The all important concept of curvature. We look at two equations for curvature and introduce the radius of curvature.
From playlist Life Science Math: Vectors
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
Curvature for the general parabola | Differential Geometry 13 | NJ Wildberger
We now extend the discussion of curvature to a general parabola, not necessarily one of the form y=x^2. This involves first of all understanding that a parabola is defined projectively as a conic which is tangent to the line at infinity. We find the general projective 3x3 matrix for suc
From playlist Differential Geometry
Reference: Differential Geometry by Do Carmo My first video! Thank you for coming and any suggestion is very welcomed! #some2
From playlist Summer of Math Exposition 2 videos
Curvature and Radius of Curvature for 2D Vector Function
This video explains how to determine curvature using short cut formula for a vector function in 2D.
From playlist Vector Valued Functions
Quadratic curvature for algebraic curves | Differential Geometry 14 | NJ Wildberger
In this video we extend the discussion of curvature from parabolas to more general conics, and hence to more general algebraic curves. The advantage of basing things on the parabola is that we get nice connections between curvature and the foci, and that once we move to studying surfaces i
From playlist Differential Geometry
Curvature for the general paraboloid | Differential Geometry 28 | NJ Wildberger
Here we introduce a somewhat novel approach to the curvature of a surface. This follows the discussion in DiffGeom23, where we looked at a paraboloid as a function of the form 2z=ax^2+2bxy+cy^2. In this lecture we generalize the discussion to the important case of a paraboloid, which we
From playlist Differential Geometry
Kyle Broder -- Recent Developments Concerning the Schwarz Lemma
A lecture I gave at the Beijing International Center for Mathematical Research geometric analysis seminar. The title being Recent Developments Concerning the Schwarz Lemma with applications to the Wu--Yau Theorem. This contains some recent results concerning the Bochner technique for the G
From playlist Research Lectures
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
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
Code-It-Yourself! Retro Arcade Racing Game - Programming from Scratch (Quick and Simple C++)
And it's Go, Go, Go! This video shows how to create a simple retro style racing game in quick and simple C++. By using simple maths and rules, quite a complex game can be presented. I like the purity of this, underneath the rules are boring, but when presented as a racing game, the enjoyme
From playlist Code-It-Yourself!
Mathematical Research Lecture -- Kyle Broder -- Curvature and Moduli
A recent talk I gave concerning the link between the curvature of the total space of a family of compact complex manifolds and the moduli-theoretic behaviour of the fibres. Part of this research appears in my Ph.D. thesis, and will appear in an upcoming preprint. 💪🙏 Support the channel b
From playlist Research Lectures
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
Parvaneh Joharinad (7/27/22): Curvature of data
Abstract: How can one determine the curvature of data and how does it help to derive the salient structural features of a data set? After determining the appropriate model to represent data, the next step is to derive the salient structural features of data based on the tools available for
From playlist Applied Geometry for Data Sciences 2022
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
T. Richard - Advanced basics of Riemannian geometry 4 (version temporaire)
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 Bochner formula and basics of Ricci flow.
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
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
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
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics