Lectures related to Vector bundle

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Covers retractions, tangent bundles, and embedded submanifolds on manifolds with proofs and examples.

Covers the properties of coatings, including trivializing opens and automorphisms.

Covers the fundamentals of analytical geometry, focusing on vectors and their operations.

Covers the application of Serre Duality in the general case, focusing on line bundles and core concepts.

Covers vector bundles, locally free sheaves, depth, Serre twisting sheaf, and graded modules in algebraic geometry.

Introduces vector definitions, displacement, addition, and applications in geometry.

Introduces retractions and vector fields on manifolds, providing examples and discussing smoothness and extension properties.

Covers smooth maps, vector fields, and retractions on manifolds, emphasizing the importance of smoothly varying curves.

Explores the concept of torsion in group theory, focusing on its Hom functoriality and its role in exact sequences.

Explores the applications of Serre duality in Enriques-Severi-Zariski lemma, foliations, and Riemann-Roch theorem.

Covers advanced physics topics such as definitions, rectilinear motion, vectors, and motion in three dimensions.

Covers market-based instruments for emission reductions and their efficiency in minimizing costs across different sources of emissions.

Explores the homotopy lifting property, demonstrating how to lift homotopic maps and solve lifting problems on different spaces.

Explores Cheeger's inequality and its implications in graph theory.

Explores isogeny graphs of supersingular elliptic curves, showing optimal mixing times for random walks and applications to cryptography.

Explores Lorentz transformations, covariant tensors, rotational invariance, and linear transformations in vector spaces.