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SUMMARY:Martin Bays (University of Oxford)
DTSTART:20250311T140000Z
DTEND:20250311T150000Z
DTSTAMP:20260421T153741Z
UID:UEAPS/49
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UEAPS/49/">A
 n asymmetric version of Elekes-Szabó via group actions</a>\nby Martin Bay
 s (University of Oxford) as part of ANTLR seminar\n\nLecture held in EFRY 
 01.05.\n\nAbstract\nElekes and Rónyai showed that a bivariate real polyno
 mial f(x\,y)\nexpands\, meaning $|f(A\,A)| \\geq c|A|^{1+\\eta}$ for all f
 inite A\, unless\nf can be written as the composition of addition or multi
 plication with\nunivariate polynomials. The proof can be seen as going via
  the group\nconfiguration theorem of model theory. I will talk about recen
 t work\nwith Tingxiang Zou\, in which we consider a more general setup whe
 re\nwe can apply a homogeneous space version of this group configuration\n
 theorem\, and yet still subsequently reduce to an abelian group. We\ndeduc
 e asymmetric expansion $|f(A\,B)| \\geq c|A|^{1+\\eta}$ even when B is\nal
 lowed to be drastically smaller than A. Moreover\, we obtain a similar\nre
 sult when y is allowed to be a tuple. Allowing x to also be a tuple\nintro
 duces new phenomena\, and if time permits I may mention some partial\nresu
 lts in this case.\n
LOCATION:https://researchseminars.org/talk/UEAPS/49/
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