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<title><string language="fre"><![CDATA[R. Bamler - Uniqueness of Weak Solutions to the Ricci Flow and Topological Applications 4]]></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>2021-06-24</dateTime></date>
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