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SUMMARY:Metric invariants from curvature-like inequalities - Florent Baudi
 er
DTSTART:20240619T130000Z
DTEND:20240619T140000Z
UID:TALK217969@talks.cam.ac.uk
CONTACT:Andras Zsak
DESCRIPTION:A central theme in the 40-year-old Ribe program is the quest f
 or metric invariants that characterize local properties of Banach spaces. 
 These invariants are usually closely related to the geometry of certain se
 quences of finite graphs (Hamming cubes\, binary trees\, diamond graphs...
 ) and provide quantitative bounds on the bi-Lipschitz distortion of those 
 graphs.\n\nA more recent program\, deeply influenced by the late Nigel Kal
 ton\, has a similar goal but for asymptotic properties instead. In this ta
 lk\, we will motivate the (asymptotic) notion of infrasup umbel convexity 
 (introduced in collaboration with Chris Gartland (UC San Diego)) and discu
 ss the value of this invariant for Heisenberg groups. This (asymptotic) in
 variant is inspired by the profound work of Lee\, Mendel\, Naor\, and Pere
 s on the (local) notion of Markov convexity. If time permits we will discu
 ss the notion of bicone convexity\, a new asymptotic invariant\, inspired 
 by the work of Eskenazis\, Mendel\, and Naor on the (local) notion of diam
 ond convexity.\n\nAll these metric invariants share the common feature of 
 being derived from point-configuration inequalities which generalize curva
 ture inequalities.
LOCATION:MR5
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