Toda Lattice, Billiards & the Viterbo Conjecture

Explore the fascinating connections between the Toda lattice, billiards, and the Viterbo conjecture in this 35-minute conference talk by V. Ramos from the Instituto de Matemática Pura e Aplicada. Delve into the world of non-linear completely integrable systems, focusing on the Toda lattice and its convergence to billiard flow in a simplex under large deformation. Discover how action-angle coordinates, originally computed for the standard system, can be adapted to the large deformation scenario. Learn about the implications of this research, including new examples of symplectomorphisms of Lagrangian products with toric domains. Examine the sequence of Lagrangian products with a symplectic systolic ratio of one and their proof as symplectic balls. Gain insights into this collaborative work with Y. Ostrover and D. Sepe, presented at the Gauge Theory and Low Dimensional Topology conference held at the University of Miami.

V. Ramos, Instituto de Matemática Pura e Aplicada: Toda lattice, billiards & the Viterbo conjecture