List: Differential Geometry | Curated by Simon Kwan

Jun 30, 2023
20 stories
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Differential Geometry
Joseph Mellor
Differential Forms and TensorsThe Levi-Civita symbol allows us to take determinants and rewrite Differential Forms in terms of tensors.
Jun 26, 2023
1
Jun 26, 2023
1
In
Cantor’s Paradise
by
CasualPhysicsEnjoyer
Geometry as the Theatre of PhysicsWhat is a manifold, and how do physicists use it?
Sep 24, 2021
1
Sep 24, 2021
1
Joseph Mellor
The Generalized Stokes’ TheoremIf there were one theorem to rule them all, it would be the Generalized Stokes’ Theorem.
May 16, 2023
3
May 16, 2023
3
Joseph Mellor
k-Chains and k-CellsTo prove the Generalized Stokes’ Theorem, we’ll some way of defining a region and its boundary.
Apr 1, 2023
Apr 1, 2023
Joseph Mellor
An Intro to ManifoldsEuclidean space is the natural environment for Calculus, but manifolds allow us to extend Calculus to curved spaces.
Apr 11, 2023
2
Apr 11, 2023
2
Joseph Mellor
The Exterior DerivativeWe’re going to derive half the identities in Vector Calculus by introducing a powerful new operator.
Mar 10, 2023
1
Mar 10, 2023
1
rohola zandie
Discrete Laplacian (1)Sometimes revisiting old concepts can give us a fresh perspective. A few days ago, I was working with the Laplace operator and tried to…
Feb 4, 2023
Feb 4, 2023
rohola zandie
Discrete Laplacian (2)In our previous post, we explored the Laplacian in both continuous and discrete forms, and how they are related. Now, we will concentrate…
Feb 7, 2023
Feb 7, 2023
Joseph Mellor
An Intro to Differential FormsDifferential forms are powerful tools, but a lot of the geometric intuition is hidden behind the formalism. Let’s fix that.
Jan 25, 2023
2
Jan 25, 2023
2
Joseph Mellor
Vectors and CovectorsCovectors are dual to vectors, and they’re fundamental to differential forms and tensors.
Dec 26, 2022
3
Dec 26, 2022
3
In
Intuition Machine
by
Carlos E. Perez
The Emerging Information Geometric Approach to Deep Learning
Sep 29, 2015
Sep 29, 2015
In
TDS Archive
by
Rahul Bhadani
Mystical World of Information GeometryTales of geometry for information theory and machine learning
Nov 9, 2022
1
Nov 9, 2022
1
Miguel Taylor
Geometric deep learning — Convolutional Neural Networks on Graphs and ManifoldsGeometric deep learning is a new field of machine learning that can learn from complex data like graphs and multi-dimensional points. It…
Apr 22, 2019
Apr 22, 2019
Kazem Mirzaei
Neural Networks, Manifolds, and TopologyRecently, there’s been a great deal of excitement and interest in deep neural networks because they’ve achieved breakthrough results in…
Apr 1, 2019
4
Apr 1, 2019
4
In
Cantor’s Paradise
by
Jørgen Veisdal
The Poincaré ConjectureWhat is the shape of the universe?
Jul 6, 2019
6
Jul 6, 2019
6
Luca Ambrogioni
An intuitive look at differential formsForms are at first glance somewhat mysterious objects! Hopefully I will make you understand how natural they are and what they are there…
Sep 6, 2020
Sep 6, 2020
CasualPhysicsEnjoyer
Late Night Musings: EmbeddingsThe Subtle Geometry of Finding Manifolds in Bigger Manifolds
Nov 2, 2021
1
Nov 2, 2021
1
In
Cantor’s Paradise
by
CasualPhysicsEnjoyer
Fibre Bundles and FibrationsThe fascinating topology of Einstein’s theory of General Relativity
Oct 27, 2021
Oct 27, 2021
In
Intuition
by
Aidan Lytle
What the Heck is a Manifold? (Part I)A brief introduction to manifold theory, with some topology and analysis for good measure
Nov 20, 2021
3
Nov 20, 2021
3
In
Intuition
by
Panos Michelakis
Understanding the Laplacian and the Harmonic FunctionsThere are a plethora of important operators in mathematics that every engineer and physicist must know. We have already talked about the…
Jan 12, 2022
1
Jan 12, 2022
1