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
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
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 elements in the homotopy group π₂(S²) ≅ ℤ. Roman Gassmann and Tabea Méndez suggested some improvements to my original ideas.
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
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
Lie Algebras and Homotopy Theory - Jacob Lurie
Members' Seminar Topic: Lie Algebras and Homotopy Theory Speaker: Jacob Lurie Affiliation: Professor, School of Mathematics Date: November 11, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Thorsten Altenkirch - 1/2 Towards a Syntax for Cubical Type Theory
One of the key problems of Homotopy Type Theory is that it introduces axioms such as extensionality and univalence for which there is no known computational interpretation. We propose to overcome this by introducing a Type Theory where a heterogenous equality is defined recursively and equ
From playlist T2-2014 : Semantics of proofs and certified mathematics
Stable Homotopy Seminar, 17: Universal Coefficient Theorem, Moore Spectra, and Limits
We finish constructing the universal coefficient spectral sequence, and look at some classical examples involving Moore spectra. As it turns out, it's really easy in stable homotopy theory to invert or localize at a prime. In particular, *rational* stable homotopy theory is completely alge
From playlist Stable Homotopy Seminar
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
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
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
Marc Levine: The rational motivic sphere spectrum and motivic Serre finiteness
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist SPECIAL 7th European congress of Mathematics Berlin 2016.
Dan Ramras: Coassembly for representation spaces
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "The Farrell-Jones conjecture" I'll discuss models for a coassembly map (the topological Atiyah-Segal map) from representation spaces to topological K-theory. At its most basic, this map carrie
From playlist HIM Lectures: Junior Trimester Program "Topology"
Markus Banagl : The L-Homology fundamental class for singular spaces and the stratified Novikov
Abstract : An oriented manifold possesses an L-homology fundamental class which is an integral refinement of its Hirzebruch L-class and assembles to the symmetric signature. In joint work with Gerd Laures and James McClure, we give a construction of such an L-homology fundamental class for
From playlist Topology
Ling Zhou (8/30/21): Other Persistence Invariants: homotopy and the cohomology ring
In this work, we study both the notions of persistent homotopy groups and persistent cohomology rings. In the case of persistent homotopy, we pay particular attention to persistent fundamental groups for which we obtain a precise description via dendrograms, as a generalization of a simila
From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021
Geoffroy Horel - Knots and Motives
The pure braid group is the fundamental group of the space of configurations of points in the complex plane. This topological space is the Betti realization of a scheme defined over the integers. It follows, by work initiated by Deligne and Goncharov, that the pronilpotent completion of th
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
Univalent Foundations Seminar - Steve Awodey
Steve Awodey Carnegie Mellon University; Member, School of Mathematics November 19, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics