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SUMMARY:A new norm related to the Gowers U^3 norm - Pablo Candela Pokorna
DTSTART:20090216T160000Z
DTEND:20090216T170000Z
UID:TALK16404@talks.cam.ac.uk
CONTACT:Anton Evseev
DESCRIPTION:The uniformity norms (or U&#94\;d norms\, for d>1 a positive i
 nteger) were introduced about ten years ago by Gowers in his effective pro
 of of Szemerédi's theorem\, and have played an important role in arithmet
 ic combinatorics ever since. The U&#94\;2 norm is naturally related to Fou
 rier analysis\, and a very active trend in current research aims to develo
 p an analogue of Fourier analysis for each U&#94\;d norm with d>2. The bod
 y of results of this research for d=3 is known as quadratic Fourier analys
 is. After an introduction to this area we will consider a new norm related
  to the U&#94\;3 norm\, and discuss some of its applications in quadratic 
 Fourier analysis\, including a strengthening of a central theorem of Green
  and Tao (the inverse theorem for the U&#94\;3 norm)\, and how this strong
 er version of the theorem can be used to give a new proof of a recent deco
 mposition-theorem of Gowers and Wolf.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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