Lectures related to Metric Spaces and Isometric Embeddings

Optimal Transport: Heat Equation and Metric Spaces

Explores optimal transport in heat equations and metric spaces.

Geodesic Convexity: Theory and Applications

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

Probability Convergence

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

Lipschitz Maps and Compact Domains

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

Metric Spaces: Topology and Continuity

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

Intrinsic Geometry of Regular Surfaces

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

Optimal Transport: Stability and Counterexamples

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

Preliminaries in Measure Theory

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

Convergence and Completeness

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

Metric Spaces: Norms and Distances

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

Generalization Error

Explores generalization error in machine learning, focusing on data distribution and hypothesis impact.

Functional Analysis I: Consequences of Baire Theorem

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

Lp Cone and Approximate Embeddings

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

Riemannian distance, geodesically convex sets

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

Preimages in a Gluing Construction

Delves into preimages of closed sets in a disjoint union.

Hyperbolic Geometry

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

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

Compression: Kraft Inequality

Explains compression and Kraft inequality in codes and sequences.

Joint Equidistribution of CM Points

Covers the joint equidistribution of CM points and the ergodic decomposition theorem in compact abelian groups.

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.