Lectures related to Contorsion tensor

Differential Forms: Basics and Applications

Introduces the concept of differential forms and their applications in n-dimensional manifolds, including the Levi-Civita tensor and volume form.

Tucker Decomposition: Multilinear rank and applications in data compression

Covers the Tucker decomposition and its applications in data compression, explaining the notion of multilinear rank and the HOSVD method.

Hodge Duality and Covariant Derivatives

Introduces Hodge duality, covariant derivatives, and key concepts in differential geometry.

Shor Algorithm: Measurement Process Analysis

Explores the analysis of the measurement process in the Shor Algorithm.

Grover Algorithm: Quantum Search

Introduces the Grover algorithm, a quantum search algorithm that speeds up searching unsorted databases.

Testing General Relativity with Cosmology

Explores Testing General Relativity with Cosmology, covering topics like the curvature tensor, teleparallelism, and black holes in f(Q).

Vectors and Tensors: Mathematical Preliminaries and Transformations

Explores mathematical preliminaries of tensors and their transformations under basis rotations.

Rotations: Angular Momentum

Covers angular momentum in rotations, including preservation of angles and vector products.

Maxwell Equations and Minkowski Spacetime

Explores Maxwell equations, Minkowski spacetime, Lorentz transformations, charge conservation, and spacetime structure in physics.

Angular Momentum: Generators and Operators

Covers angular momentum generators, operators, and finite rotations in quantum mechanics.

Riemannian connections: Proof sketch

Presents the fundamental theorem of Riemannian geometry and demonstrates the uniqueness of the Riemannian connection.

Riemannian connections: What they are and why we care

Covers Riemannian connections, emphasizing their properties and significance in geometry.

Covariant Derivatives and Christoffel Symbols

Covers accelerated and inertial coordinate systems, Jacobian, volume elements, covariant derivatives, Christoffel symbols, Lorentz case, and metric tensor properties.

Riemannian connections

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.

Vorticity Equation: Levi-Civita Symbol

Explores the vorticity equation, Levi-Civita symbol, stress tensor, and helicity derivation.