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SUMMARY:Quantitative stability for the Brascamp–Lieb inequality and mome
 nt measures
DTSTART:20260701T083000Z
DTEND:20260701T093000Z
DTSTAMP:20260706T081800Z
UID:indico-event-16902@indico.math.cnrs.fr
DESCRIPTION:Speakers: Joao Machado (LMCRC Huawei)\n\nIn this talk\, we pre
 sent recent results on quantitative stability for the Brascamp–Lieb ineq
 uality\, around the variance with respect to a log-concave measure. Severa
 l proofs of this inequality are known in the literature. Classical approac
 hes rely in particular on the Bakry–Émery Γ-calculus\, while others\, 
 such as that of Bobkov and Ledoux (2000)\, are based on the Prékopa–Lei
 ndler inequality.\nWe explain how the optimal quantitative stability versi
 on of the Prékopa–Leindler inequality obtained by Figalli\, van Hintum\
 , and Tiba (2025) can be combined with the theory of moment measures to st
 rengthen the Bobkov–Ledoux proof strategy. This approach yields a quanti
 tative stability version of the Brascamp–Lieb inequality with several re
 markable properties: optimality of the stability exponent and a constant d
 epending only on the dimension.\nIn particular\, this constant is universa
 l over the class of log-concave measures with essentially continuous conve
 x potentials. This minimal regularity assumption on the convex potential i
 s optimal to ensure non-degeneracy of the associated moment measure\, as s
 hown by Cordero-Erausquin and Klartag (2015). Finally\, we discuss how thi
 s result can be used to understand quantitative stability for moment measu
 res themselves\, highlighting the close links between these two problems.\
 nThis is joint work with João Pedro Ramos: https://arxiv.org/abs/2511.226
 36\n\nhttps://indico.math.cnrs.fr/event/16902/
LOCATION:112 (Braconnier)
URL:https://indico.math.cnrs.fr/event/16902/
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