Calculus 3: Vector Calculus in 2D (35 of 39) What is the Sign of Curvature?
Visit http://ilectureonline.com for more math and science lectures! In this video I will show how to identify what is the sign of a curvature. For example, when the angle is getting bigger K is greater than 0, and when the angle is getting smaller K is less than 0. Next video in the seri
From playlist CALCULUS 3 CH 3 VECTOR CALCULUS
Can you give a feel for how the math of General Relativity allows for anti-gravity?
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From playlist Science Unplugged: General Relativity
M. Lesourd - Positive Scalar Curvature on Noncompact Manifolds and the Positive Mass Theorem (vt)
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 particular the idea to use surfaces of prescribed mean curvature (as opposed to minimal surfaces). Ha
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
The meaning of positive curl in a fluid flow can sometimes look a bit different from the clear cut rotation-around-a-point examples discussed in previous videos.
From playlist Multivariable calculus
Curvature and Radius of Curvature for a function of x.
This video explains how to determine curvature using short cut formula for a function of x.
From playlist Vector Valued Functions
Jonathan Rosenberg: Positive scalar curvature on a class of spin pseudomanifolds.
Talk by Jonathan Rosenberg in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar on April 22, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
M. Lesourd - Positive Scalar Curvature on Noncompact Manifolds and the Positive Mass Theorem
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 particular the idea to use surfaces of prescribed mean curvature (as opposed to minimal surfaces). Ha
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Bernhard Hanke - Surgery, bordism and scalar curvature
One of the most influential results in scalar curvature geometry, due to Gromov-Lawson and Schoen-Yau, is the construction of metrics with positive scalar curvature by surgery. Combined with powerful tools from geometric topology, this has strong implications for the classification of suc
From playlist Not Only Scalar Curvature Seminar
Chao Li: Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions
Talk by Chao Li in Global Noncommutative Geometry Seminar (Americas) on December 3, 2021. https://globalncgseminar.org/talks/tba-18/
From playlist Global Noncommutative Geometry Seminar (Americas)
Rudolf Zeidler: Scalar curvature comparison via the Dirac operator
Talk by Rudolf Zeidler in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on September 23, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
Renato Bettiol - Scalar curvature rigidity and extremality in dimension 4
In this talk, I will discuss the Finsler--Thorpe trick for curvature operators in dimension 4, and how it can be combined with twisted spinor methods to show that large classes of compact 4-manifolds, with or without boundary, with nonnegative sectional curvature are area-extremal for scal
From playlist Not Only Scalar Curvature Seminar
Rudolf Zeidler - Scalar and mean curvature comparison via the Dirac operator
I will explain a spinorial approach towards a comparison and rigidity principle involving scalar and mean curvature for certain warped products over intervals. This is motivated by recent scalar curvature comparison questions of Gromov, in particular distance estimates under lower scalar c
From playlist Talks of Mathematics Münster's reseachers
Bobo Hua (7/27/22): Curvature conditions on graphs
Abstract: We will introduce various curvature notions on graphs, including combinatorial curvature for planar graphs, Bakry-Emery curvature, and Ollivier curvature. Under curvature conditions, we prove some analytic and geometric results for graphs with nonnegative curvature. This is based
From playlist Applied Geometry for Data Sciences 2022
Stephen Lynch: Collapsing and noncollapsing convex ancient solutions
Abstract: An important problem in mean curvature flow is to find conditions on initial data that rule out 'collapsing' singularity models, such as the Grim Reaper. A prevalent class of singularity models are the convex ancient solutions. We will discuss a result proven with T. Bourni and M
From playlist MATRIX-SMRI Symposium: Singularities in Geometric Flows
C. Li - Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions (version temporaire)
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 manifold of dimension 4 (resp. 5) has vanishing π2 (resp. vanishing π2 and π3), then a finite co
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
GPDE Workshop - Synthetic formulations - Cedric Villani
Cedric Villani IAS/ENS-France February 23, 2009 For more videos, visit http://video.ias.edu
From playlist Mathematics
Curvature of a Riemannian Manifold | Riemannian Geometry
In this lecture, we define the exponential mapping, the Riemannian curvature tensor, Ricci curvature tensor, and scalar curvature. The focus is on an intuitive explanation of the curvature tensors. The curvature tensor of a Riemannian metric is a very large stumbling block for many student
From playlist All Videos
C. Li - Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions
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 manifold of dimension 4 (resp. 5) has vanishing π2 (resp. vanishing π2 and π3), then a finite co
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics