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SUMMARY:Three Avatars of Schoenberg's Theorem on Positive Definite Functio
 ns on Spheres
DTSTART:20260519T120000Z
DTEND:20260519T133000Z
DTSTAMP:20260523T230800Z
UID:indico-event-16593@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Sujit Sakharam Damase (Indian Institute of Science)\
 n\nSchoenberg’s theorem on positive definite functions on spheres manife
 sts in three distinct “avatars”: in the study of matrix preservers\, t
 he harmonic analysis of homogeneous spaces\, and the representation theory
  of infinite-dimensional groups. I will discuss these connections\, starti
 ng from the classical entrywise calculus of the Schur product theorem and 
 extending to the asymptotic behavior of spherical functions on Olshanski s
 pherical pairs.\nAs a geometric application\, we will see how this framewo
 rk recovers the linear programming bounds of Delsarte–Goethals–Seidel 
 and Kabatiansky–Levenshtein for spherical codes\, which in turn yield up
 per bounds for sphere packing densities. I will then extend Schoenberg’s
  classical framework to partially defined positivity preservers on discret
 e domains\, and apply this machinery to the problem of soft thresholding f
 or correlation matrices in high-dimensional statistics.\nThis is joint wor
 k with James Pascoe.\n \n========\nPour être informé des prochains sém
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  corps du message vide.\n\nhttps://indico.math.cnrs.fr/event/16593/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/16593/
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