Notions of Scalar Curvature - Mikhail Gromov
Emerging Topics Working Group Topic: Notions of Scalar Curvature Speaker: Mikhail Gromov Affiliation: IHES Date: October 16, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Mikhail Gromov - Invitation to scalar curvature
There are three great domains in geometry, which lie on the boundary of "soft" and "rigid": (1) low dimensional, especially 4-dimensional topology/geometry; (2) symplectic topology/geometry; (3) scalar curvature bounded from below. I will try to elucidate in my lecture common fe
From playlist Not Only Scalar Curvature Seminar
Yuguang Shi - Quasi-local mass and geometry of scalar curvature
Quasi-local mass is a basic notion in General Relativity. Geometrically, it can be regarded as a geometric quantity of a boundary of a 3-dimensional compact Riemannian manifold. Usually, it is in terms of area and mean curvature of the boundary. It is interesting to see that some of quasi
From playlist Not Only Scalar Curvature Seminar
Christian Bär - Boundary value problems for Dirac operators
This introduction to boundary value problems for Dirac operators will not focus on analytic technicalities but rather provide a working knowledge to anyone who wants to apply the theory, i.e. in the study of positive scalar curvature. We will systematically study "elliptic boundary conditi
From playlist Not Only Scalar Curvature Seminar
What is General Relativity? Lesson 68: The Einstein Tensor
What is General Relativity? Lesson 68: The Einstein Tensor The Einstein tensor defined! Using the Ricci tensor and the curvature scalar we can calculate the curvature scalar of a slice of a manifold using the Einstein tensor. Please consider supporting this channel via Patreon: https:/
From playlist What is General Relativity?
What is General Relativity? Lesson 65: Scalar curvature Part 14
What is General Relativity? Lesson 65: Scalar curvature Part 14 We continue our examination of Section 4.4.6 of "A Simple Introduction to Particle Physics Part II - Geometric Foundations of Relativity." We are pushing to the end of this analysis. In this lesson we work with a coordinate t
From playlist What is General Relativity?
What is General Relativity? Lesson 54 - Scalar Curvature Part 3: Riemann Normal Coordinates
What is General Relativity? Lesson 54 -Scalar Curvature Part 3 Riemann Normal Coordinates This is the second of a few lectures about the Scalar Curvature and its interpretation. The goal is to get us to a point where we can have an interpretation of the Einstein Tensor and therefore an i
From playlist What is General Relativity?
Artem Pulemotov -- The prescribed Ricci curvature problem on homogenous spaces
Lecture given by Professor Artem Pulemotov (University of Queensland) on the prescribed Ricci curvature problem on homogeneous spaces. This was recorded at the Banff International Research Station, the conference being Geometric Flows: Recent Developments and Applications (April 2015). Th
From playlist Research Lectures
What is General Relativity? Lesson 66: Scalar Curvature Part 15
What is General Relativity? Lesson 66: Scalar Curvature Part 15 We FINISH our examination of Section 4.4.6 of "A Simple Introduction to Particle Physics Part II - Geometric Foundations of Relativity." Here we finally learn how the scalar curvature can be interpreted as a correction to the
From playlist What is General Relativity?
What is General Relativity? Lesson 52: Scalar Curvature Part I
What is General Relativity? Lesson 52: Scalar Curvature Part I This is the first of a few lectures about the Scalar Curvature and its interpretation. The goal is to get us to a point where we can have an interpretation of the Einstein Tensor and therefore an interpretation of the Einstein
From playlist What is General Relativity?
Alice Chang: Conformal Geometry on 4-manifolds
Abstract: In this talk, I will report on the study of integral conformal invariants on 4-manifolds and applications to the study of topology and diffeomorphism type of a class of 4-manifolds. The key ingredient is the study of the integral of 2 of the Schouten tensor which is the part of i
From playlist Abel in... [Lectures]
Sun-Yung Alice Chang: Conformal Invariants and Differential Equations
This lecture was held at The University of Oslo, May 24, 2006 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations. Program for the Abel Lectures 2006 1. “A Scandinavian Chapter in Analysis” by Lennart Carleson, Kungliga Tekniska Högskolan, Swed
From playlist Abel Lectures
Emmy Noether Lecture: Conformal geometry on 4-manifolds — Sun-Yung Alice Chang — ICM2018
Conformal geometry on 4-manifolds Sun-Yung Alice Chang Abstract: In this talk, I will report on the study of a class of integral conformal invariants on 4-manifolds and applications to the study of topology and diffeomorphism type of a class of 4-manifolds. The key ingredient is the study
From playlist Special / Prizes Lectures
Liam Mazurowski - Recent developments in constant mean curvature hypersurfaces II
Continuing from the previous talk, we will first discuss two min-max theorems for constructing prescribed mean curvature hypersurfaces in non-compact spaces. The first concerns the existence of prescribed mean curvature hypersurfaces in Euclidean space, and the second concerns the existen
From playlist Not Only Scalar Curvature Seminar
Spacetime positive mass theorem - Lan-Hsuan Huang
Workshop on Geometric Functionals: Analysis and Applications Topic: Spacetime positive mass theorem Speaker: Lan-Hsuan Huang Affiliation: University of Connecticut; von Neumann Fellow, School of Mathematics Date: March 5, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Recent advances in Geometric Analysis - 8 June 2018
http://crm.sns.it/event/435 Centro di Ricerca Matematica Ennio De Giorgi The aim of the workshop is to bring together experts working on different sides of Geometric Analysis: PDE aspects, minimal or constant mean curvature surfaces, geometric inequalities, applications to general relativ
From playlist Centro di Ricerca Matematica Ennio De Giorgi
Xin Zhou - Recent developments in constant mean curvature hypersurfaces I
We will survey some recent existence theory of closed constant mean curvature hypersurfaces using the min-max method. We hope to discuss some old and new open problems on this topic as well. Xin Zhou (Cornell)
From playlist Not Only Scalar Curvature Seminar
Philippe G LeFloch - Weakly regular spacetimes with T2 symmetry
I will discuss the initial value problem for the Einstein equations and present results concerning the existence and asymptotic behavior of spacetimes, when the initial data set is assumed to be T2 symmetric and satisfies weak regularity conditions so that the spacetimes may exhibit impul
From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale
6C Second equation for curvature on the blackboard
In this lecture I show you a second equation for curvature.
From playlist Life Science Math: Vectors
Index Theory and Flexibility in Positive Scalar Curve Geometry -Bernhard Hanke
Emerging Topics Working Group Topic: Index Theory and Flexibility in Positive Scalar Curve Geometry Speaker: Bernhard Hanke Affilaion: Augsburg University Date: October 18, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics