Lectures related to Projectors and Tensor Product of Representations

Character of Dirac and Projectors

Discusses Dirac's character and projectors in high-dimensional spaces with matrices and vectors.

Tensor Product: Bilinear Maps

Covers the concept of tensor product in the context of bilinear maps and explores the uniqueness of tensor products.

Tensor Products of Modules

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

Projectors on Invariant Subspaces

Covers projectors on invariant subspaces in quantum physics and their applications.

Tensors: Motivations and Introduction

Covers the basics of tensors, including their definition, properties, and decomposition, starting with a motivating example involving Gaussian distributions.

Principles of Quantum Physics

Covers the principles of quantum physics, focusing on tensor product spaces and entangled vectors.

Cohomology: Cross Product

Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.

Reduced Density Matrices: System+Environment

Covers the concept of density matrices and the system-environment interaction.

Tensor Products and Symmetric Power

Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.

Decomposition Principle: Linear Algebra

Explores the decomposition principle in linear algebra, showing how a vector space can be split into two subspaces.

Homotopy Theory in Chain Complexes

Explores acyclic fibrations and cylinder objects in chain complexes.

Chemical Environments: Representations and Correlations

Explores chemical environment representations, symmetrized correlations, and machine learning applications at the atomic scale.

Hidden Subgroup Algorithm

Covers the Hidden Subgroup Algorithm in quantum computing, emphasizing projectors and measurement postulates.

Linear Algebra in Dirac Notation

Covers linear algebra in Dirac notation, focusing on vector spaces and quantum bits.

Lie Algebras and Representations

Explores Lie algebras, representations, tensor products, and commutation relations in mathematics.

Thermodynamics of Continuous Media

Covers historical thermodynamics, continuity equations, state functions, and Cartesian products in scalar and vectorial forms.

Diagonalization: Symmetries

Explores symmetries in linear algebra, focusing on matrices and their properties.

Coulomb Gas and Spin Chain: Quantum Group Applications

Explores the relationship between Coulomb gas models and spin chains in quantum groups.

Tensor Spaces and Unitary Representations

Explores tensor spaces, unitary representations, and prime factorization in mathematical presentations.

Representations of SU(2): Symmetries and Transformations

Covers the representations of SU(2) and their transformations in quantum mechanics.