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<title><string language="fre"><![CDATA[A. Mondino - Time-like Ricci curvature bounds via optimal transport]]></string></title>
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<string language="fre"><![CDATA[The
goal of the talk is to present a recent work in collaboration with 
Cavalletti (SISSA) on optimal transport in Lorentzian synthetic spaces. 
The aim is to set up a “Lorentzian analog” of the celebrated 
Lott-Sturm-Villani theory of CD(K,N) metric measure spaces. The key idea
being to analyse convexity properties of Entropy functionals along 
future directed timelike geodesics (with respect to a suitable 
Lorentzian Wasserstein distance) of probability measures. The smooth 
Lorentzian setting was previously investigated by McCann and 
Mondino-Suhr.
After
recalling the general setting of Lorentzian synthetic spaces (including
remarkable examples fitting the framework), I will discuss some basics 
of optimal transport theory thereof in order to define "timelike Ricci 
curvature bounded below and dimension bounded above''  for a (possibly 
non-smooth)  Lorentzian space. The notion of  "timelike Ricci curvature 
bounded below and dimension bounded above''  for a (possibly 
non-smooth)  Lorentzian space is stable under a suitable weak 
convergence of Lorentzian synthetic spaces, giving a glimpse on the 
strength of the proposed approach.
As
an application of the optimal transport approach to timelike Ricci 
curvature lower bounds, I will discuss an extension of the  Hawking's 
Singularity Theorem (in sharp form) to the synthetic setting.]]></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[Time-like]]></string></keyword><keyword><string language="fre"><![CDATA[optimal transport]]></string></keyword><keyword><string language="fre"><![CDATA[Lorentzian synthetic spaces]]></string></keyword>
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FN:Andrea MONDINO
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<date><dateTime>2021-06-30</dateTime></date>
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