Differential forms | Complex manifolds
In mathematics, a complex differential form is a differential form on a manifold (usually a complex manifold) which is permitted to have complex coefficients. Complex forms have broad applications in differential geometry. On complex manifolds, they are fundamental and serve as the basis for much of algebraic geometry, Kähler geometry, and Hodge theory. Over non-complex manifolds, they also play a role in the study of almost complex structures, the theory of spinors, and CR structures. Typically, complex forms are considered because of some desirable decomposition that the forms admit. On a complex manifold, for instance, any complex k-form can be decomposed uniquely into a sum of so-called (p,q)-forms: roughly, wedges of p differentials of the holomorphic coordinates with q differentials of their complex conjugates. The ensemble of (p,q)-forms becomes the primitive object of study, and determines a finer geometrical structure on the manifold than the k-forms. Even finer structures exist, for example, in cases where Hodge theory applies. (Wikipedia).
Complex Numbers for ODEs (1 of 4)
ODEs: We define and present basic properties of the complex numbers. This part includes addition, subtraction, scalar multiplication, complex conjugate and modulus.
From playlist Differential Equations
Differential Equations: Complex Roots of the Characteristic Equation
Homogeneous, constant-coefficient differential equations have a characteristic or auxiliary equation. The solution(s) of this equation yield the particular solutions to the homogeneous differential equation which, when combined, produce a general solution. In this video, we explore the cas
From playlist Differential Equations
Solve the general solution for differentiable equation with trig
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Differential Equations
Find the particular solution given the conditions and second derivative
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Solve Differential Equation (Particular Solution) #Integration
Introduction to Differential Equations
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Introduction to Differential Equations - The types of differential equations, ordinary versus partial. - How to find the order of a differential equation.
From playlist Differential Equations
Second order differential equation: complex roots
Free ebook http://bookboon.com/en/learn-calculus-2-on-your-mobile-device-ebook How to solve second order differential equations when the characteristic equation has complex roots.
From playlist Differential equations
How to determine the general solution to a differential equation
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Differential Equations
What are differential equations?
► My Differential Equations course: https://www.kristakingmath.com/differential-equations-course Differential equations are usually classified into two general categories: partial differential equations, which are also called partial derivatives, and ordinary differential equations. Part
From playlist Popular Questions
How to solve a separable differential equation
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Solve Differential Equation (Particular Solution) #Integration
A Gentle Approach to Crystalline Cohomology - Jacob Lurie
Members’ Colloquium Topic: A Gentle Approach to Crystalline Cohomology Speaker: Jacob Lurie Affiliation: Professor, School of Mathematics Date: February 28, 2022 Let X be a smooth affine algebraic variety over the field C of complex numbers (that is, a smooth submanifold of C^n which can
From playlist Mathematics
Henri Moscovici. Differentiable Characters and Hopf Cyclic Cohomology
Talk by Henri Moscovici in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/... on October 20, 2020.
From playlist Global Noncommutative Geometry Seminar (Europe)
Hilbert Space Techniques in Complex Analysis and Geometry (Lecture - 2) by Dror Varolin
PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo
From playlist Cauchy-Riemann Equations in Higher Dimensions 2019
Pre-recorded lecture 8: Differentially non-degenerate singular points and global theorems
MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems Pre-recorded lecture: These lectures were recorded as part of a cooperation between the Chinese-Russian Mathematical Center (Beijing) and the Moscow Center of Fundamental and Applied Mathematics (Moscow). Nijenhuis Geomet
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry companion lectures (Sino-Russian Mathematical Centre)
John Terilla : A collection of Homotopy Random Variables
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 29, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Geometry
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
Georg Tamme: Differential algebraic K theory
The lecture was held within the framework of the Hausdorff Trimester Program: Non-commutative Geometry and its Applications and the Workshop: Number theory and non-commutative geometry 28.11.2014
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Pierre Albin: The sub-Riemannian limit of a contact manifold
Talk by Pierre Albin in the Global Noncommutative Geometry Seminar (Americas) on January 29, 2021. https://globalncgseminar.org/talks/tba-5/?utm_source=mailpoet&utm_medium=email&utm_campaign=global-noncommutative-geometry-seminar-americas-01292021_14
From playlist Global Noncommutative Geometry Seminar (Americas)
Lagrangians, symplectomorphisms and zeroes of moment maps - Yann Rollin
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Lagrangians, symplectomorphisms and zeroes of moment maps Speaker: Yann Rollin Affiliation: Nantes University Date: April 08, 2022 I will present two constructions of Kähler manifolds, endowed with Hamiltonia
From playlist Mathematics
Kevin Buzzard (lecture 19/20) Automorphic Forms And The Langlands Program [2017]
Full course playlist: https://www.youtube.com/playlist?list=PLhsb6tmzSpiysoRR0bZozub-MM0k3mdFR http://wwwf.imperial.ac.uk/~buzzard/MSRI/ Summer Graduate School Automorphic Forms and the Langlands Program July 24, 2017 - August 04, 2017 Kevin Buzzard (Imperial College, London) https://w
From playlist MSRI Summer School: Automorphic Forms And The Langlands Program, by Kevin Buzzard [2017]
Differential Equations: Exact DEs Example 1
It's important to be able to classify a differential equation so we can pick the right method to solve it. In this video, I run through the steps of how to classify a first order differential equation as separable, linear, exact, or neither.
From playlist Differential Equations