Concept
Metrizable space
Related lectures (28)
Introduction: Course syllabus
Introduces the course syllabus, grading scheme, and classical and quantum computation models.
Optimal Transport: Disintegration Theorem
Covers the Disintegration Theorem in the context of Optimal Transport.
Open Mapping Theorem
Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.
Local Homeomorphisms and Coverings
Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.
Optimal Transport: Regularity and Brenier's Theorem
Explores optimal transport regularity and Brenier's theorem, discussing continuity and convexity concepts.
Linear Binary Classification: Perceptron, SGD, Fisher's LDA
Covers the Perceptron model, SGD, and Fisher's Linear Discriminant in binary classification.
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.
Bar Construction: Homology Groups and Classifying Space
Covers the bar construction method, homology groups, classifying space, and the Hopf formula.
Categories and Functors
Explores building categories from graphs and the encoding of information by functors.
Riemannian distance, geodesically convex sets
Covers the structure of Riemannian manifolds, geodesic convexity, and the Riemannian distance function.