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
In this video, I cover the notion of continuity, as used in topology. The beautiful thing is that this doesn't use epsilon-delta at all, and instead just something purely geometric. Enjoy this topology-adventure! Topology Playlist: https://youtube.com/playlist?list=PLJb1qAQIrmmA13vj9xkHGG
From playlist Topology
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
Gluing is a good method to construct new topological spaces from known ones. Here a rectangles is glued along the edges to form a torus. Often the fundamental group of the glued object can be calculated from the pieces (here a rectangles) and the glue (here two intersecting circles). Th
From playlist Algebraic Topology
In this video, I define connectedness, which is a very important concept in topology and math in general. Essentially, it means that your space only consists of one piece, whereas disconnected spaces have two or more pieces. I also define the related notion of path-connectedness. Topology
From playlist 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
In this video, we give an important motivation for studying Topological Cyclic Homology, so called "trace methods". Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.php?qa=tc-lecture Homepage with further information: https://w
From playlist Topological Cyclic Homology
The role of topology and compactness (...) - CEB T2 2017 - Varadhan - 3/3
S.R.S. Varadhan (Courant Institute) - 09/06/2017 The role of topology and compactness in the theory of large deviations When a large deviation result is proved there is some topology involved in the statement because it affects the class of sets for which the estimates hold. Often the cho
From playlist 2017 - T2 - Stochastic Dynamics out of Equilibrium - CEB Trimester
Recursively Defined Sets - An Intro
Recursively defined sets are an important concept in mathematics, computer science, and other fields because they provide a framework for defining complex objects or structures in a simple, iterative way. By starting with a few basic objects and applying a set of rules repeatedly, we can g
From playlist All Things Recursive - with Math and CS Perspective
Spatial refinements and Khovanov homology – Robert Lipshitz & Sucharit Sarkar – ICM2018
Topology Invited Lecture 6.11 Spatial refinements and Khovanov homology Robert Lipshitz & Sucharit Sarkar Abstract: We review the construction and context of a stable homotopy refinement of Khovanov homology. © International Congress of Mathematicians – ICM www.icm2018.org Os direi
From playlist Topology
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
This is a short overview of the main content of our course on Topological Cyclic Homology. Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.php?qa=tc-lecture Homepage with further information: https://www.uni-muenster.de/IVV5WS
From playlist Topological Cyclic Homology
Timothy Gowers on the works of John Milnor
Sir William Timothy Gowers is a British mathematician and a Royal Society Research Professor at the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge. This video is a clip from the Abel Prize Announcement 2011.
From playlist Popular presentations
Sarit Agami (3/5/19): Modeling and replicating persistence diagrams
Title: Modeling and replicating persistence diagrams Abstract: Persistence diagrams are useful displays that give summary information about the topological features of some phenomenon. Usually, only one persistence diagram is available, and replicated persistence diagrams are needed for s
From playlist AATRN 2019
SHM - 16/01/15 - Constructivismes en mathématiques - Thierry Coquand
Thierry Coquand (Université de Gothenburg), « Théorie des types et mathématiques constructives »
From playlist Les constructivismes mathématiques - Séminaire d'Histoire des Mathématiques
Peter Scholze: The pro-etale site
Abstract: We explain our joint work with Bhargav Bhatt, whose goal is to simplify the foundations of ell-adic cohomology by introducing a new site, called the pro-etale site, in which the naive definition of ell-adic sheaves and the six functors is the correct one. The lecture was held wi
From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
Yuri Berest : Spaces of quasi-invariants
CONFERENCE Recording during the thematic meeting : « Chromatic Homotopy, K-Theory and Functors» the January 26, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathematicians on CIR
From playlist Topology
Wolfram Physics Project: Solving the Einstein Equations & Other PDEs Tuesday, Mar. 9, 2021
This is a Wolfram Physics Project working session on solving the Einstein equations and other PDE's in the Wolfram Model. Begins at 1:18 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check ou
From playlist Wolfram Physics Project Livestream Archive
Transport Layer Security: Part 1
Fundamental concepts of TLS are discussed. SSL is analyzed. HTTPS & SSH are presented.
From playlist Network Security