The Toda lattice and the Viterbo conjecture

Vinicius Ramos (Instituto de Matemática Pura e Aplicada)

07-Jun-2022, 15:00-16:00 (22 months ago)

Abstract: The Toda lattice is one of the earliest examples of non-linear completely integrable systems. Under a large deformation, the Hamiltonian flow can be seen to converge to a billiard flow in a simplex. In the 1970s, action-angle coordinates were computed for the standard system using a non-canonical transformation and some spectral theory. In this talk, I will explain how to adapt these coordinates to the situation to a large deformation and how this leads to new examples of symplectomorphisms of Lagrangian products with toric domains. In particular, we find a sequence of Lagrangian products whose symplectic systolic ratio is one and we prove that they are symplectomorphic to balls. This is joint work with Y. Ostrover and D. Sepe.

algebraic geometrydifferential geometrysymplectic geometry

Audience: researchers in the topic


Geometria em Lisboa (IST)

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