Metric Spaces and Isometric Embeddings

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Related lectures (30)

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Applied Topology: Compression Schemes and Range Patches

Explores compression schemes, texture recognition, range patches, evolution, and variants on persistence in applied topology.

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.

Functional Analysis I: Foundations and Applications

Covers the foundations of modern analysis, introductory functional analysis, and applications in MAB111.

Sparsest Cut: ARV Theorem

Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.

Norms and Valuations on Fields

Covers the construction of Qp, norms, valuations, and Ostrovski's theorem.

Normed Spaces

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Embedding in Metric Spaces

Explores embedding in metric spaces, discussing mappings, distances, and convergence.

Optimal Transport: Gradient Flows

Explores optimal transport, gradient flows, the implicit Euler scheme, and the heat equation in the context of Dirichlet energy functional.

The Class Number Formula: Counting and Lipschitz Principle

Covers the Class Number Formula and a counting problem related to the lattice and Lipschitz principle.

Distance and geodesics: Distance, geodesics and complete manifolds

Covers the concept of distance induced by the Riemannian metric on manifolds.