Mathematical software | Free mathematics software
SageManifolds (following styling of SageMath) is an extension fully integrated into SageMath, to be used as a package for differential geometry and tensor calculus. The official page for the project is sagemanifolds.obspm.fr. It can be used on CoCalc. SageManifolds deals with differentiable manifolds of arbitrary dimension. The basic objects are tensor fields and not in a given vector frame or coordinate chart. In other words, various charts and frames can be introduced on the manifold and a given tensor field can have representations in each of them. An important class of treated manifolds is that of pseudo-Riemannian manifolds, among which Riemannian manifolds and Lorentzian manifolds, with applications to General Relativity. In particular, SageManifolds implements the computation of the Riemann curvature tensor and associated objects (Ricci tensor, Weyl tensor). SageManifolds can also deal with generic affine connections, not necessarily Levi-Civita ones. (Wikipedia).
Manifolds - Part 2 - Interior, Exterior, Boundary, Closure
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From playlist Manifolds
Manifolds - Part 6 - Second-Countable Space
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From playlist Manifolds
In this #SHORTS video, we offer a brief idea of what a (smooth) manifold is. Smooth manifolds, topological manifolds, Riemannian manifolds, complex manifolds, are some of the main objects in the vast field of geometry. These spaces are (topological) spaces that are locally Euclidean. đź‘Ť To
From playlist All Videos
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
Éric Gourgoulhon : Calcul tensoriel formel sur les variétés différentielles - Partie 1
Résumé : Le calcul tensoriel sur les variétés différentielles comprend l'arithmétique des champs tensoriels, le produit tensoriel, les contractions, la symétrisation et l'antisymétrisation, la dérivée de Lie le long d'un champ vectoriel, le transport par une application différentiable (pul
From playlist Mathematical Aspects of Computer Science
Explaining by Removing: A Unified Framework for Model Explanation | AISC
Speaker(s): Ian Covert Host(s): Ali Al-Sherif Find the recording, slides, and more info at https://ai.science/e/explaining-by-removing-a-unified-framework-for-model-explanation--ao4ZaboI76dQLPhX40Bg Motivation / Abstract This work highlights the common patterns in 20+ different ML explan
From playlist Explainability and Ethics
Manifolds - Part 16 - Smooth Maps (Definition)
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From playlist Manifolds
Rebekah Palmer: Totally Geodesic Surfaces in Knot Complements with Small Crossing Number
Rebekah Palmer, Temple University Title: Totally Geodesic Surfaces in Knot Complements with Small Crossing Number Studying totally geodesic surfaces has been essential in understanding the geometry and topology of hyperbolic 3-manifolds. Recently, Bader-Fisher-Miller-Stover showed that con
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Manifolds - Part 4 - Quotient Spaces
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From playlist Manifolds
Pablo Portilla | TĂŞte-Ă -tĂŞte graphs and Seifert Manifolds
Worldwide Center of Mathematics Lecture Seminar Series
From playlist Center of Math Research: the Worldwide Lecture Seminar Series
Modern Inflation Cosmology - 2018
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From playlist Natural Sciences
Manifolds - Part 13 - Examples of Smooth Manifolds
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From playlist Manifolds
C0 contact geometry of isotropic submanifolds - Maksim Stokić
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Three 20-minute research talks Topic: C0 contact geometry of isotropic submanifolds Speaker: Maksim Stokić Affiliation: Tel Aviv University Date: May 27, 2022 Homeomorphism is called contact if it can be written a
From playlist Mathematics
In this video I recreate the talk I gave in defense of my masters thesis! Introduction (0:00) The object of my affection (1:01) Why care? (5:50) What I've done (10:30)
From playlist Unitary Schwartz forms & the Weil Representation
Graham ELLIS - Computational group theory, cohomology of groups and topological methods 4
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
How to get started with Graph ML? (Blog walkthrough)
❤️ Become The AI Epiphany Patreon ❤️ ► https://www.patreon.com/theaiepiphany ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ In this video, I walk you through my blog on getting started with Graph ML. I talk about research, learning, cool Graph ML apps, resources to get you started, my GAT project, and beyond!
From playlist Graph Neural Nets
Manifolds - Part 5 - Projective Space
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From playlist Manifolds
Manifolds - Part 1 - Introduction and Topology
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From playlist Manifolds
Michael R. Douglas - How will we do mathematics in 2030?
Abstract: We make the case that over the coming decade, computer assisted reasoning will become far more widely used in the mathematical sciences. This includes interactive and automatic theorem verification, symbolic algebra, and emerging technologies such as formal knowledge repositories
From playlist 2nd workshop Nokia-IHES / AI: what's next?