Lectures related to Pullback (differential geometry)

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

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

Explores smooth maps, differentials, composition properties, linearity, and extensions on manifolds.

Covers smooth maps on manifolds, defining functions, tangent spaces, and differentials.

Explores meromorphic differentials on Riemann surfaces and modular forms on congruence subgroups.

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

Introduces multilinear forms in linear algebra, emphasizing clarity and logic in presentation.

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.

Covers manifolds, topology, smooth maps, and tangent vectors in detail.

Explores permutations, signature, and alternating multilinear forms in vectors.

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

Explores modular forms, discussing pullback maps, meromorphic differentials, and the Riemann-Roch theorem.

Discusses linear Lie groups, their definitions, properties, and the relationship between integral curves and vector fields.

Covers multilinear forms in n variables over a k-vector space, emphasizing notation and applications.

Introduces differentiating vector fields along curves on manifolds with connections and the unique operator satisfying specific properties.

Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.

Covers limits and colimits, focusing on equalizers and coequalizers in category theory.