Structures on manifolds | Differential topology
In mathematics, a smooth structure on a manifold allows for an unambiguous notion of smooth function. In particular, a smooth structure allows one to perform mathematical analysis on the manifold. (Wikipedia).
Crystalline vs Amorphous materials
Materials are either crystalline or amorphous. They contain long-range periodic order or they do not. This leads to very different properties! Crystalline materials can be either polycrystalline or single crystal in nature. we can see evidence of single crystals in faceting of crystal face
From playlist Materials Sciences 101 - Introduction to Materials Science & Engineering 2020
Generalized Conway Game of Life - SmoothLife4
Oscillatory structures are also possible.
From playlist SmoothLife
Fractals are typically not self-similar
An explanation of fractal dimension. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/fractals-thanks And by Affirm: https://www.affirm.com/careers H
From playlist Explainers
Not-So-Close Packed Crystal Structures
A description of two crystal structures that are created from not-so-close packed structures.
From playlist Atomic Structures and Bonding
This video defines a cylindrical surface and explains how to graph a cylindrical surface. http://mathispower4u.yolasite.com/
From playlist Quadric, Surfaces, Cylindrical Coordinates and Spherical Coordinates
SmoothLife with three scales, i.e. outer radii differing by factors of 3, similar to McCabe's multiscale Turing patterns. The rules on all three scales are the same, although they could also be different. Download from sourceforge available http://sourceforge.net/projects/smoothlife/ .
From playlist SmoothLife
This came as a surprise. Although it looks like an example with smooth time-stepping, it is not. It is with original, simple time-stepping. I'm not exactly sure what this means. Maybe my smooth time-stepping method is superfluous.
From playlist SmoothLife
Prerequisites of a smooth function.
From playlist Advanced Calculus / Multivariable Calculus
Complex surfaces 4: Ruled surfaces
This talk gives an informal survey of ruled surfaces and their role in the Enriques classification. We give a few examples of ruled surfaces, summarize the basic invariants of surfaces, and sketch how one classifies the surfaces of Kodaira dimension minus infinity.
From playlist Algebraic geometry: extra topics
Derived orbifold chart lifts of flow categories and bimodules - Guangbo Xu
Guangbo Xu's Seminar Topic: Derived orbifold chart lifts of flow categories and bimodules Speaker: Guangbo Xu Affiliation: University of North Carolina; Member, School of Mathematics Date: October 14, 2022 In Hamiltonian Floer theory one needs to regularize infinitely many moduli spaces.
From playlist Mathematics
Helmut Hofer Institute for Advanced Study April 4, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Some algebro-geometric aspects of limiting mixed Hodge structure - Phillip Griffiths
Phillip Griffiths Professor Emeritus, School of Mathematics December 16, 2014 This will be an expository talk, mostly drawn from the literature and with emphasis on the several parameter case of degenerating families of algebraic varieties. More videos on http://video.ias.edu
From playlist Mathematics
Smoothing finite group actions on three-manifolds – John Pardon – ICM2018
Topology Invited Lecture 6.13 Smoothing finite group actions on three-manifolds John Pardon Abstract: There exist continuous finite group actions on three-manifolds which are not smoothable, in the sense that they are not smooth with respect to any smooth structure. For example, Bing co
From playlist Topology
Prerequisites III: Manifolds & Fiber Bundles - Maurice Weiler
Video recording of the First Italian Summer School on Geometric Deep Learning, which took place in July 2022 in Pescara. Slides: https://www.sci.unich.it/geodeep2022/slides/Manifolds_and_Fiber_Bundles.pdf
From playlist First Italian School on Geometric Deep Learning - Pescara 2022
Co-manifold learning with missing data - Eric Chi
Virtual Workshop on Missing Data Challenges in Computation Statistics and Applications Topic: Co-manifold learning with missing data Speaker: Eric Chi Date: September 9, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Manifolds 2.1 : Smooth and Differentiable Structures
In this video, I introduce smooth manifolds, C^k manifolds, as well as these on manifolds with boundary, the chart transition maps and C^k maps between manifolds. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet Playlist :
From playlist Manifolds
John Pardon, Smoothing finite group actions on three-manifolds
2018 Clay Research Conference, CMI at 20
From playlist CMI at 20
Hodge Theory -- From Abel to Deligne - Phillip Griffiths
Phillip Griffiths School of Mathematics, Institute for Advanced Study October 14, 2013 For more videos, visit http://video.ias.edu
From playlist Mathematics
AMS construction for Floer moduli spaces - Guangbo Xu
Guangbo Xu's Seminar Topic: AMS construction for Floer moduli spaces Speaker: Guangbo Xu Affiliation: University of North Carolina; Member, School of Mathematics Date: October 18, 2022 I will explain how to generalize Abouzaid-McLean-Smith's construction to Floer moduli spaces. As we nee
From playlist Mathematics
What Are Allotropes of Metalloids and Metals | Properties of Matter | Chemistry | FuseSchool
What Are Allotropes of Metalloids and Metals Learn the basics about allotropes of metalloids and metals, as a part of the overall properties of matter topic. An allotrope is basically a different form of the same element, each with distinct physical and chemical properties. For example
From playlist CHEMISTRY