2021

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J. Fine - Knots, minimal surfaces and J-holomorphic curves

Vidéos

J. Fine - Knots, minimal surfaces and J-holomorphic curves
Conférence
01:01:02
J. Fine - Knots, minimal surfaces and J-holomorphic curves
Fine
Joël

I will describe work in progress, parts of which are joint with Marcelo Alves. Let L be a knot or link in the 3-sphere. I will explain how one can count minimal surfaces in hyperbolic 4-space

D. Tewodrose - Limits of Riemannian manifolds satisfying a uniform Kato condition
Conférence
01:07:59
D. Tewodrose - Limits of Riemannian manifolds satisfying a uniform Kato condition
Tewodrose
David

I will present a joint work with G. Carron and I. Mondello where we study Kato limit spaces. These are metric measure spaces obtained as Gromov-Hausdorff limits of smooth n-dimensional Riemannian

P. Burkhardt - Pointwise lower scalar curvature bounds for C0 metrics via regularizing Ricci flow
Conférence
01:00:08
P. Burkhardt - Pointwise lower scalar curvature bounds for C0 metrics via regularizing Ricci flow
Burkhardt-Guim
Paula

We propose a class of local definitions of weak lower scalar curvature bounds that is well defined for C0 metrics. We show the following: that our definitions are stable under greater-than-second

D. Stern - Harmonic map methods in spectral geometry
Conférence
01:00:08
D. Stern - Harmonic map methods in spectral geometry
Stern
Daniel

Over the last fifty years, the problem of finding sharp upper bounds for area-normalized Laplacian eigenvalues on closed surfaces has attracted the attention of many geometers, due in part to

M. Lesourd - Positive Scalar Curvature on Noncompact Manifolds and the Positive Mass Theorem
Conférence
01:15:11
M. Lesourd - Positive Scalar Curvature on Noncompact Manifolds and the Positive Mass Theorem
Lesourd
Martin

The study of positive scalar curvature on noncompact manifolds has seen significant progress in the last few years. A major role has been played by Gromov's results and conjectures, and in

Y. Lai - A family of 3d steady gradient Ricci solitons that are flying wings
Conférence
01:02:33
Y. Lai - A family of 3d steady gradient Ricci solitons that are flying wings
Lai
Yi

We find a family of 3d steady gradient Ricci solitons that are flying wings. This verifies a conjecture by Hamilton. For a 3d flying wing, we show that the scalar curvature does not vanish at

C. Li - Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions
Conférence
01:03:34
C. Li - Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions
Li
Chao

In this talk, I will discuss some recent developments on the topology of closed manifolds admitting Riemannian metrics of positive scalar curvature. In particular, we will prove if a closed PSC

D. Semola - Boundary regularity and stability under lower Ricci bounds
Conférence
01:02:13
D. Semola - Boundary regularity and stability under lower Ricci bounds
Semola
Daniele

The theory of non smooth spaces with lower Ricci Curvature bounds has undergone huge developments in the last thirty years. On the one hand the impetus came from Gromov’s precompactness theorem

A. Mondino - Time-like Ricci curvature bounds via optimal transport
Conférence
01:14:44
A. Mondino - Time-like Ricci curvature bounds via optimal transport
Mondino
Andrea

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

R. Bamler - Compactness and partial regularity theory of Ricci flows in higher dimensions
Conférence
01:13:18
R. Bamler - Compactness and partial regularity theory of Ricci flows in higher dimensions
Bamler
Richard H.

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.

