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SUMMARY:Guy Moshkovitz (CUNY)
DTSTART:20210423T170000Z
DTEND:20210423T183000Z
DTSTAMP:20260423T024727Z
UID:CAGS/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAGS/11/">An
  Optimal Inverse Theorem</a>\nby Guy Moshkovitz (CUNY) as part of Columbia
  algebraic geometry seminar\n\n\nAbstract\nThe geometric rank of a k-tenso
 r\, or a (k-1)-linear map\, is the codimension of its kernel variety\, whi
 ch is the variety cut out by the (k-1)-linear forms (for k=2 this is simpl
 y matrix rank).\nUsing a carefully chosen subvariety of the kernel that sa
 tisfies certain smoothness and F-rationality properties\, together with a 
 new iterative process for decomposing successive derivatives of a tensor o
 n a variety\, we prove that the partition rank of Naslund and the analytic
  rank of Gowers and Wolf are equivalent\, up to a constant depending on k\
 , over any large enough finite field. Proving the equivalence between thes
 e two quantities is the main question in the "bias implies low rank" line 
 of work in higher-order Fourier analysis\, and was reiterated by multiple 
 authors.\n\nJoint work with Alex Cohen.\n
LOCATION:https://researchseminars.org/talk/CAGS/11/
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