In differential geometry, an equivariant differential form on a manifold M acted upon by a Lie group G is a polynomial map from the Lie algebra to the space of differential forms on M that are equivariant; i.e., In other words, an equivariant differential form is an invariant element of For an equivariant differential form , the equivariant exterior derivative of is defined by where d is the usual exterior derivative and is the interior product by the fundamental vector field generated by X.It is easy to see (use the fact the Lie derivative of along is zero) and one then puts which is called the equivariant cohomology of M (which coincides with the ordinary equivariant cohomology defined in terms of Borel construction.) The definition is due to H. Cartan. The notion has an application to the equivariant index theory. -closed or -exact forms are called equivariantly closed or equivariantly exact. The integral of an equivariantly closed form may be evaluated from its restriction to the fixed point by means of the localization formula. (Wikipedia).
The method of determining eigenvalues as part of calculating the sets of solutions to a linear system of ordinary first-order differential equations.
From playlist A Second Course in Differential Equations
MATH272 - 01/31/2018: Eigenvalues, Eigenvectors, ODES
videography - Eric Melton, UVM
From playlist Partial Differential Equations
Differential Equatons: Find the Order and Classify as Linear or Nonlinear
This video explains how to determine the order of a differential equation and how to determine if it is linear or nonlinear. http://mathispower4u.com
From playlist Introduction to Differential Equations
A11 Eigenvalues with complex numbers
Eigenvalues which contain complex numbers.
From playlist A Second Course in Differential Equations
With the eigenvalues for the system known, we move on the the eigenvectors that form part of the set of solutions.
From playlist A Second Course in Differential Equations
A08 Example problem of repeated real eigenvalues
Here is an example problem with repeated eigenvalues.
From playlist A Second Course in Differential Equations
System of odes with complex eigenvalues | Lecture 41 | Differential Equations for Engineers
Solution of a system of linear first-order differential equations with complex-conjugate eigenvalues. Join me on Coursera: https://www.coursera.org/learn/differential-equations-engineers Lecture notes at http://www.math.ust.hk/~machas/differential-equations-for-engineers.pdf Subscribe t
From playlist Differential Equations for Engineers
System of linear equations: one eigenvector
Illustrates the solution of a system of two linear, homogeneus equations with one real eigenvalue and one eigenvector. Free books: http://bookboon.com/en/differential-equations-with-youtube-examples-ebook http://www.math.ust.hk/~machas/differential-equations.pdf
From playlist Differential Equations with YouTube Examples
(3.5) Types of Behavior of 2D Linear Homogeneous Const Coefficient Systems of ODEs Using Eigenvalues
This lesson explains how to determine the type of of the solution to linear homogeneous constant coefficient systems of ordinary differential equations https://mathispower4u.com
From playlist Differential Equations: Complete Set of Course Videos
Act globally, compute...points and localization - Tara Holm
Tara Holm Cornell University; von Neumann Fellow, School of Mathematics October 20, 2014 Localization is a topological technique that allows us to make global equivariant computations in terms of local data at the fixed points. For example, we may compute a global integral by summing inte
From playlist Mathematics
Equivariant structures in mirror symmetry - James Pascaleff
James Pascaleff University of Illinois at Urbana-Champaign October 17, 2014 When a variety XX is equipped with the action of an algebraic group GG, it is natural to study the GG-equivariant vector bundles or coherent sheaves on XX. When XX furthermore has a mirror partner YY, one can ask
From playlist Mathematics
Dianel Isaksen - 3/3 Motivic and Equivariant Stable Homotopy Groups
Notes: https://nextcloud.ihes.fr/index.php/s/4N5kk6MNT5DMqfp I will discuss a program for computing C2-equivariant, ℝ-motivic, ℂ-motivic, and classical stable homotopy groups, emphasizing the connections and relationships between the four homotopical contexts. The Adams spectral sequence
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
Mike Hill - Real and Hyperreal Equivariant and Motivic Computations
Foundational work of Hu—Kriz and Dugger showed that for Real spectra, we can often compute as easily as non-equivariantly. The general equivariant slice filtration was developed to show how this philosophy extends from 𝐶2-equivariant homotopy to larger cyclic 2-groups, and this has some fa
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
Equivariant Eisenstein Classes, Critical Values of Hecke L-Functions.... by Guido Kings
Program Recent developments around p-adic modular forms (ONLINE) ORGANIZERS: Debargha Banerjee (IISER Pune, India) and Denis Benois (University of Bordeaux, France) DATE: 30 November 2020 to 04 December 2020 VENUE: Online This is a follow up of the conference organized last year arou
From playlist Recent Developments Around P-adic Modular Forms (Online)
Twisted matrix factorizations and loop groups - Daniel Freed
Daniel Freed University of Texas, Austin; Member, School of Mathematics and Natural Sciences February 9, 2015 The data of a compact Lie group GG and a degree 4 cohomology class on its classifying space leads to invariants in low-dimensional topology as well as important representations of
From playlist Mathematics
Cyclic homology and S1S1-equivariant symplectic cohomology - Sheel Ganatra
Sheel Ganatra Stanford University November 21, 2014 In this talk, we study two natural circle actions in Floer theory, one on symplectic cohomology and one on the Hochschild homology of the Fukaya category. We show that the geometric open-closed string map between these two complexes is S
From playlist Mathematics
Branimir Cacic:A reconstruction theorem for ConnesLandi deformations of commutative spectral tripels
We give an extension of Connes's reconstruction theorem for commutative spectral triples to so-called Connes—Landi or isospectral deformations of commutative spectral triples along the action of a compact Abelian Lie group G. We do so by proposing an abstract definition for such spectral t
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Stanford CS330: Deep Multi-task and Meta Learning | 2020 | Lecture 17: Frontiers and Open-Challenges
For more information about Stanford’s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/ai To follow along with the course, visit: https://cs330.stanford.edu/ To view all online courses and programs offered by Stanford, visit: http://online.stanford.
From playlist Stanford CS330: Deep Multi-task and Meta Learning | Autumn 2020
Video6_3: Review of matrices. Eigenvalues and eigenvectors. Elementary differential equations
Elementary differential equations Video6_3. Review of matrices. Eigenvalues and eigenvectors. Example of two real and distinct eigenvalues. Course playlist: https://www.youtube.com/playlist?list=PLbxFfU5GKZz0GbSSFMjZQyZtCq-0ol_jD
From playlist Elementary Differential Equations