Hamiltonian dynamics on convex polytopes

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

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

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

Explores Bourgain's theorem on sparsest cut in graphs, emphasizing semimetrics and cut optimization.

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

Explores convex sets, Minkowski-Weyl theorem, and Separation theorem in convex analysis.

Explores the Closest Vector Problem and Voronoi cells in lattice reduction algorithms.

Explores fields deriving from a potential, emphasizing integral and linear aspects.

Covers the Zig Zag Lemma and the long exact sequence of relative homology.

Explores optimal transport and gradient flows in Rd, emphasizing convergence and the role of Lipschitz and Picard-Lindelöf theorems.