Lectures related to Twister Extract

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

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

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

Chemical Environments: Representations and Correlations

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

Tensors: Motivations and Introduction

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

Cohomology: Cross Product

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

Tensor Products and Symmetric Power

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

Homotopy Theory in Chain Complexes

Explores acyclic fibrations and cylinder objects in chain complexes.

Linear Algebra in Dirac Notation

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

Tensor Spaces and Unitary Representations

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

Thermodynamics of Continuous Media

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

Lie Algebras and Representations

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

Coulomb Gas and Spin Chain: Quantum Group Applications

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

Tensors & Indices Recap

Covers the basics of tensors and indices, including contravariant vectors and tensor operations.

Linear Quantum Calculus in Dirac Notation

Covers linear algebra in Dirac notation, emphasizing the scalar product and density product in quantum computations.

Representations of SU(2): Symmetries and Transformations

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

Projectors and Tensor Product of Representations

Explores projectors and tensor product of representations, covering their applications and properties.

Tensor Operations: Dot and Cross Products

Covers tensor operations, focusing on dot and cross products and their geometric interpretation.

States of Composite Systems

Covers the concept of states of composite systems in Hilbert space and the tensor or outer product.

Algebraic Manipulations: Indices and Tensors in Continuum Mechanics

Provides an overview of algebraic manipulations involving indices and tensors in continuum mechanics.