Homotopy theory | Topology | Properties of topological spaces
In mathematics, a topological space X is contractible if the identity map on X is null-homotopic, i.e. if it is homotopic to some constant map. Intuitively, a contractible space is one that can be continuously shrunk to a point within that space. (Wikipedia).
This video explains the definition of a vector space and provides examples of vector spaces.
From playlist Vector Spaces
What exactly is space? Brian Greene explains what the "stuff" around us is. Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https:
From playlist Science Unplugged: Physics
Introduction to Metric Spaces - Definition of a Metric. - The metric on R - The Euclidean Metric on R^n - A metric on the set of all bounded functions - The discrete metric
From playlist Topology
Metric space definition and examples. Welcome to the beautiful world of topology and analysis! In this video, I present the important concept of a metric space, and give 10 examples. The idea of a metric space is to generalize the concept of absolute values and distances to sets more gener
From playlist Topology
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
Worldwide Calculus: Euclidean Space
Lecture on 'Euclidean Space' from 'Worldwide Multivariable Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Multivariable Spaces and Functions
What is a Vector Space? (Abstract Algebra)
Vector spaces are one of the fundamental objects you study in abstract algebra. They are a significant generalization of the 2- and 3-dimensional vectors you study in science. In this lesson we talk about the definition of a vector space and give a few surprising examples. Be sure to su
From playlist Abstract Algebra
Special Relativity: 2 - Spacetime Diagrams
An introduction to spacetime diagrams which are a valuable tool used to understand special relativity. The second in a series on special and general relativity. Let us know what you think of these videos by filling out our short survey at http://tinyurl.com/astronomy-pulsar. Thank you!
From playlist Special Relativity
Dual spaces and linear functionals In this video, I introduce the concept of a dual space, which is the analog of a "shadow world" version, but for vector spaces. I also give some examples of linear and non-linear functionals. This seems like an innocent topic, but it has a huge number of
From playlist Dual Spaces
What is General Relativity? Lesson 14: The covariant derivative of a covector
We start by demonstrating that contraction commutes with directional covariant derivative and then derive the CFREE and COMP expressions for the covariant derivative of a covector.
From playlist What is General Relativity?
What is a Tensor? Lesson 12 (redux): Contraction and index gymnastics
What is a Tensor? Lesson 12 (redux): Contraction and index gymnastics I have redone the index gymnastics lecture to try and fill in the details regarding contractions. I will keep them both in the playlist for now.
From playlist What is a Tensor?
What is General Relativity? Lesson 15 The covariant derivative of a (p,q)-rank tensor
In this lesson we review all the CFREE algebraic rules and the COMP conversions and then demonstrate the CFREE and COMP formulas for the covariant derivative of an arbitrary tensor.
From playlist What is General Relativity?
Matthew Zaremsky (5/21/21): Vietoris-Rips complexes and geometric group theory
This talk will serve as an overview of the role Vietoris-Rips complexes play in geometric group theory, and in particular in the study of topological finiteness properties of groups. Most famously, Rips proved that Vietoris-Rips complexes of hyperbolic groups are eventually contractible, w
From playlist Vietoris-Rips Seminar
Graham ELLIS - Computational group theory, cohomology of groups and topological methods 2
The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computation
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
F. Baudoin - Uniform sub-Laplacian comparison theorems on Sasakian manifolds
We will discuss sharp estimates for the sub-Laplacian of a family of distances converging to the sub-Riemannian one. We will deduce results for the sub-Riemannian distance. Uniform measure contraction properties will also be discussed. This is joint work with Erlend Grong, Kazumasa Kuwada
From playlist Journées Sous-Riemanniennes 2018
Some Lattice Subgroups that cannot Act on the line(after Deroin and Hurtado) by Dave Morris
PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis
From playlist Ergodic Theory and Dynamical Systems 2022
Paul Arne Østvær: A1 contractible varieties
The lecture was held within the framework of the Hausdorff Trimester Program : Workshop "K-theory in algebraic geometry and number theory"
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
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?
Tenth SIAM Activity Group on FME Virtual Talk
Speaker: Rene Carmona, Paul M. Wythes '55 Professor of Engineering and Finance, ORFE & PACM, Princeton University, Title: Contract theory and mean field games to inform epidemic models. Abstract: After a short introduction to contract theory, we review recent results on models involving
From playlist SIAM Activity Group on FME Virtual Talk Series
