Convex Bodies: Properties and Theorems

Related lectures (11)

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

Explores the Brunn-Minkowski inequality in convex geometry and related concepts.

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

Explores the similarity of convex bodies, affine transformations, the Johen's Theover theorem, and KKT conditions.

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

Covers isoperimetric inequalities and Gaussian measure on Euclidean space.

Explores integer programming, John's Theorem, and the reduction to shortest vector computations in convex bodies.

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

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

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