In algebraic topology, given a continuous map f: X → Y of topological spaces and a ring R, the pullback along f on cohomology theory is a grade-preserving R-algebra homomorphism: from the cohomology ring of Y with coefficients in R to that of X. The use of the superscript is meant to indicate its contravariant nature: it reverses the direction of the map. For example, if X, Y are manifolds, R the field of real numbers, and the cohomology is de Rham cohomology, then the pullback is induced by the pullback of differential forms. The homotopy invariance of cohomology states that if two maps f, g: X → Y are homotopic to each other, then they determine the same pullback: f* = g*. In contrast, a pushforward for de Rham cohomology for example is given by integration-along-fibers. (Wikipedia).
Coulomb's Law (2 of 7) Calculate the Force Between Two Charges
Using Coulomb's law shows how to calculate the magitude and direction of the electric force between two charged particles. Coulomb's law states that the magnitude of the force between two point charges is directly proportional to the product of the magnitudes of charges and inversely propo
From playlist Coulomb's Law and the Electric Force
Coulomb's Law (3 of 7) Force Between Two One Coulomb Charges
Using Coulomb's law shows how to calculate the electric force between two 1 Coulombs charges that are separated by a distance of 1 meter. Coulomb's law states that the magnitude of the force between two point charges is directly proportional to the product of the magnitudes of charges and
From playlist Coulomb's Law and the Electric Force
Coulomb's Law (7 of 7) Force on Three Charges Arranged in a Right Triangle
How to use Coulomb's law to calculate the net force on one charge from two other charges arranged in a right triangle. Coulomb's law states that the magnitude of the force between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportio
From playlist Coulomb's Law and the Electric Force
Coulomb's Law (6 of 7) Force from Three Charges Arranged in a Triangle
How to use Coulombs law to calculate the net force on one charge from two other charges arranged in a triangular shape. Coulomb's law states that the magnitude of the force between two point charges is directly proportional to the product of the magnitudes of charges and inversely proport
From playlist Coulomb's Law and the Electric Force
Newton’s Universal Gravitation vs Coulomb’s Law
This video explains the differences and similarities between Newton’s Universal Law of Gravitation and Coulomb’s Law for electrostatic forces. Newton’s Universal Law of Gravitation is used to calculate the magnitude of the force of attraction between two objects that have mass and Coulomb’
From playlist Coulomb's Law and the Electric Force
Coulomb's Law (5 of 7) Force from Three Charges in a Straight Line
How to use Coulomb's law to calculate the net force on one charge from two other charges. Coulomb's law states that the magnitude of the force between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the dist
From playlist Coulomb's Law and the Electric Force
Coulomb's Law (1 of 7) An Explanation
An explanation of coulombs law, the equation and the forces on charged particles. Coulomb's law states that the magnitude of the force between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance bet
From playlist Coulomb's Law and the Electric Force
Physics 12.2.1a - Coulomb`s Law
An explanation of Coulomb's Law. From the physics course by Derek Owens. The distance learning course is available at http://www.derekowens.com
From playlist Physics - Electric Charge
Cohomological Field Theories from GLSMs (Lecture 2) by David Favero
PROGRAM: VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE & TIME: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual fie
From playlist Vortex Moduli - 2023
Coulomb's Law (4 of 7) Force of a Proton and an Electron in Hydrogen Atom
Using Coulomb's law to calculate magnitude of the electric force between a proton and an electron in hydrogen atom. Coulomb's law states that the magnitude of the force between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional
From playlist Coulomb's Law and the Electric Force
Graham ELLIS - Computational group theory, cohomology of groups and topological methods 4
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
Tom Bachmann - Pullbacks for the Rost-Schmid Complex
Notes: https://nextcloud.ihes.fr/index.php/s/9AE3otsf8XJ6M8a Let 𝑘 be a perfect field and 𝑀 a strictly homotopy invariant sheaf of abelian groups on Sm_𝑘. The cousin complex can be used to compute the cohomology of a smooth variety 𝑋 over 𝑘 with coefficients in 𝑀. However, if 𝑋 → 𝑌 is a m
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
Lars Hesselholt: Around topological Hochschild homology (Lecture 3)
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "Workshop: Hermitian K-theory and trace methods" Introduced by Bökstedt in the late eighties, topological Hochschild homology is a manifestation of the dual visions of Connes and Waldhausen to
From playlist HIM Lectures: Junior Trimester Program "Topology"
Anabelian Geometry - Kummer Classes
To functions f we associate cohomology classes. Using galois sections we can evaluate these functions. Recovering the Kummer classes of the jacobi theta function
From playlist Anabelian Geometry
Alexander Dranishnikov (9/22/22): On the LS-category of group homomorphisms
In 50s Eilenberg and Ganea proved that the Lusternik-Schnirelmann category of a discrete group Γ equals its cohomological dimension, cat(Γ) = cd(Γ). We discuss a possibility of the similar equality cat(φ) = cd(φ) for group homomorphisms φ : Γ → Λ. We prove this equality for some classes of
From playlist Topological Complexity Seminar
Automorphic Cohomology II (Carayol's Work and an Application) - Phillip Griffiths
Automorphic Cohomology II (Carayol's Work and an Application) Phillip Griffiths Institute for Advanced Study February 17, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
Étale cohomology 9/10/2020 Part 1
Enough injectives, derived functors
From playlist Étale cohomology and the Weil conjectures
B. Bhatt - Prisms and deformations of de Rham cohomology
Prisms are generalizations of perfectoid rings to a setting where "Frobenius need not be an isomorphism". I will explain the definition and use it to construct a prismatic site for any scheme. The resulting prismatic cohomology often gives a one-parameter deformation of de Rham cohomology.
From playlist Arithmetic and Algebraic Geometry: A conference in honor of Ofer Gabber on the occasion of his 60th birthday
Nero Budur: Absolute sets and the Decomposition Theorem
Abstract: We give a new, more conceptual proof of the Decomposition Theorem for semisimple perverse sheaves of rank-one origin, assuming it for those of constant-sheaf origin, that is, assuming the geometric case proven by Beilinson-Bernstein-Deligne-Gabber. Joint work with Botong Wang. R
From playlist Algebraic and Complex Geometry
Applying the law of cosines to solve a word problem
Learn how to solve for the lengths of the sides and the measures of the angles of a triangle using the law of cosines. The law of cosines is used in determining the lengths of the sides or the measures of the angles of a triangle when no angle measure and the length of the side opposite th
From playlist Solve Law of Cosines (Word Problem) #ObliqueTriangles