Manifolds #5: Tangent Space (part 1)
Today, we introduce the notion of tangent vectors and the tangent vector space at a point on a manifold.
From playlist Manifolds
Manifolds 1.3 : More Examples (Animation Included)
In this video, I introduce the manifolds of product manifolds, tori/the torus, real vectorspaces, matrices, and linear map spaces. This video uses a math animation for visualization. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : http://docdro.id/5koj5
From playlist Manifolds
What is a Manifold? Lesson 15: The cylinder as a quotient space
What is a Manifold? Lesson 15: The cylinder as a quotient space This lesson covers several different ideas on the way to showing how the cylinder can be described as a quotient space. Lot's of ideas in this lecture! ... too many probably....
From playlist What is a Manifold?
What is the 4th Dimension REALLY? - 4D Golf Devlog #2
A more practical explanation for those interested in exploring 4D spaces. For those not already familiar with basic 4D concepts, here's some videos I can recommend: "Visualizing 4D Geometry" https://www.youtube.com/watch?v=4URVJ3D8e8k "The things you'll find in higher dimensions" https:/
From playlist 4D Golf
Manifolds - Part 6 - Second-Countable Space
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From playlist Manifolds
Manifolds 1.5 : Manifolds with Boundary (Animation Included)
CORRECTION : https://youtu.be/quqk2X_zvB8 In this video, I introduce manifolds with boundary, including the famous Mobius Strip. This video uses a math animation for visualization. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet Playlist :
From playlist Manifolds
Manifolds #4: Differentiability
Today, we take a look at a look at how to define the differentiability of a function involving a manifold. This will allow us to define the notion of a tangent vector space in the following video.
From playlist Manifolds
Geometry and Arithmetic of Calabi-Yau Manifolds by Philip Candelas FRS
07 April 2017, 16:00 to 17:00 VENUE: Ramanujan Lecture Hall, ICTS, Bangalore Calabi-Yau manifolds play an important role in physics owing to the part they play in passing from a 10-dimensional string theory vacuum to the observed world of four dimensions. The process of calculating the
From playlist DISTINGUISHED LECTURES
PiTP-String Compactifications, Part 1 - Edward Witten
PiTP-String Compactifications, Part 1 Edward Witten Institute for Advanced Study July 24, 2008
From playlist PiTP 2008
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
On the Gromov width of polygon spaces - Alessia Mandini
Alessia Mandini University of Pavia October 31, 2014 After Gromov's foundational work in 1985, problems of symplectic embeddings lie in the heart of symplectic geometry. The Gromov width of a symplectic manifold (M,ω)(M,ω) is a symplectic invariant that measures, roughly speaking, the siz
From playlist Mathematics
What is a Manifold? Lesson 9: The Tangent Space-Definition
What is a Manifold? Lesson 9: The Tangent Space-Definition This lesson is longer than the others because it is rather technical. I made a slip up at about minute 56 which is annotated in the video and mentioned in the first comment.
From playlist What is a Manifold?
Homology Smale-Barden manifolds with K-contact and Sasakian structures by Aleksy Tralle
Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio
From playlist Higgs Bundles
A frontal view on Lefschetz fibrations II - Rodger Casals
Augmentations and Legendrians at the IAS Topic: A frontal view on Lefschetz fibrations II Speaker: Roger Casals Date: Friday, February 12 In this series of two talks we will discuss Weinstein structures endowed with a Lefschetz fibration in terms of the Legendrian front projection. The ma
From playlist Mathematics
Stochastic Model Reduction in Climate Science by Georg Gottwald (Part 4)
ORGANIZERS: Amit Apte, Soumitro Banerjee, Pranay Goel, Partha Guha, Neelima Gupte, Govindan Rangarajan and Somdatta Sinha DATES: Monday 23 May, 2016 - Saturday 23 Jul, 2016 VENUE: Madhava Lecture Hall, ICTS, Bangalore This program is first-of-its-kind in India with a specific focus to p
From playlist Summer Research Program on Dynamics of Complex Systems
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
Dynamics and Bifurcations of Piecewise - Smooth ODEs (Lecture 2) by David Simpson
PROGRAM DYNAMICS OF COMPLEX SYSTEMS 2018 ORGANIZERS Amit Apte, Soumitro Banerjee, Pranay Goel, Partha Guha, Neelima Gupte, Govindan Rangarajan and Somdatta Sinha DATE: 16 June 2018 to 30 June 2018 VENUE: Ramanujan hall for Summer School held from 16 - 25 June, 2018; Madhava hall for W
From playlist Dynamics of Complex systems 2018
Manifolds 1.2 : Examples of Manifolds
In this video, I describe basic examples of manifolds. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : http://docdro.id/IZO0G25
From playlist Manifolds
What is General Relativity? Lesson 8: Intro to the metric connection and the induced metric.
This lesson is an introduction to the concept of the metric connection followed by a long exercise in classical differential geometry. It is a long lesson because I complete a full example: the derivation of the metric of the "glome" induced by the Euclidean metric of 4-dimensional space.
From playlist What is General Relativity?