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SUMMARY:Sum-product inequalities and geometric incidence counting - Misha 
 Rudnev (University of Bristol)
DTSTART:20091109T160000Z
DTEND:20091109T170000Z
UID:TALK20867@talks.cam.ac.uk
CONTACT:Boris Bukh
DESCRIPTION:The sum-product theory aims to give as much as possible quanti
 tative development to a paradigm that if all pairs of elements of a finite
  set A in a ring R generate few distinct sums and products\, relative to t
 he size of A\, then A must be close to a subring.\n\nA closely related geo
 metric question is to give non-trivial bounds on the number of incidences 
 between a family of straight lines and points in a Desarguesian plane. The
  first question of this kind\, perhaps\, is\, given a set of points\, to p
 rovide a lower bound on a number of distinct straight lines determined by 
 all pairs of points. \n\nThis talk discusses some reasonably recent result
 s in the Euclidean and prime field settings\, along the lines of the inter
 play of the above two general questions.
LOCATION:MR12\, CMS
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