R. Perales - Recent Intrinsic Flat Convergence Theorems
Conférence
00:54:15
R. Perales - Recent Intrinsic Flat Convergence Theorems
Perales Aguilar
Raquel

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

T. Ozuch - Noncollapsed degeneration and desingularization of Einstein 4-manifolds
Conférence
01:03:54
T. Ozuch - Noncollapsed degeneration and desingularization of Einstein 4-manifolds
Ozuch
Tristan

We study the noncollapsed singularity formation of Einstein 4-manifolds. We prove that any smooth Einstein 4-manifold close to a singular one in a mere Gromov-Hausdorff (GH) sense is the result

F. Schulze - Mean curvature flow with generic initial data
Conférence
01:01:55
F. Schulze - Mean curvature flow with generic initial data
Schulze
Felix

Mean curvature flow is the gradient flow of the area functional and constitutes a natural geometric heat equation on the space of hypersurfaces in an ambient Riemannian manifold. It is believed,

A. Song - On the essential minimal volume of Einstein 4-manifolds
Conférence
00:56:53
A. Song - On the essential minimal volume of Einstein 4-manifolds
Song
Antoine

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

A. Lytchak - Convex subsets in generic manifolds
Cours
00:52:01
A. Lytchak - Convex subsets in generic manifolds
Lytchak
Alexander

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

C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 4
Cours
01:36:18
C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 4
Sormani
Christina

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

C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 3
Cours
01:43:31
C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 3
Sormani
Christina

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

C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 2
Cours
01:32:52
C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 2
Sormani
Christina

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

C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 1
Cours
01:21:32
C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 1
Sormani
Christina

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

F. Schulze - An introduction to weak mean curvature flow 3
Cours
01:23:01
F. Schulze - An introduction to weak mean curvature flow 3
Schulze
Felix

It has become clear in recent years that to understand mean curvature flow through singularities it is essential to work with weak solutions to mean curvature flow. We will give a brief

F. Schulze - An introduction to weak mean curvature flow 2
Cours
01:27:35
F. Schulze - An introduction to weak mean curvature flow 2
Schulze
Felix

It has become clear in recent years that to understand mean curvature flow through singularities it is essential to work with weak solutions to mean curvature flow. We will give a brief

F. Schulze - An introduction to weak mean curvature flow 1
Cours
01:26:28
F. Schulze - An introduction to weak mean curvature flow 1
Schulze
Felix

It has become clear in recent years that to understand mean curvature flow through singularities it is essential to work with weak solutions to mean curvature flow. We will give a brief

T. Richard - Advanced basics of Riemannian geometry 4
Cours
01:34:50
T. Richard - Advanced basics of Riemannian geometry 4
Richard
Thomas

We will present some of the tools used by the more advanced lectures. The topics discussed will include : Gromov Hausdorff distance, comparison theorems for sectional and Ricci curvature, the

T. Richard - Advanced basics of Riemannian geometry 3
Cours
01:30:19
T. Richard - Advanced basics of Riemannian geometry 3
Richard
Thomas

We will present some of the tools used by the more advanced lectures. The topics discussed will include : Gromov Hausdorff distance, comparison theorems for sectional and Ricci curvature, the

T. Richard - Advanced basics of Riemannian geometry 2
Cours
01:21:32
T. Richard - Advanced basics of Riemannian geometry 2
Richard
Thomas

We will present some of the tools used by the more advanced lectures. The topics discussed will include : Gromov Hausdorff distance, comparison theorems for sectional and Ricci curvature, the

T. Richard - Advanced basics of Riemannian geometry 1
Cours
01:30:43
T. Richard - Advanced basics of Riemannian geometry 1
Richard
Thomas

We will present some of the tools used by the more advanced lectures. The topics discussed will include : Gromov Hausdorff distance, comparison theorems for sectional and Ricci curvature, the

A. Mondino - Metric measure spaces satisfying Ricci curvature lower bounds 4
Cours
01:44:26
A. Mondino - Metric measure spaces satisfying Ricci curvature lower bounds 4
Mondino
Andrea

The 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

A. Mondino - Metric measure spaces satisfying Ricci curvature lower bounds 3
Cours
01:41:38
A. Mondino - Metric measure spaces satisfying Ricci curvature lower bounds 3
Mondino
Andrea

The 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

A. Mondino - Metric measure spaces satisfying Ricci curvature lower bounds 2
Cours
01:44:16
A. Mondino - Metric measure spaces satisfying Ricci curvature lower bounds 2
Mondino
Andrea

