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SUMMARY:Mingfeng Chen (University of Wisconsin-Madison)
DTSTART:20250225T210000Z
DTEND:20250225T220000Z
DTSTAMP:20260423T005705Z
UID:OARS/67
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OARS/67/">Th
 e dichotomy of Nikodym sets and local smoothing estimates for wave equatio
 ns</a>\nby Mingfeng Chen (University of Wisconsin-Madison) as part of OARS
  Online Analysis Research Seminar\n\n\nAbstract\nWe show that Nikodym sets
  and local smoothing estimates for linear wave equations form a dichotomy:
  If Nikodym sets for a family of curves exist\, then the related maximal o
 perator is not bounded on $L^p(\\mathbb{R}^2)$ for any $p<\\infty$\; if Ni
 kodym sets do not exist\, then local smoothing estimates hold\, and the re
 lated maximal operator is bounded on $L^p(\\mathbb{R}^2)$ for some $p<\\in
 fty$. We also determine the sharp exponent for $L^p$ bounds. This is joint
  work with Shaoming Guo.\n
LOCATION:https://researchseminars.org/talk/OARS/67/
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