BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Phil Gressman (University of Pennsylvania) DTSTART:20241112T190000Z DTEND:20241112T200000Z DTSTAMP:20260423T005705Z UID:OARS/63 DESCRIPTION:Title: Un derstanding affine symmetry in geometric harmonic analysis\nby Phil Gr essman (University of Pennsylvania) as part of OARS Online Analysis Resear ch Seminar\n\n\nAbstract\nMany geometrically-inspired problems of interest in harmonic analysis\, including $L^p$-improving properties of Radon-like transforms and appropriate formulations of the Fourier restriction proble m\, exhibit natural affine invariance. In some cases\, this can mean that the geometry of submanifolds viewed as subsets of Euclidean space fails to capture important subtleties in much the same way that understanding the size of the entries of a matrix fails to capture its nondegeneracy propert ies. In this talk\, I will discuss how these ideas relate to recent work o n characterizing the $L^p-L^q$ norm of Radon-like transforms for pairs $(1 /p\,1/q)$ on a natural scaling line. Along the way\, natural connections t o Geometric Invariant Theory will be described. This work is part of a bro ader project to understand other geometrically-flavored nonnegative operat ors related to fractional integration\; some initial work on this broader project will be presented as time permits.\n LOCATION:https://researchseminars.org/talk/OARS/63/ END:VEVENT END:VCALENDAR