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SUMMARY:Maximal functions\, Nikodym sets and local smoothing estimates
DTSTART:20261009T120000Z
DTEND:20261009T130000Z
DTSTAMP:20261010T192800Z
UID:indico-event-17508@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Chen Mingfeng (IHES)\n\nSéminaire d'Analyse\nI will
  discuss some recent works related to maximal operators and Nikodym sets i
 n the plane. Nikodym constructed a measure-zero Borel set in the plane tha
 t contains a line segment passing through each point in the unit square. F
 enton and Falconer asked whether a similar construction is possible when 
 “lines through a point” are replaced by ”circles with a prescribed c
 enter.” This was answered in the negative by Bourgain and Marstrand. We 
 study a generalization of this question\, in which “lines through a poin
 t” or “circles with prescribed center” are replaced by general analy
 tic families of plane curves. Using decouping\, we prove new maximal func
 tion and local smoothing estimates for families of curves satisfying a mul
 ti-parameter analogue of Sogge's cinematic curvature condition. Combining 
 with a recent nonlinear generalization of Falconer's prescribed projection
  theorem to construct Nikodym-type sets\, we characterize when Nikodym-typ
 e sets exist for analytic families of plane curves.\n========\nPour être 
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 énom et nom) et laissez le corps du message vide.\n\nhttps://indico.math.
 cnrs.fr/event/17508/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/17508/
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