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METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20241101T173836Z
DTSTART:20241106T151500Z
DTEND:20241106T163000Z
SUMMARY:Logic seminar: Abhiram Natarajan
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}syu-m2bo9sa
 k-va6p5f
DESCRIPTION:Title: Polynomial and Pfaffian Partitioning of Semi-Pfaffian 
 Sets with Applications\n\nAbstract: The polynomial partitioning theorem 
 of Guth and Katz\, in addition to helping nearly resolve Erdos' distinct
  distances problem\, has resulted in a wide swath of improvements not ju
 st in incidence geometry\, but in areas such as harmonic analysis as wel
 l. The polynomial partitioning theorem only applies to a finite set of s
 emi-algebraic sets\, and thus is not applicable when the sets involved a
 re more general than semi-algebraic sets. Incidence geometry questions\,
  where the involved sets are sets definable in arbitrary o-minimal struc
 tures\, has not progressed as much as the case where the sets involved a
 re semi-algebraic\, and one reason for this is the absence of a polynomi
 al partitioning theorem that works in the definable setting.\n\nWe gener
 alize the polynomial partitioning theorem of Guth and Katz to a finite s
 et of semi-Pfaffian sets. Additionally\, we also obtain a partitioning t
 heorem for semi-Pfaffian sets where instead of using a polynomial to par
 tition the space\, we are able to partition the space using a Pfaffian s
 et instead. The latter method has an important advantage.\n\nFinally\, w
 e are able to derive at least one immediate application of our new theor
 em.\n\nJoint work with Martin Lotz and Nicolai Vorobjov.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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