The Toda Lattice, Parallelohedra, and Symplectic Balls

In this talk, we explain how the classical Toda lattice model, one of the earliest examples of nonlinear completely integrable systems, can be used to demonstrate that certain configurations in the classical phase space are symplectic balls in disguise. No background in symplectic geometry is needed. The talk is based on joint work with Vinicius Ramos and Daniele Sepe.