Kirill Vaninsky, Hamiltonian formalism for the finite open Toda lative and it's spectral curves

A Poisson formalism for integrable systems is a well-studied topic. Nevertheless,

there is no approach which will cover all known examples integrable with the machinery of

spectral curves. Very often there are no answers even to the simplest questions. We will formulate the main conjecture of the author regarding Poisson structures for these integrable systems. As an example, we consider the finite open Toda lattice.