Lectures related to Optimal Transport: Theory and Applications

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

Covers cyclically monotone sets in optimal transport theory and their properties.

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Covers the approximation of functions in Sobolev spaces using smooth functions.

Explores Lagrange multipliers, minimax theorems, and convex subsets in optimal transport theory.

Explores the chain rule for compositions of differential functions in higher dimensions, emphasizing gradients and directional changes.

Covers the Theoreus Chain Role for Lipschitz functions and its practical applications.

Explores unconstrained optimization theory, covering global and local minima, convexity, and gradient concepts.

Explores sub/super harmonic functions and their applications in a theoretical context.

Covers the Meyers-Serrin theorem in analysis, discussing the conditions for functions in different spaces.

Explores convex sets, their properties, and applications in optimization.

Explores Coxeter groups, word length, simple reflections, and unique elements.

Covers the generalization of the TAF theorem, lateral derivatives, limits of derivatives, and indeterminacy.

Delves into the concept of proof in mathematics, emphasizing the importance of evidence and logical reasoning.

Introduces the key concepts of convexity and its applications in different fields.

Explores the theory and application of quadrature formulas for numerical analysis.

Explores the theory of implicit functions, their properties, and illustrative examples.

Explores the theorems on maximum and minimum values of functions and their relation to continuity.

Covers hitting probabilities in Markov chains with disjoint subsets, the function h(i), theorems, proofs, and expected time to hit calculations.

Explores VC dimension, gradient descent, convex sets, and Lipschitz functions in convex optimization.