Lectures related to Optimal Transport: Theory and Applications

Explains how entropy measures uncertainty in a system based on possible outcomes.

Explores variational formulation for measuring information content and divergence between probability distributions.

Discusses conditional entropy and its role in information theory and data compression.

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

Explores tail bounds, information bounds, and maximal leakage in the context of generalization error.

Explores optimal transport theory with a focus on heat equations and Wasserstein distance.

Explores infimum, supremum, and absolute value concepts with examples and proofs.

Explores the theory of optimal transport, focusing on Lipschitz functions and uniqueness of solutions.

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

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

Reviews information measures like entropy and introduces mutual information as a measure of information between random variables.

Covers information measures like entropy and Kullback-Leibler divergence.

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

Explores functors, natural transformations, and the theory of groups, emphasizing the importance of comparisons and structure preservation.

Explores active learning in Group Theory, focusing on products, coproducts, adjunctions, and natural transformations.

Explores entropy bounds, conditional entropy theorems, and the chain rule for entropies, illustrating their application through examples.

Covers entropy, its definition, and its implications in thermodynamics.

Covers the Fourier inversion formula, exploring its mathematical concepts and applications, emphasizing the importance of understanding the sign.

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

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