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TZID:Europe/Paris
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DTSTART:20260329T010000
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DTSTART:20261025T010000
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DTSTART;TZID=Europe/Paris:20260615T104500
DTEND;TZID=Europe/Paris:20260615T114500
DTSTAMP:20260608T155659
CREATED:20260608T091630Z
LAST-MODIFIED:20260608T091724Z
UID:21800-1781520300-1781523900@www.math.ens.psl.eu
SUMMARY:Convexity in Whitney Problems
DESCRIPTION:Suppose E is a compact subset of R^n\, and we are given a function f\, mapping E to the real numbers. How can we tell if the function lies on a smooth convex function? Can we construct an almost optimal\, smooth\, convex interpolant of the function? These are examples of Whitney-type extension and trace problems; while theoretical\, they are driven by practical questions of interpolation of data\, where convexity is a natural constraint. I will begin with an answer to these questions by presenting work of mine proving there is a Finiteness Principle for the non-linear space of strongly convex functions in $C^{1\,1}(\mathbb{R}^n)$. This work is the first attempt to understand the constrained interpolation problem for convex functions in $C^{1\,1}(\mathbb{R}^n)$. We will spend time discussing useful techniques and tools from analysis as well as important open problems in the field.
URL:https://www.math.ens.psl.eu/evenement/convexity-in-whitney-problems/
LOCATION:Salle W (ENS)
CATEGORIES:Séminaire de l'équipe Analyse
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