Measure theory | Definitions of mathematical integration
In the mathematical fields of differential geometry and geometric measure theory, homological integration or geometric integration is a method for extending the notion of the integral to manifolds. Rather than functions or differential forms, the integral is defined over currents on a manifold. The theory is "homological" because currents themselves are defined by duality with differential forms. To wit, the space Dk of k-currents on a manifold M is defined as the dual space, in the sense of distributions, of the space of k-forms Ωk on M. Thus there is a pairing between k-currents T and k-forms α, denoted here by Under this duality pairing, the exterior derivative goes over to a boundary operator defined by for all α ∈ Ωk. This is a homological rather than cohomological construction. (Wikipedia).
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
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
Homomorphisms (Abstract Algebra)
A homomorphism is a function between two groups. It's a way to compare two groups for structural similarities. Homomorphisms are a powerful tool for studying and cataloging groups. Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W ♦♦♦♦♦♦♦♦♦♦ W
From playlist Abstract Algebra
Isomorphisms in abstract algebra
In this video I take a look at an example of a homomorphism that is both onto and one-to-one, i.e both surjective and injection, which makes it a bijection. Such a homomorphism is termed an isomorphism. Through the example, I review the construction of Cayley's tables for integers mod 4
From playlist Abstract algebra
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
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
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
Integration 12 Trigonometric Integration Part 2 Example 4.mov
Another example of trigonometric integration.
From playlist Integration
Integration 1 Riemann Sums Part 1 - YouTube sharing.mov
Introduction to Riemann Sums
From playlist Integration
[BOURBAKI 2019] Manolescu’s work on the triangulation conjecture - Stipsicz - 15/06/19
András STIPSICZ Manolescu’s work on the triangulation conjecture The triangulation conjecture (asking whether a manifold is necessarily a simplicial complex) has been recently resolved in the negative by Ciprian Manolescu. His proof is based on work of Galweski–Stern and Matumoto, reduci
From playlist BOURBAKI - 2019
Dimers, networks, and integrable systems - Anton Izosimov
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Dimers, networks, and integrable systems Speaker: Anton Izosimov Affiliation: The University of Arizona Date: March 18, 2022 I will review two combinatorial constructions of integrable systems: Goncharov-Keny
From playlist Mathematics
Matthew Hedden - Irreducible homology S1xS2's which aren't zero surgeries on a knot
June 20, 2018 - This talk was part of the 2018 RTG mini-conference Low-dimensional topology and its interactions with symplectic geometry I'll discuss constructions of manifolds with the homology of S^1xS^2 which don't arise as Dehn surgery on a knot in S^3. Our examples have weight one
From playlist 2018 RTG mini-conference on low-dimensional topology and its interactions with symplectic geometry I
Paul Turner: A hitchhiker's guide to Khovanov homology - Part II
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 Geometry
Lukasz Fidkowski - Symmetry Protected Topological phases, cobordism, and QCA - IPAM at UCLA
Recorded 02 September 2021. Lukasz Fidkowski of the University of Washington presents "Symmetry Protected Topological phases, cobordism, and QCA" at IPAM's Graduate Summer School: Mathematics of Topological Phases of Matter. Abstract: We give an overview of the cobordism classification of
From playlist Graduate Summer School 2021: Mathematics of Topological Phases of Matter
Varolgunes 2022 02 18Reynaud models from relative Floer theory - Umut Varolgunes
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Reynaud models from relative Floer theory Speaker: Umut Varolgunes Affiliation: Boğaziçi University Date: February 18, 2022 I will start by explaining the construction of a formal scheme starting with an inte
From playlist Mathematics
Francis BROWN - Graph Complexes, Invariant Differential Forms and Feynman integrals
Kontsevich introduced the graph complex GC2 in 1993 and raised the problem of determining its cohomology. This problem is of renewed importance following the recent work of Chan-Galatius-Payne, who related it to the cohomology of the moduli spaces Mg of curves of genus g. It is known by Wi
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
Secondary products in SUSY QFT by Tudor Dimofte
Program: Quantum Fields, Geometry and Representation Theory ORGANIZERS : Aswin Balasubramanian, Saurav Bhaumik, Indranil Biswas, Abhijit Gadde, Rajesh Gopakumar and Mahan Mj DATE & TIME : 16 July 2018 to 27 July 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore The power of symmetries
From playlist Quantum Fields, Geometry and Representation Theory
Integration 12 Trigonometric Integration Part 2 Example 3.mov
Another example of trigonometric integration.
From playlist Integration
Xiang Tang: Cyclic Cocycles for Proper Lie Group Actions
Talk by Xiang Tang in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on February 23, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)