Riemannian metrics and gradients: Riemannian gradients

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Covers the definition of retraction, open submanifolds, local defining functions, tangent spaces, and Riemannian metrics.

Covers optimization on manifolds, focusing on smooth manifolds and functions, and the process of gradient descent.

Introduces Manopt, a toolbox for optimization on manifolds, focusing on solving optimization problems on smooth manifolds using the Matlab version.

Covers Newton's method on Riemannian manifolds, focusing on second-order optimality conditions and quadratic convergence.

Explores symmetries, Riemannian connection, vector fields, and Lie bracket in geometry.

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

Covers Hessians, symmetry, and examples related to vector fields, functions, and manifolds.

Covers the Grassmann manifold and retractions on submanifolds.

Explores geodesics in the Wasserstein space, emphasizing constant speed geodesics and their properties.

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

Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.

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

Explores Euclid's first proposition, ancient symmetria, and Vitruvius' architectural figures.

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