In mathematics, the equivariant algebraic K-theory is an algebraic K-theory associated to the category of equivariant coherent sheaves on an algebraic scheme X with action of a linear algebraic group G, via Quillen's Q-construction; thus, by definition, In particular, is the Grothendieck group of . The theory was developed by R. W. Thomason in 1980s. Specifically, he proved equivariant analogs of fundamental theorems such as the localization theorem. Equivalently, may be defined as the of the category of coherent sheaves on the quotient stack . (Hence, the equivariant K-theory is a specific case of the .) A version of the Lefschetz fixed-point theorem holds in the setting of equivariant (algebraic) K-theory. (Wikipedia).
Linear Algebra: Ch 3 - Eigenvalues and Eigenvectors (5 of 35) What is an Eigenvector?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain and show (in general) what is and how to find an eigenvector. Next video in this series can be seen at: https://youtu.be/SGJHiuRb4_s
From playlist LINEAR ALGEBRA 3: EIGENVALUES AND EIGENVECTORS
Linear Algebra - Lecture 33 - Eigenvectors and Eigenvalues
In this lecture, we define eigenvectors and eigenvalues of a square matrix. We also prove a couple of useful theorems related to these concepts.
From playlist Linear Algebra Lectures
10A An Introduction to Eigenvalues and Eigenvectors
A short description of eigenvalues and eigenvectors.
From playlist Linear Algebra
Beyond Eigenspaces: Real Invariant Planes
Linear Algebra: In the context of real vector spaces, one often needs to work with complex eigenvalues. Let A be a real nxn matrix A. We show that, in R^n, there exists at least one of: an (nonzero) eigenvector for A, or a 2-dimensional subspace (plane) invariant under A.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
Beyond Eigenspaces 2: Complex Form
Linear Algebra: As an application of the Spectral Theorem for real vector spaces, we show that every 2x2 matrix with no real eigenvalues can be represented as [x -y / y x] for some basis. This representation reflects common algebraic properties of the complex numbers.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
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
Teena Gerhardt - 3/3 Algebraic K-theory and Trace Methods
Algebraic K-theory is an invariant of rings and ring spectra which illustrates a fascinating interplay between algebra and topology. Defined using topological tools, this invariant has important applications to algebraic geometry, number theory, and geometric topology. One fruitful approac
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
Solving Systems of Differential Equations with Eigenvalues and Eigenvectors
We now show how to solve a generic matrix system of linear ordinary differential equations (ODEs) using eigenvalues and eigenvectors. This is one of the most powerful techniques in linear systems theory, with applications in stability theory and control. Code examples are given in Pyt
From playlist Engineering Math: Differential Equations and Dynamical Systems
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
Linear Algebra: Ch 3 - Eigenvalues and Eigenvectors (6 of 35) How to Find the Eigenvector
Visit http://ilectureonline.com for more math and science lectures! In this video I will find eigenvectors=? given a 2x2 matrix and 2 eigenvalues. Next video in this series can be seen at: https://youtu.be/EaormewNDpM
From playlist LINEAR ALGEBRA 3: EIGENVALUES AND EIGENVECTORS
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
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
Ralf Meyer: On the classification of group actions on C*-algebras up to equivariant KK-equivalence
Talk by Ralf Meyer in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on November 10, 2020.
From playlist Global Noncommutative Geometry Seminar (Europe)
Teena Gerhardt - 2/3 Algebraic K-theory and Trace Methods
Algebraic K-theory is an invariant of rings and ring spectra which illustrates a fascinating interplay between algebra and topology. Defined using topological tools, this invariant has important applications to algebraic geometry, number theory, and geometric topology. One fruitful approac
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
Mark Grant (10/22/20): Bredon cohomology and LS-categorical invariants
Title: Bredon cohomology and LS-categorical invariants Abstract: Farber posed the problem of describing the topological complexity of aspherical spaces in terms of algebraic invariants of their fundamental groups. In Part One of this talk, I’ll discuss joint work with Farber, Lupton and O
From playlist Topological Complexity Seminar
(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
Gus Lonergan: Geometric Satake over KU
SMRI Algebra and Geometry Online: Gus Lonergan (A Priori Investment Management LLC) Abstract: We describe a K-theoretic version of the equivariant constructible derived category. We state (with evidence!) a ‘geometric Satake’ conjecture relating its value on the affine Grassmannian to re
From playlist SMRI Algebra and Geometry Online
Angélica M. Osorno - Equivariant Infinite Loop Space Machines
An equivariant infinite loop space machine is a functor that constructs genuine equivariant spectra out of simpler categorical or space level data. In the late 80’s Lewis–May–Steinberger and Shimakawa developed generalizations of the operadic approach and the G-space approach respectively.
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
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
A11 Eigenvalues with complex numbers
Eigenvalues which contain complex numbers.
From playlist A Second Course in Differential Equations