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
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
Homophily Solution - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
Lecture 14: The Definition of TC
In this video, we finally give the definition of topological cyclic homology. In fact, we will give two definitions: the first is abstract in terms of a mapping spectrum spectrum in cyclotomic spectra and then we unfold this to a concrete definition on terms of negative topological cyclic
From playlist Topological Cyclic Homology
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
Homophily - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
Lecture 5: Periodic and cyclic homology
In this video, we construct periodic and cyclic homology and compute examples. 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/WebHop/user
From playlist Topological Cyclic Homology
An introduction to homology | Algebraic Topology | NJ Wildberger
We briefly describe the higher homotopy groups which extend the fundamental group to higher dimensions, trying to capture what it means for a space to have higher dimensional holes. Homology is a commutative theory which also deals with this issue, assigning to a space X a series of homolo
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
Kai Smith: Character Varieties of Tangles and Singular Instanton Homology
Kai Smith, Indiana University Title: Character Varieties of Tangles and Singular Instanton Homology Singular Instanton Homology ($I^\natural$) is a knot homology theory defined by Kronheimer and Mrowka which has been instrumental in proving fundamental facts about Khovanov homology. Unfort
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Knots, three-manifolds and instantons – Peter Kronheimer & Tomasz Mrowka – ICM2018
Plenary Lecture 11 Knots, three-manifolds and instantons Peter Kronheimer & Tomasz Mrowka Abstract: Over the past four decades, input from geometry and analysis has been central to progress in the field of low-dimensional topology. This talk will focus on one aspect of these developments
From playlist Plenary Lectures
An introduction to persistent homology
Title: An introduction to persistent homology Venue: Webinar for DELTA (Descriptors of Energy Landscape by Topological Analysis Abstract: This talk is an introduction to applied and computational topology, in particular as related to the study of energy landscapes arising in chemistry. W
From playlist Tutorials
Henry Adams (6/4/20): Descriptors of Energy Landscapes using Topological Analysis (DELTA)
Title: Descriptors of Energy Landscapes using Topological Analysis (DELTA) Abstract: Many of the properties of a chemical system are described by its energy landscape, a real-valued function defined on a high-dimensional domain. I will explain how topology, and in particular persistent ho
From playlist DELTA (Descriptors of Energy Landscape by Topological Analysis), Webinar 2020
Omer Bobrowski: Random Simplicial Complexes, Lecture III
A simplicial complex is a collection of vertices, edges, triangles, tetrahedra and higher dimensional simplexes glued together. In other words, it is a higher-dimensional generalization of a graph. In recent years there has been a growing effort in developing the theory of random simplicia
From playlist Workshop: High dimensional spatial random systems
Stable Homotopy Seminar, 16: The Whitehead, Hurewicz, Universal Coefficient, and Künneth Theorems
These are some generalizations of facts from unstable algebraic topology that are useful for calculating in the category of spectra. The Whitehead and Hurewicz theorems say that a map of connective spectra that's a homology isomorphism is a weak equivalence, and that the lowest nonzero hom
From playlist Stable Homotopy Seminar
Classification of n-component links with Khovanov homology of rank 2^n - Boyu Zhang
Symplectic Dynamics/Geometry Seminar Topic: Classification of n-component links with Khovanov homology of rank 2^n Speaker: Boyu Zhang Affiliation: Princeton University Date: February 24, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Applied topology 6: Homology Abstract: We give a visual introduction to homology groups. Roughly speaking, i-dimensional homology "counts the number of i-dimensional holes" in a space. This video accompanies the class "Topological Data Analysis" at Colorado State University: https://www.
From playlist Applied Topology - Henry Adams - 2021
Sensors, sampling, and scale selection: a homological approach - Don Sheehy
Don Sheehy University of Connecticut April 18, 2015 In their seminal work on homological sensor networks, de Silva and Ghrist showed the surprising fact that its possible to certify the coverage of a coordinate free sensor network even with very minimal knowledge of the space to be covere
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