Computing homology groups | Algebraic Topology | NJ Wildberger
The definition of the homology groups H_n(X) of a space X, say a simplicial complex, is quite abstract: we consider the complex of abelian groups generated by vertices, edges, 2-dim faces etc, then define boundary maps between them, then take the quotient of kernels mod boundaries at each
From playlist Algebraic Topology
Homotopy elements in the homotopy group π₂(S²) ≅ ℤ. Roman Gassmann and Tabea Méndez suggested some improvements to my original ideas.
From playlist Algebraic Topology
What do number theorists know about homotopy groups? - Piotr Pstragowski
Short Talks by Postdoctoral Members Topic: What do number theorists know about homotopy groups? Speaker: Piotr Pstragowski Affiliation: Member, School of Mathematics Date: September 29, 2022
From playlist Mathematics
Homotopy Group - (1)Dan Licata, (2)Guillaume Brunerie, (3)Peter Lumsdaine
(1)Carnegie Mellon Univ.; Member, School of Math, (2)School of Math., IAS, (3)Dalhousie Univ.; Member, School of Math April 11, 2013 In this general survey talk, we will describe an approach to doing homotopy theory within Univalent Foundations. Whereas classical homotopy theory may be des
From playlist Mathematics
Homotopy type theory: working invariantly in homotopy theory -Guillaume Brunerie
Short talks by postdoctoral members Topic: Homotopy type theory: working invariantly in homotopy theory Speaker: Guillaume Brunerie Affiliation: Member, School of Mathematics Date: September 26, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Introduction to Homotopy Theory- Part 5- Transition to Abstract Homotopy Theory
Credits: nLab: https://ncatlab.org/nlab/show/Introdu... Animation library: https://github.com/3b1b/manim Music: ► Artist Attribution • Music By: "KaizanBlu" • Track Name: "Remember (Extended Mix)" • YouTube Track Link: https://bit.ly/31Ma5s0 • Spotify Track Link: https://spoti.fi/
From playlist Introduction to Homotopy Theory
Group homomorphisms and isomorphisms
Jacob talks about homomorphisms and isomorphisms of groups, which are functions that can help you tell a lot about the properties of groups.
From playlist Basics: Group Theory
What is a Group Homomorphism? Definition and Example (Abstract Algebra)
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys What is a Group Homomorphism? Definition and Example (Abstract Algebra)
From playlist Abstract Algebra
Introduction to Homotopy Theory- PART 1: UNIVERSAL CONSTRUCTIONS
The goal of this series is to develop homotopy theory from a categorical perspective, alongside the theory of model categories. We do this with the hope of eventually developing stable homotopy theory, a personal goal a passion of mine. I'm going to follow nLab's notes, but I hope to add t
From playlist Introduction to Homotopy Theory
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
Ling Zhou (5/10/22): Persistent homotopy groups of metric spaces
By capturing both geometric and topological features of datasets, persistent homology has shown its promise in applications. Motivated by the fact that homotopy in general contains more information than homology, we study notions of persistent homotopy groups of compact metric spaces, toge
From playlist Bridging Applied and Quantitative Topology 2022
Ling Zhou (1/21/22): Persistent homotopy groups of metric spaces
In this talk, I will quickly overview previous work on discrete homotopy groups by Plaut et al. and Barcelo et al., and work blending homotopy groups with persistence, including those by Frosini and Mulazzani, Letscher, Jardine, Blumberg and Lesnick, and by Bantan et al. By capturing both
From playlist Vietoris-Rips Seminar
Pablo Suárez-Serrato: "Quantifying the Topology of Coma"
Deep Learning and Medical Applications 2020 "Quantifying the Topology of Coma" Pablo Suárez-Serrato - National Autonomous University of Mexico (UNAM), Instituto de Matemáticas Abstract: Whether comparing networks to each other or to random expectation, measuring similarity is essential t
From playlist Deep Learning and Medical Applications 2020
Christoph Winges: On the isomorphism conjecture for Waldhausen's algebraic K-theory of spaces
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "The Farrell-Jones conjecture" I will survey recent progress on the isomorphism conjecture for Waldhausen's "algebraic K-theory of spaces" functor, and how this relates to the original isomorp
From playlist HIM Lectures: Junior Trimester Program "Topology"
Topology in statistical physics - 3 by Subhro Bhattacharjee
PROGRAM BANGALORE SCHOOL ON STATISTICAL PHYSICS - XI (ONLINE) ORGANIZERS: Abhishek Dhar and Sanjib Sabhapandit DATE: 29 June 2020 to 10 July 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the school will be conducted thro
From playlist Bangalore School on Statistical Physics - XI (Online)
Charles Rezk - 3/4 Higher Topos Theory
Course at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/RezkNotesToposesOnlinePart3.pdf In this series of lectures I will give an introduction to the concept of "infinity
From playlist Toposes online
Invariant homotopy theory in the univalent foundations - Guillaume Brunerie
Topic: Invariant homotopy theory in the univalent foundations Speaker: Guillaume Brunerie, Member, School of Mathematics Time/Room: 4:00pm - 4:15pm/S-101 More videos on http://video.ias.edu
From playlist Mathematics
Almgren's isomorphism theorem and parametric isoperimetric inequalities - Yevgeny Liokumovich
Variational Methods in Geometry Seminar Topic: Almgren's isomorphism theorem and parametric isoperimetric inequalities Speaker: Yevgeny Liokumovich Affiliation: Massachusetts Institute of Technology; Member, School of Mathematics Date: November 20, 2018 For more video please visit http:/
From playlist Variational Methods in Geometry
Homomorphisms in abstract algebra
In this video we add some more definition to our toolbox before we go any further in our study into group theory and abstract algebra. The definition at hand is the homomorphism. A homomorphism is a function that maps the elements for one group to another whilst maintaining their structu
From playlist Abstract algebra
Fedor Manin (3/19/22): Linear nullhomotopies of maps to spheres
I will explain some aspects of how to build (null)homotopies of maps to simply connected spaces with controlled Lipschitz constant. Most of the difficulties appear already in the case of maps between spheres, where the result is as follows: every nullhomotopic, $L$-Lipschitz map $S^m \to
From playlist Vietoris-Rips Seminar