The 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

A. Mondino - Metric measure spaces satisfying Ricci curvature lower bounds 1
Cours
01:46:04
A. Mondino - Metric measure spaces satisfying Ricci curvature lower bounds 1
Mondino
Andrea

The 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

G. Courtois - Compactness and Finiteness Results for Gromov-Hyperbolic Spaces 4
Cours
01:28:17
G. Courtois - Compactness and Finiteness Results for Gromov-Hyperbolic Spaces 4
Courtois
Gilles
Besson
Gérard

This is a series of lectures on Bishop--Gromov's type inequalities adapted to metric spaces. We consider the case of Gromov-hyperbolic spaces and draw consequences of these inequalities such as

G. Courtois - Compactness and Finiteness Results for Gromov-Hyperbolic Spaces 3
Cours
01:25:55
G. Courtois - Compactness and Finiteness Results for Gromov-Hyperbolic Spaces 3
Courtois
Gilles
Besson
Gérard

This is a series of lectures on Bishop--Gromov's type inequalities adapted to metric spaces. We consider the case of Gromov-hyperbolic spaces and draw consequences of these inequalities such as

G. Courtois - Compactness and Finiteness Results for Gromov-Hyperbolic Spaces 2
Cours
01:28:23
G. Courtois - Compactness and Finiteness Results for Gromov-Hyperbolic Spaces 2
Courtois
Gilles
Besson
Gérard

This is a series of lectures on Bishop--Gromov's type inequalities adapted to metric spaces. We consider the case of Gromov-hyperbolic spaces and draw consequences of these inequalities such as

G. Courtois - Compactness and Finiteness Results for Gromov-Hyperbolic Spaces 1
Cours
01:37:09
G. Courtois - Compactness and Finiteness Results for Gromov-Hyperbolic Spaces 1
Courtois
Gilles
Besson
Gérard

This is a series of lectures on Bishop--Gromov's type inequalities adapted to metric spaces. We consider the case of Gromov-hyperbolic spaces and draw consequences of these inequalities such as

P. Castillon - CAT(k)-spaces 4
Cours
01:20:14
P. Castillon - CAT(k)-spaces 4
Besson
Gérard
Castillon
Philippe

The purpose of this course is to introduce the synthetic treatment of sectional curvature upper-bound on metric spaces. The basic idea of A.D. Alexandrov was to characterize the curvature bounds

P. Castillon - CAT(k)-spaces 3
Cours
01:35:14
P. Castillon - CAT(k)-spaces 3
Besson
Gérard
Castillon
Philippe

The purpose of this course is to introduce the synthetic treatment of sectional curvature upper-bound on metric spaces. The basic idea of A.D. Alexandrov was to characterize the curvature bounds

P. Castillon - CAT(k)-spaces 2
Cours
01:34:16
P. Castillon - CAT(k)-spaces 2
Besson
Gérard
Castillon
Philippe

The purpose of this course is to introduce the synthetic treatment of sectional curvature upper-bound on metric spaces. The basic idea of A.D. Alexandrov was to characterize the curvature bounds

R. Bamler - Uniqueness of Weak Solutions to the Ricci Flow and Topological Applications 4
Cours
00:57:39
R. Bamler - Uniqueness of Weak Solutions to the Ricci Flow and Topological Applications 4
Bamler
Richard H.

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

R. Bamler - Uniqueness of Weak Solutions to the Ricci Flow and Topological Applications 3
Cours
01:32:41
R. Bamler - Uniqueness of Weak Solutions to the Ricci Flow and Topological Applications 3
Bamler
Richard H.

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

R. Bamler - Uniqueness of Weak Solutions to the Ricci Flow and Topological Applications 2
Cours
01:31:24
R. Bamler - Uniqueness of Weak Solutions to the Ricci Flow and Topological Applications 2
Bamler
Richard H.

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

R. Bamler - Uniqueness of Weak Solutions to the Ricci Flow and Topological Applications 1
Cours
01:31:42
R. Bamler - Uniqueness of Weak Solutions to the Ricci Flow and Topological Applications 1
Bamler
Richard H.

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

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