Lectures related to Intrinsic metric

Introduces geodesic convexity on Riemannian manifolds and explores its properties.

Introduces metric spaces, topology, and continuity, emphasizing the importance of open sets and the Hausdorff property.

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

Explores distance, geodesics, and complete manifolds, emphasizing the existence of minimizing geodesics and the concept of metric completeness.

Explores geodesically strongly convex functions and their relation to the Polyak-Łojasiewicz condition.

Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.

Explores embeddings into l_inf, including theorems, applications, and Frechet embeddings.

Covers the concept of Lp cone and approximate embeddings in metric spaces.

Delves into preimages of closed sets in a disjoint union.

Covers metric spaces, isometric embeddings, and equilateral spaces with examples and proofs.

Explores optimal transport in heat equations and metric spaces.

Covers convergence, completeness, and properties of metric spaces and Banach spaces.

Explores the implications of Baire Theorem in functional analysis and metric spaces.

Covers Lipschitz maps, compact domains, changing variables, counting problems, and probability of ideals.

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

Explores norms, distances, scalar products, and norm convergence in metric spaces.

Covers stability in optimal transport and provides examples of discontinuous optimal solutions.

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

Explores probability convergence, discussing conditions for random variable sequences to converge and the uniqueness of convergence.

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