Lectures related to Smooth scheme

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

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

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

Covers the approximation of functions in Sobolev spaces using smooth functions.

Explores upgrading foundations from embedded to general manifolds in optimization, discussing smooth sets and tangent vectors.

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

Presents a proof that smooth projective varieties with nef anti-canonical divisor have surjective Albanese morphism.

Explores algebraic cycles, etale cohomology, and counterexamples to the Hodge conjecture.

Explores étale motivic cohomology and the Hodge conjecture with a focus on counter-examples.

Covers the classification of compact p-adic manifolds using the C.o.V-formula and explores smooth algebraic varieties and Hensel's lemma.

Covers the Laplace equation, decomposition of linear problems, and solutions through separation of variables.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Explores smooth functions on manifolds, emphasizing continuity and atlas topologies.

Discusses advanced optimization techniques, focusing on faster and projected gradient descent methods in machine learning.

Explores the definition of connections for smooth vector fields on manifolds.

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

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

Explores integration theory over real numbers and Berkovich spaces, revealing intriguing asymmetries and unsolved conjectures.

Explores the regularity of curves over a field and the importance of specific properties for curve regularity.

Explores regularity in algebraic geometry and the geometric implications of the Jacobian criterion.