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PRODID:-//Columba Systems Ltd//NONSGML CPNG/SpringViewer/ICal Output/3.3-
 M3//EN
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METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20260204T123601Z
DTSTART:20260211T150000Z
DTEND:20260211T160000Z
SUMMARY:Logic Seminar - Martin Bays
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}x1kl-ml80fn
 rm-gonurw
DESCRIPTION:Speaker: Martin Bays (University of Oxford)\n\nGroups from no
 n-expansion in higher dimension\n\nCall a complex polynomial f(x\,y) _ex
 panding_ if there is e>0 such that for all sufficiently large finite set
 s A and B of complex numbers with |B| >= |A|\, we have |f(A\,B)| > |A|^{
 1+e}. A result of Elekes and Rónyai shows that the only non-expanding po
 lynomials f(x\,y) are those obtained from addition or multiplication by 
 composing with unary polynomials. Thinking of B as parametrising a famil
 y of unary polynomials f_b(x) = f(x\,b)\, we can see this conclusion as 
 placing B in an algebraic group acting via f. Generalising in these term
 s\, arbitrary nilpotent algebraic groups and their actions can arise. I 
 will review some results indicating that this should be the most general
  situation\, including work of Tingxiang Zou and myself which confirms t
 his in certain cases\, using methods from model theory and from additive
  and incidence combinatorics.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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