Lectures related to Geodesic Convexity: Theory and Applications

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

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

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

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

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

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

Explores Hamiltonian dynamics on convex polytopes, covering symplectic capacities, EHZ capacity, and systolic ratio maximizers.

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

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Explores elementary results in convex optimization, including affine, convex, and conic hulls, proper cones, and convex functions.

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

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

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

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

Explores optimal transport in heat equations and metric spaces.

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

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

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

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

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.