Lectures related to Metric space

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

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

Covers the structure of Riemannian manifolds, geodesic convexity, and the Riemannian distance function.

Explores thermodynamic formalism for weakly coarse expanding dynamical systems, covering equilibrium states, visual metrics, and symbolic coding.

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

Explores the intrinsic geometry of regular surfaces and isometric transformations, including spheres and cylinders.

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

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

Explores setting up experiments, interview guides, and self-experimentation in research methods.

Explores Conformal Transformations, emphasizing scale transformations and correlation functions.

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

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

Delves into preimages of closed sets in a disjoint union.

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

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

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

Explores optimal transport in heat equations and metric spaces.

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

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.