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CATEGORIES:Discrete Analysis Seminar
SUMMARY:Inverse theorem for the Gowers U(4) norm - Ben Gre
en (University of Cambridge)
DTSTART;TZID=Europe/London:20091016T163000
DTEND;TZID=Europe/London:20091016T173000
UID:TALK20765AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/20765
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 function f is at least delta then f correlat
es with an object called an s-step nilsequence. Th
e resolution of this family of conjectures is the
last uncompleted step in a programme of Tao and I
to count quite general linear configurations of pr
imes asymptotically.\n\nI will review much of the
above and then say something about the recent proo
f of the inverse conjecture for the U(4) norm by T
ao\, Ziegler and I. The U(2) result is classical a
nd the U(3) inverse conjecture was established by
Tao and I four years ago. It looks very likely tha
t the new argument proves the general case and we
are currently trying to write that up.
LOCATION:MR13\, CMS
CONTACT:Boris Bukh
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