BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Marco Vitturi (University College Cork)
DTSTART:20220615T160000Z
DTEND:20220615T170000Z
DTSTAMP:20260423T021306Z
UID:HAeS/34
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HAeS/34/">A 
 restricted 2-plane transform related to Fourier Restriction in codimension
  2</a>\nby Marco Vitturi (University College Cork) as part of Harmonic ana
 lysis e-seminars\n\n\nAbstract\nThe $2-$plane transform is the operator th
 at maps a function to its averages along affine $2-$planes. We consider th
 e operator obtained by restricting the allowed directions of the $2-$plane
 s to those normal to a fixed surface $S$ (quadratic\, for simplicity) of c
 odimension $2$. By duality and discretisation\, $L^p\\to L^q$ estimates fo
 r such an operator imply Kakeya-type estimates for the supports of Fourier
 -transformed wave-packets adapted to the surface $S$ (wave-packet decompos
 itions being a powerful tool in proving Fourier Restriction results). We c
 onnect this operator to Gressman's theory of affine invariant measures by 
 showing that if the surface is well-curved à la Gressman (meaning\, the a
 ffine invariant surface measure on S is non-vanishing) then the restricted
  $2-$plane transform is $L^p\\to L^q$ bounded in the maximal range of $(p\
 ,q)$ exponents allowed. The proof relies on a characterisation of well-cur
 vedness in Geometric Invariant Theory terms\, which will be discussed.\nJo
 int work with S. Dendrinos and A. Mustata.\n
LOCATION:https://researchseminars.org/talk/HAeS/34/
END:VEVENT
END:VCALENDAR