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SUMMARY:Why are bilinear forms important in analytic number theory? - Adam
  Harper\, Cambridge
DTSTART:20111111T160000Z
DTEND:20111111T170000Z
UID:TALK33381@talks.cam.ac.uk
CONTACT:Ben Green
DESCRIPTION:Many problems in number theory involve obtaining good estimate
 s\nfor sums over primes\, sums weighted by arithmetic functions\, or simil
 ar.\nOne possible approach to this\, which is often branded as "the method
  of\nType II sums"\, involves somehow reorganising the sum of interest so 
 that it\nhas a bilinear shape. In this seminar I will try to explain some 
 examples\nwhere this technique is useful. The talk will be almost complete
 ly\nexpository\, but amongst other things I will present a simpler proof o
 f a\nrecent bilinear sums result of Bourgain\, Sarnak and Ziegler. I may a
 lso\nmake a (tenuous) connection with some of my recent work on S-unit\neq
 uations.
LOCATION:MR15\, CMS
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