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SUMMARY:Bounds for sets lacking x\,x+y\,x+y^2 - Sarah Peluse\, Stanford Un
 iversity
DTSTART:20181210T134500Z
DTEND:20181210T144500Z
UID:TALK114067@talks.cam.ac.uk
CONTACT:Aled Walker
DESCRIPTION:Let P_1\,...\,P_m be polynomials with zero constant term. Berg
 elson and Leibman's generalization of Szemerédi's theorem to polynomial p
 rogressions states that any subset A of [N] that lacks nontrivial progress
 ions of the form x\,x+P_1(y)\,\\dots\,x+P_m(y) satisfies |A|=o(N). Proving
  quantitative bounds in the Bergelson--Leibman theorem is an interesting a
 nd difficult generalization of the problem of proving bounds in Szemerédi
 ’s theorem\, and bounds are known only in a very small number of special
  cases. In this talk\, I'll discuss a bound for subsets of [N] lacking the
  progression x\,x+y\,x+y^2\, which is the first progression of length at l
 east three involving polynomials of differing degree for which a bound is 
 known. This is joint work with Sean Prendiville.
LOCATION:MR4\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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