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<title><string language="fre"><![CDATA[A. Mondino - Metric measure spaces satisfying Ricci curvature lower bounds 1]]></string></title>
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idea of compactifying the space of Riemannian manifolds satisfying 
Ricci curvature lower bounds goes back to Gromov in the '80ies and was 
pushed by Cheeger-Colding in the ‘90ies, who investigated the structure 
of spaces arising as Gromov-Hausdorff limits of smooth Riemannian 
manifolds satisfying Ricci curvature lower bounds. A completely new 
approach based on Optimal Transport was proposed by Lott-Villani and 
Sturm around ten years ago; via this approach, one can give a precise 
sense of what means for a non-smooth space (more precisely for a metric 
measure space) to satisfy a Ricci curvature lower bound and a 
dimensional upper bound. This approach has been refined in the last 
years by a number of authors (most notably Ambrosio-Gigli- Savarè) and a
number of fundamental tools have now been established, permitting to 
give further insights in the theory and applications which are new even 
for smooth Riemannian manifolds. The goal of the lectures is to give an 
introduction to the theory and discuss some of the applications.]]></string></description>
<keyword><string language="fre"><![CDATA[Grenoble]]></string></keyword><keyword><string language="fre"><![CDATA[eem2021]]></string></keyword><keyword><string language="fre"><![CDATA[contraintes de courbures et espaces métriques]]></string></keyword><keyword><string language="fre"><![CDATA[curvature constraints and spaces of metrics]]></string></keyword><keyword><string language="fre"><![CDATA[Ricci curvature]]></string></keyword><keyword><string language="fre"><![CDATA[lower bounds]]></string></keyword>
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<date><dateTime>2021-06-21</dateTime></date>
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<date><dateTime>2021-06-21</dateTime></date>
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