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SUMMARY:Sum-product theorems for polynomials - Boris Bukh (University of C
 ambridge)
DTSTART:20091123T160000Z
DTEND:20091123T170000Z
UID:TALK21493@talks.cam.ac.uk
CONTACT:Boris Bukh
DESCRIPTION:Suppose A is a set of numbers and f(x\,y) is a polynomial\, ho
 w small can f(A\,A) be? If f(x\,y)=x+y\nor f(x\,y)=xy\, then f(A\,A) can b
 e very small indeed if A is a progression. However\, Erdős and Szemerédi
  proved that A+A and AA cannot be simultaneously small when A is a set of 
 real numbers. Their results has been generalized to other rings\, and have
  found numerous applications in number theory\, combinatorics\,\ntheoretic
 al computer science\, and other fields.\n\nIn this talk\, I will survey th
 e classical sum-product estimates\, and will discuss several new results f
 or other\npolynomial functions f. Joint work with Jacob Tsimerman.
LOCATION:MR4\, CMS
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