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<title><string language="fre"><![CDATA[R. Bamler - Uniqueness of Weak Solutions to the Ricci Flow and Topological Applications 3]]></string></title>
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<string language="fre"><![CDATA[I will present recent work with Kleiner in which we verify two 
topological conjectures using Ricci flow. First, we classify the 
homotopy type of every 3-dimensional spherical space form. This proves 
the Generalized Smale Conjecture and gives an alternative proof of the 
Smale Conjecture, which was originally due to Hatcher. Second, we show 
that the space of metrics with positive scalar curvature on every 
3-manifold is either contractible or empty. This completes work 
initiated by Marques.
At the heart of our proof is a new uniqueness and stability theorem for 
singular Ricci flows. Singular Ricci flows can be seen as an improvement
of Ricci flows with surgery, which were used in Perelman’s proof of the
Poincaré and Geometrization Conjectures. The latter flows had the 
drawback that they were not uniquely determined by their initial data, 
as their construction depended on various auxiliary surgery parameters. 
Perelman conjectured that there must be a canonical, weak Ricci flow 
that automatically ""flows through its singularities” at an 
infinitesimal scale. Our work on the uniqueness of singular Ricci flows 
gives an affirmative answer to Perelman's conjecture and allows the 
study of continuous families of singular Ricci flows, leading to the 
topological applications mentioned above.
The lectures will roughly be structured as follows:
(1) Preliminaries of Ricci flow, Blow-up analysis of singularities, 
Statement of the main results
(2) Local stability Analysis
(3) Comparing singular Ricci flows, Proof of the uniqueness and 
stability result
(4) Continuous families of singular Ricci flows, Proof of the 
topological theorems.]]></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>
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<date><dateTime>2021-06-23</dateTime></date>
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