and additiv
 e number theory (CANT 2021)\n\n\nAbstract\nA finite subset $A$ of a group 
 $G$ is said to have \\emph{$k$-tripling} \nif $|AAA|\\leq k|A|$. I will re
 port on recent joint work with A. Pillay\, in which \nwe study the structu
 re finite sets $A$ with $k$-tripling\, under the additional \nassumption t
 hat the bipartite graph relation $xy\\in A$ omits some induced \nsubgraph 
 of a fixed size $d$. In this case\, we show that $A$ is approximately \na 
 union of a bounded  number  of translates of a coset nilprogression in $G$
  \nof bounded rank and step (where ``bounded" is in terms of $k$\, $d$\, \
 nand a chosen approximation error $\\epsilon>0$). Our methods combine the 
 work \nof Breuillard\, Green\, and Tao on the structure of approximate gro
 ups\, together \nwith model-theoretic tools based on the study of groups d
 efinable in NIP theories.\n
LOCATION:https://researchseminars.org/talk/CANT2020/67/
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