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Lecture
What is a smooth manifold? - Through defining functions
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Related lectures (32)
Infinitesimal Deformations: One-Dimensional Maps
Explores infinitesimal deformations of one-dimensional maps, discussing common characteristics, methods, and recent results in expanding and piecewise expanding maps.
Differentiating Vector Fields: Definition
Introduces differentiating vector fields along curves on manifolds with connections and the unique operator satisfying specific properties.
Differentiating Vector Fields: How Not to Do It
Discusses the challenges in differentiating vector fields on submanifolds and the importance of choosing the right method.
Optimization on Manifolds
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Covers optimization on manifolds, focusing on smooth manifolds and functions, and the process of gradient descent.
Connections: motivation and definition
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Explores the definition of connections for smooth vector fields on manifolds.
Smooth maps on manifolds and differentials
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Covers smooth maps on manifolds, defining functions, tangent spaces, and differentials.
Riemannian connections
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Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.
Manifolds: Charts and Compatibility
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Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.
General Manifolds and Topology
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Covers manifolds, topology, smooth maps, and tangent vectors in detail.
Manopt: Optimization Toolbox for Manifolds
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Introduces Manopt, a toolbox for optimization on manifolds, focusing on solving optimization problems on smooth manifolds using the Matlab version.
Embedded Submanifolds: Stiefel Manifold
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Covers embedded submanifolds, Stiefel manifold, tangent spaces, and differential ranks.
Grassmann manifold and Retractions
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Covers the Grassmann manifold and retractions on submanifolds.
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