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SUMMARY:An inverse theorem for the Gowers U^3 norm relative to quadratic l
 evel sets - Sean Prendiville (Lancaster University)
DTSTART:20241127T133000Z
DTEND:20241127T150000Z
UID:TALK223852@talks.cam.ac.uk
CONTACT:Julia Wolf
DESCRIPTION:The Gowers uniformity norms have become well-used tools in add
 itive combinatorics\, ergodic theory and analytic number theory. We discus
 s an effective version of the inverse theorem for the Gowers U^3-norm for 
 functions supported on high-rank quadratic level sets in finite vector spa
 ces. This enables one to run density increment arguments with respect to q
 uadratic level sets\, which are analogues of Bohr sets in the context of q
 uadratic Fourier analysis on finite vector spaces.  For instance\, one can
  derive a polyexponential bound on the Ramsey number of  three-term progre
 ssions which are the same colour as their common difference ("Brauer quadr
 uples")\, a result it seems difficult to obtain by other means.
LOCATION:MR4\, CMS
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