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

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 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 animation

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

From playlist Algebraic Topology

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

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

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

Algebraic Topology - 11.3 - Homotopy Equivalence

We sketch why that the homotopy category is a category.

From playlist Algebraic Topology

Group Homomorphisms - Abstract Algebra

A group homomorphism is a function between two groups that identifies similarities between them. This essential tool in abstract algebra lets you find two groups which are identical (but may not appear to be), only similar, or completely different from one another. Homomorphisms will be

From playlist Abstract Algebra

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

A geometric model for the bounded derived category of a gentle algebra, Sibylle Schroll Lecture 2

Gentle algebras are quadratic monomial algebras whose representation theory is well understood. In recent years they have played a central role in several different subjects such as in cluster algebras where they occur as Jacobian algebras of quivers with potentials obtained from triangula

From playlist Winter School on “Connections between representation Winter School on “Connections between representation theory and geometry"

Basic Homotopy Theory by Samik Basu

PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics

From playlist Dualities in Topology and Algebra (Online)

Even spaces and motivic resolutions - Michael Hopkins

Vladimir Voevodsky Memorial Conference Topic: Even spaces and motivic resolutions Speaker: Michael Hopkins Affiliation: Harvard University Date: September 13, 2018 For more video please visit http://video.ias.edu

From playlist Mathematics

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

Stable Homotopy Seminar, 9: Infinite Loop Spaces, and Homotopy Colimits

The fibrant spectra are the Ω-spectra, and we can give an elegant explicit description of the fibrant replacement. The "infinite loop space" functor, which is the derived right adjoint to the suspension spectrum, is then given by taking the 0th space of an equivalent Ω-spectrum. This allow

From playlist Stable Homotopy Seminar

Erin Wolf Chambers (5/12/22): Computing optimal homotopies

The question of how to measure similarity between curves in various settings has received much attention recently, motivated by applications in GIS data analysis, medical imaging, and computer graphics. Geometric measures such as Hausdorff and Fr\'echet distance have efficient algorithms,

From playlist Bridging Applied and Quantitative Topology 2022

Christoph Winges: Automorphisms of manifolds and the Farrell Jones conjectures

The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. Building on previous work of Bartels, Lück, Reich and others studying the algebraic K-theory and L-theory of discrete group rings, the validity of the Farrell-Jones Conjecture has be

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

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