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Nombre de programmes trouvés : 3322
Conférences

le (54m16s)

R. Perales - Recent Intrinsic Flat Convergence Theorems

Given a closed and oriented manifold M and Riemannian tensors g0, g1, ... on M that satisfy g0 < gj, vol(M, gj)→vol (M, g0) and diam(M, gj)≤D we will see that (M, gj) converges to (M, g0) in the intrinsic flat sense. We also generalize this to the non-empty bundary setting. We remark that under the onditions we do not nexessarily obtain smooth, C0 or even Gromov-Hausdorff convergence. furthermore, these results can be applied to show stability of a class of tori and a class of complete and asymptotically flat manifolds. That is, any sequence ...
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Conférences

le (1h13m19s)

R. Bamler - Compactness and partial regularity theory of Ricci flows in higher dimensions

We present a new compactness theory of Ricci flows. This theory states that any sequence of Ricci flows that is pointed in an appropriate sense, subsequentially converges to a synthetic flow. Under a natural non-collapsing condition, this limiting flow is smooth on the complement of a singular set of parabolic codimension at least 4. We furthermore obtain a stratification of the singular set with optimal dimensional bounds depending on the symmetries of the tangent flows. Our methods also imply the corresponding quantitative stratification result ...
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Cours magistraux

le (52m2s)

A. Lytchak - Convex subsets in generic manifolds

In the talk I would like to discuss some  statements and questions about convex subsets and convex hulls in generic Riemannian manifolds of dimension at least 3. The statements, obtained jointly with Anton Petrunin,  are elementary but somewhat  surprising for the Euclidean intuition. For instance, the convex hull of any finite non-collinearset  turns out to be  either   the whole manifold or non-closed.
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Conférences

le (56m54s)

A. Song - On the essential minimal volume of Einstein 4-manifolds

Given a positive epsilon, a closed Einstein 4-manifold admits a natural thick-thin decomposition. I will explain how, for any delta, one can modify the Einstein metric to a bounded sectional curvature metric so that the thick part has volume linearly bounded by the Euler characteristic and the thin part has injectivity radius less than delta. I will also discuss relations to conjectural obstructions to collapsing with bounded sectional curvature or to the existence of Einstein metrics.
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Cours magistraux

le (1h36m19s)

C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 4

We introduce various notions of convergence of Riemannian manifolds and metric spaces.  We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature.   We close the course by presenting methods and theorems that may be applied to prove these open questions including older techniques developed with Lakzian, with Huang and Lee, and with Portegies.  I will also present key new results of Allen and Perales.   Students and postdocs interested in ...
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