Topology (What is a Topology?)
What is a Topology? Here is an introduction to one of the main areas in mathematics - Topology. #topology Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additional cash, b
From playlist Topology
Astrophysics: Ch. 2 Star Equilibrium (2 of TBD) What Makes a Nebula Collapse into a Star?
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn what is needed to for a nebula to collapse into a star. Previous video in this series can be seen at: https://youtu.b
From playlist ASTROPHYSICS 2 STAR EQUILIBRIUM
What Is Dark Matter's Role In The Formation Of Galaxies?
Episode 3 of 5 Check us out on iTunes! http://testtube.com/podcast Please Subscribe! http://testu.be/1FjtHn5 While we don't really know where galaxies come from or how they form, we have several theories. Funnily enough, all of them seem to involve the mysterious dark matter. +
From playlist How The Universe And Everything In It Formed
I define closed sets, an important notion in topology and analysis. It is defined in terms of limit points, and has a priori nothing to do with open sets. Yet I show the important result that a set is closed if and only if its complement is open. More topology videos can be found on my pla
From playlist Topology
Topology 1.3 : Basis for a Topology
In this video, I define what a basis for a topology is. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Topology
This video is about compactness and some of its basic properties.
From playlist Basics: Topology
Teach Astronomy - Topology of the Universe
http://www.teachastronomy.com/ Astronomers sometimes talk about the topology of the universe which is a mathematical description of the three dimensional structure in terms of mathematical shapes. Using this formalism astronomers are of course simplifying something that's actually very co
From playlist 20. Galaxy Interaction and Motion
Definition of a Topological Space
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Topological Space
From playlist Topology
A. Song - On the essential minimal volume of Einstein 4-manifolds
Given a positive epsilon, a closed Einstein 4-manifold admits a natural thick-thin decomposition. I will explain how, for any delta, one can modify the Einstein metric to a bounded sectional curvature metric so that the thick part has volume linearly bounded by the Euler characteristic and
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Randomness and topology in correlated insulators by Itamar Kimchi
PROGRAM FRUSTRATED METALS AND INSULATORS (HYBRID) ORGANIZERS: Federico Becca (University of Trieste, Italy), Subhro Bhattacharjee (ICTS-TIFR, India), Yasir Iqbal (IIT Madras, India), Bella Lake (Helmholtz-Zentrum Berlin für Materialien und Energie, Germany), Yogesh Singh (IISER Mohali, In
From playlist FRUSTRATED METALS AND INSULATORS (HYBRID, 2022)
A. Song - On the essential minimal volume of Einstein 4-manifolds (version temporaire)
Given a positive epsilon, a closed Einstein 4-manifold admits a natural thick-thin decomposition. I will explain how, for any delta, one can modify the Einstein metric to a bounded sectional curvature metric so that the thick part has volume linearly bounded by the Euler characteristic and
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
John Morgan, Perelman's work on the Poincaré Conjecture and geometrization of 3-manifolds
2018 Clay Research Conference, CMI at 20 Correction: the work cited at 1:02:30 is of Richard Bamler.
From playlist CMI at 20
A. Song - What is the (essential) minimal volume? 1 (version temporaire)
I will discuss the notion of minimal volume and some of its variants. The minimal volume of a manifold is defined as the infimum of the volume over all metrics with sectional curvature between -1 and 1. Such an invariant is closely related to "collapsing theory", a far reaching set of resu
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
A. Song - What is the (essential) minimal volume? 1
I will discuss the notion of minimal volume and some of its variants. The minimal volume of a manifold is defined as the infimum of the volume over all metrics with sectional curvature between -1 and 1. Such an invariant is closely related to "collapsing theory", a far reaching set of resu
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
How can mathematicians tell basketballs and donuts apart?
This video will give a very brief introduction to what kinds of problems are tackled in topology. Specifically, how algebraic tools can be used to determine whether or not two objects are the "same" topologically. This video is for Grant Sanderson's (i.e. 3blue1brown) "Summer of Math Exp
From playlist Summer of Math Exposition Youtube Videos
Abhishek Rathod (7/27/70): Hardness results in discrete Morse theory for 2-complexes
Title: Hardness results in discrete Morse theory for 2-complexes Abstract: In this talk, we will discuss the problem of minimizing the number of critical simplices (Min-Morse Matching) from the point of view of inapproximability and parameterized complexity. Letting n denote the size of a
From playlist ATMCS/AATRN 2020
A. Wright - Mirzakhani's work on Earthquakes (Part 1)
We will give the proof of Mirzakhani's theorem that the earthquake flow and Teichmuller unipotent flow are measurably isomorphic. We will assume some familiarity with quadratic differentials, but no familiarity with earthquakes, and the first lecture will be devoted to preliminaries. The s
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
My submission for the Summer of Math Exposition competition: https://www.youtube.com/watch?v=ojjzXyQCzso An introduction to the idea behind the mathematical definition of continuity. If you are familiar with the epsilon-delta definition of continuity, you may recognise it here, where I
From playlist Summer of Math Exposition Youtube Videos