Lectures related to Optimal Transport: Regularity and Brenier's Theorem

Geodesic Convexity: Theory and Applications

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

Optimal Transport: Rockafellar Theorem

Explores the Rockafellar Theorem in optimal transport, focusing on c-cyclical monotonicity and convex functions.

Convex Optimization: Gradient Descent

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

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Optimal Transport: Convexity and Inequalities

Explores optimal transport, emphasizing convexity properties and inequalities in compact sets.

KKT and Convex Optimization

Covers the KKT conditions and convex optimization, discussing constraint qualifications and tangent cones of convex sets.

Optimal Transport: Theory and Applications

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

Approximation by Smooth Functions

Discusses approximation by smooth functions and the convergence of function sequences in normed vector spaces.

Convexity: Functions and Global Minima

Explores convex functions, global minima, and their relationship with differentiability.

Properties of Complete Spaces

Covers the properties of complete spaces, including completeness, expectations, embeddings, subsets, norms, Holder's inequality, and uniform integrability.

Proofs: Logic, Mathematics & Algorithms

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

Convex Optimization: Convex Functions

Covers the concept of convex functions and their applications in optimization problems.

Weak Derivatives: Definition and Properties

Covers weak derivatives, their properties, and applications in functional analysis.

Preliminaries in Measure Theory

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

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Variational Problems: Convexity and Coercivity

Explores variational problems, emphasizing convexity and coercivity conditions in functionals with integral side constraints.

Rigidity in Negative Curvature

Delves into the rigidity of negatively curved manifolds and the interplay between curvature and symmetry.

Optimal Transport: Heat Equation and Metric Spaces

Explores optimal transport in heat equations and metric spaces.