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SUMMARY:A generalized Legendre duality relation and Gaussian saturation
DTSTART:20250515T120000Z
DTEND:20250515T150000Z
DTSTAMP:20260416T010500Z
UID:indico-event-12917@indico.math.cnrs.fr
DESCRIPTION:Speakers: Shohei Nakamura (Birmingham University)\n\nThis talk
  is based on the joint work with Hiroshi Tsuji (Saitama\, Japan). \nMotiv
 ated by the Wasserstein barycenter problem\, Kolesnikov-Werner recently ex
 tended  notions of the polar duality of convex bodies and the Legendre du
 ality for functions to those of multiple inputs. Based on these notions\, 
 they formulated the multiple-input extension of the Blaschke--Santal\\'{o}
  inequality and the symmetric Talagrand inequality for Wasserstein barycen
 ter. They then proved these inequalities for unconditional convex bodies a
 nd unconditional functions.  \nIn this talk\, we confirm that these inequ
 alities hold under the evenness assumption. \nOur proof is based on an ob
 servation that these Blaschke--Santal\\'{o}-type inequalities may be regar
 ded as the limiting case of so-called inverse Brascamp--Lieb inequality. T
 his family of inequalities were introduced by Chen--Dafnis--Paouris\, and 
 then further investigated by Barthe--Wolff. \n\nhttps://indico.math.cnrs.
 fr/event/12917/
LOCATION:Salle Olga Ladyjenskaïa (IHP - Bâtiment Borel)
URL:https://indico.math.cnrs.fr/event/12917/
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