Differential operators | Differential geometry
In mathematics and theoretical physics, an invariant differential operator is a kind of mathematical map from some objects to an object of similar type. These objects are typically functions on , functions on a manifold, vector valued functions, vector fields, or, more generally, sections of a vector bundle. In an invariant differential operator , the term differential operator indicates that the value of the map depends only on and the derivatives of in . The word invariant indicates that the operator contains some symmetry. This means that there is a group with a group action on the functions (or other objects in question) and this action is preserved by the operator: Usually, the action of the group has the meaning of a change of coordinates (change of observer) and the invariance means that the operator has the same expression in all admissible coordinates. (Wikipedia).
Schemes 46: Differential operators
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In this lecture we define differential operators on rings, and calculate the universal (normalized) differential operator of order n. As a special case we fin
From playlist Algebraic geometry II: Schemes
Eva Gallardo Gutiérrez: The invariant subspace problem: a concrete operator theory approach
Abstract: The Invariant Subspace Problem for (separable) Hilbert spaces is a long-standing open question that traces back to Jonhn Von Neumann's works in the fifties asking, in particular, if every bounded linear operator acting on an infinite dimensional separable Hilbert space has a non-
From playlist Analysis and its Applications
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This video explains how to classify differential equations based upon their properties https://mathispower4u.com
From playlist Differential Equations: Complete Set of Course Videos
Partial Derivatives and the Gradient of a Function
We've introduced the differential operator before, during a few of our calculus lessons. But now we will be using this operator more and more over the prime symbol we are used to when describing differentiation, as from now on we will frequently be differentiating with respect to a specifi
From playlist Mathematics (All Of It)
Commutative algebra 4 (Invariant theory)
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. This lecture is an informal historical summary of a few results of classical invariant theory, mainly to show just how complic
From playlist Commutative algebra
Introduction to Differential Equation Terminology
This video defines a differential equation and then classifies differential equations by type, order, and linearity. Search Library at http://mathispower4u.wordpress.com
From playlist Introduction to Differential Equations
D-Notation and Determine a Linear Differential Operator of a Linear Differential Equation
This video defines D notation, explains how to write a linear differential equation using D-notation, and then explains how to determine the linear differential operator of a linear differential equation. https://mathispower4u.com
From playlist Differential Equations: Complete Set of Course Videos
Differential Isomorphism and Equivalence of Algebraic Varieties Board at 49:35 Sum_i=1^N 2/(x-phi_i(y,t))^2
From playlist Fall 2017
(2.3.1) Introduction to Higher Order Linear Differential Equations and Related Theorem
The video introduces higher order linear differential equations and related theorems on superposition, existence and uniqueness, and linear independence. https://mathispower4u.com
From playlist Differential Equations: Complete Set of Course Videos
Title: Differential Algebra of Invariants and Invariant Variational Calculus
From playlist Applications of Computer Algebra 2014
Fourier transform for Class D-modules - David Ben Zvi
Locally Symmetric Spaces Seminar Topic: Fourier transform for Class D-modules Speaker: David Ben Zvi Affiliation: University of Texas at Austin; Member, School of Mathematics Date: Febuary 13, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Paolo Piazza: Proper actions of Lie groups and numeric invariants of Dirac operators
HYBRID EVENT shall explain how to define and investigate primary and secondary invariants of G-invariant Dirac operators on a cocompact G-proper manifold, with G a connected real reductive Lie group. This involves cyclic cohomology and Ktheory. After treating the case of cyclic cocycles a
From playlist Lie Theory and Generalizations
Koopman Observable Subspaces & Finite Linear Representations of Nonlinear Dynamics for Control
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From playlist Research Abstracts from Brunton Lab
Sun-Yung Alice Chang: Conformal Invariants and Differential Equations
This lecture was held at The University of Oslo, May 24, 2006 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations. Program for the Abel Lectures 2006 1. “A Scandinavian Chapter in Analysis” by Lennart Carleson, Kungliga Tekniska Högskolan, Swed
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Explicit, Epsilon-Balanced Codes Close to the Gilbert-Varshamov Bound II - Amnon Ta-Shma Computer Science/Discrete Mathematics Seminar II Topic: Explicit, Epsilon-Balanced Codes Close to the Gilbert-Varshamov Bound II Speaker: Amnon Ta-Shma Affiliation: Tel Aviv University Date: January 3
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Markus Pflaum: The transverse index theorem for proper cocompact actions of Lie groupoids
The talk is based on joint work with H. Posthuma and X. Tang. We consider a proper cocompact action of a Lie groupoid and define a higher index pairing between invariant elliptic differential operators and smooth groupoid cohomology classes. We prove a cohomological index formula for this
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Kevin Buzzard (lecture 18/20) 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]
Rapid and Accurate Reachability Analysis for Nonlinear Systems by Exploiting Model Redundancy
From playlist Spring 2019 Kolchin Seminar
Introduction to Differential Inequalities
What is a differential inequality and how are they useful? Inequalities are a very practical part of mathematics: They give us an idea of the size of things -- an estimate. They can give us a location for things. It is usually far easier to satisfy assumptions involving inequalities t
From playlist Advanced Studies in Ordinary Differential Equations