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SUMMARY:Inverse theorem for the Gowers U(4) norm - Ben Green (University o
 f Cambridge)
DTSTART:20091016T153000Z
DTEND:20091016T163000Z
UID:TALK20765@talks.cam.ac.uk
CONTACT:Boris Bukh
DESCRIPTION:The Gowers norms\, which come in a family U(2)\, U(3)\, U(4)\,
  ...are important objects of study in additive combinatorics. The inverse 
 conjecture for the Gowers norms predicts that if the U(s+1) norm of a func
 tion f is at least delta then f correlates with an object called an s-step
  nilsequence. The resolution of this family of conjectures is the last unc
 ompleted step in a programme of Tao and I to count quite general linear co
 nfigurations of primes asymptotically.\n\nI will review much of the above 
 and then say something about the recent proof of the inverse conjecture fo
 r the U(4) norm by Tao\, Ziegler and I. The U(2) result is classical and t
 he U(3) inverse conjecture was established by Tao and I four years ago. It
  looks very likely that the new argument proves the general case and we ar
 e currently trying to write that up.
LOCATION:MR13\, CMS
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