Regular homotopy

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

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

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

Algebraic Topology - 11.3 - Homotopy Equivalence

We sketch why that the homotopy category is a category.

From playlist Algebraic Topology

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

Homotopy animation

An interesting homotopy (in fact, an ambient isotopy) of two surfaces.

From playlist Algebraic Topology

Introduction to Homotopy Theory- PART 2: (TOPOLOGICAL) HOMOTOPY

We move on to the second section of nLab's introduction to homotopy theory, homotopy. Topics covered include left/right homotopy, topolocial path/cylinder objects, homotopy groups, and weak/standard homotopy equivalences. PLEASE leave any misconceptions I had or inaccuracies in my video i

From playlist Introduction to Homotopy Theory

Graham ELLIS - Computational group theory, cohomology of groups and topological methods 2

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

Lie Groups and Lie Algebras: Lesson 34 -Introduction to Homotopy

Lie Groups and Lie Algebras: Introduction to Homotopy In order to proceed with Gilmore's study of Lie groups and Lie algebras we now need a concept from algebraic topology. That concept is the notion of homotopy and the Fundamental Group of a topological space. In this lecture we provide

From playlist Lie Groups and Lie Algebras

John Greenlees: The singularity category of C^*(BG) for a finite group G

SMRI Algebra and Geometry Online John Greenlees (Warwick University) Abstract: The cohomology ring H^*(BG) (with coefficients in a field k of characteristic p) is a very special graded commutative ring, but this comes out much more clearly if one uses the cochains C^*(BG), which can be vi

From playlist SMRI Algebra and Geometry Online

Introduction to Homotopy Theory- Part 4: Fibrations

Wow! This one was a lot more detailed than usual, so I'd really recommend going through the proofs with the nLab in hand. I tried to elucidate some of their explanations, but it's still good to have both, so hopefully in between both of our presentations you can find understanding. And as

From playlist Introduction to Homotopy Theory

Landau-Ginzburg - Seminar 6 - Matrix factorisations and geometry

This seminar series is about the bicategory of Landau-Ginzburg models LG, hypersurface singularities and matrix factorisations. In this seminar Rohan Hitchcock defines matrix factorisations and gives some examples, and explains how to extract an algebraic set from a matrix factorisation.

From playlist Metauni

Federico Binda: Towards a motivic homotopy theory without A1 invariance

The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. Federico Binda: Towards a motivic (homotopy) theory without A1-invariance Abstract: Motivic homotopy theory as conceived by Morel and Voevodsky is based on the crucial observation t

From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"

Homological Algebra(Homo Alg 1) by Graham Ellis

DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra

From playlist Group Theory and Computational Methods

Homotopy

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

Kęstutis Česnavičius - Purity for Flat Cohomology

The absolute cohomological purity conjecture of Grothendieck proved by Gabber ensures that on regular schemes étale cohomology classes of fixed cohomological degree extend uniquely over closed subschemes of large codimension. I will discuss the corresponding phenomenon for flat cohomology.

From playlist Journée Gretchen & Barry Mazur

Homomorphisms in abstract algebra examples

Yesterday we took a look at the definition of a homomorphism. In today's lecture I want to show you a couple of example of homomorphisms. One example gives us a group, but I take the time to prove that it is a group just to remind ourselves of the properties of a group. In this video th

From playlist Abstract algebra

Henry Adams (3/12/21): Vietoris-Rips thickenings: Problems for birds and frogs

An artificial distinction is to describe some mathematicians as birds, who from their high vantage point connect disparate areas of mathematics through broad theories, and other mathematicians as frogs, who dig deep into particular problems to solve them one at a time. Neither type of math

From playlist Vietoris-Rips Seminar