In mathematics, an adjoint bundle is a vector bundle naturally associated to any principal bundle. The fibers of the adjoint bundle carry a Lie algebra structure making the adjoint bundle into a (nonassociative) algebra bundle. Adjoint bundles have important applications in the theory of connections as well as in gauge theory. (Wikipedia).

Adjoint / Daggered Operators in Quantum Mechanics

In this video, we will explain adjoint operators in quantum mechanics. First of all, for any operator A, we can define its adjoint, A-dagger, via this equation. The idea behind this is, that while operators in quantum mechanics usually act towards the right, adjoint operators act to the le

From playlist Quantum Mechanics, Quantum Field Theory

Algebraic properties of the adjoint. Null space and range of the adjoint. The matrix of T* is the conjugate transpose of the matrix of T.

From playlist Linear Algebra Done Right

Matrices | Adjoint of a Matrix (Examples) | Don't Memorise

From playlist Matrices

Matrices | Adjoint of a Matrix | Don't Memorise

From playlist Matrices

We show the connection between the method of adjoints in optimal control to the implicit function theorem ansatz. We relate the costate or adjoint state variable to Lagrange multipliers.

Self-adjoint operators. All eigenvalues of a self-adjoint operator are real. On a complex vector space, if the inner product of Tv and v is real for every vector v, then T is self-adjoint.

From playlist Linear Algebra Done Right

Product groups

Now that we have defined and understand quotient groups, we need to look at product groups. In this video I define the product of two groups as well as the group operation, proving that it is indeed a group.

From playlist Abstract algebra

The adjoint Brascamp-Lieb inequality - Terence Tao

Analysis and Mathematical Physics Topic: The adjoint Brascamp-Lieb inequality Speaker: Terence Tao Affiliation: University of California, Los Angeles Date: March 08, 2023 The Brascamp-Lieb inequality is a fundamental inequality in analysis, generalizing more classical inequalities such a

From playlist Mathematics

Christian Bär: Local index theory for Lorentzian manifolds

HYBRID EVENT We prove a local version of the index theorem for Dirac-type operators on globally hyperbolic Lorentzian manifolds with Cauchy boundary. In case the Cauchy hypersurface is compact, we do not assume self-adjointness of the Dirac operator on the spacetime or of the associated el

From playlist Mathematical Physics

Multivariable Calculus | The dot product.

We present the definition of the dot product as well as a geometric interpretation and some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Vectors for Multivariable Calculus

A Riemann-Roch theorem in Bott-Chern cohomology - Jean-Michel Bismut

Jean-Michel Bismut Université Paris-Sud April 21, 2014 If MM is a complex manifold, the Bott-Chern cohomology H(⋅,⋅)BC(M,C)HBC(⋅,⋅)(M,C) of MM is a refinement of de Rham cohomology, that takes into account the p,q p,q grading of smooth differential forms. By results of Bott and Chern, vect

From playlist Mathematics

Ana Balibanu: The partial compactification of the universal centralizer

Abstract: Let G be a semisimple algebraic group of adjoint type. The universal centralizer is the family of centralizers in G of regular elements in Lie(G), parametrized by their conjugacy classes. It has a natural symplectic structure, obtained by Hamiltonian reduction from the cotangent

From playlist Algebra

Hilbert Space Techniques in Complex Analysis and Geometry (Lecture 4) 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

Duality In Higher Categories IV by Pranav Pandit

PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics

From playlist Dualities in Topology and Algebra (Online)

Coherent sheaves, Chern character, and RRG

Distinguished Lecture Series by Jean-Michel Bismut (Université Paris-Saclay, France)

From playlist Distinguished Visitors Lecture Series

Christian Bär - Boundary value problems for Dirac operators

This introduction to boundary value problems for Dirac operators will not focus on analytic technicalities but rather provide a working knowledge to anyone who wants to apply the theory, i.e. in the study of positive scalar curvature. We will systematically study "elliptic boundary conditi

From playlist Not Only Scalar Curvature Seminar

Michael Harris - 3/3 Derived Aspects of the Langlands Program

We discuss ways in which derived structures have recently emerged in connection with the Langlands correspondence, with an emphasis on derived Galois deformation rings and derived Hecke algebras. Michael Harris (Columbia Univ.) Tony Feng (MIT)

From playlist 2022 Summer School on the Langlands program

Reflexive Relations and Examples

Let A be a set. A relation R on A is a subset of A x A. Let R be a relation on A. We say R is reflexive of aRa for all a in A. In this video we go over this definition more carefully and we do several examples where we determine if the relation is reflexive. I hope this helps someone who i

From playlist Relations