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Hamiltonian dynamics on convex polytopes
This lecture by the instructor covers Hamiltonian dynamics on convex polytopes, focusing on symplectic capacities, Ekeland-Hofer-Zehnder capacity, sub-additivity for hyperplane cuts, and maximizers of systolic ratio. The lecture delves into various conjectures, including those by Hermann, Hofer, Viterbo, and Akopyan-Karasev-Petrov. It explores the EHZ capacity, closed characteristics, and Viterbo's conjecture for simplices in R4. The main results regarding the EHZ capacity for convex polytopes are discussed, along with examples and proofs related to the systolic ratio maximizers and sub-additivity for hyperplane cuts.