Percy Deift is Silver Professor of Mathematics at New York University. He is a Fellow of the American Mathematical Society, a member of the American Academy of Arts and Sciences, a member of the National Academy of Sciences and a member of the American Academy of Sciences and Letters. He is a winner of the George Pólya Prize, a Guggenheim Fellow and a winner of the Henri Poincare Prize. Guillaume Dubach is Professeur Monge at École Polytechnique, Paris. He was awarded the 2019 Wilhelm Magnus Prize and the 2024 Shiing-Shen Chern Young Faculty Award. Carlos Tomei is Professor in the Department of Mathematics at the Pontifical Catholic University of Rio de Janeiro (PUC-Rio). He is a member of the Brazilian Academy of Sciences and a SIAM Fellow. Thomas Trogdon is Professor in the Department of Applied Mathematics at the University of Washington. He won the 2013 SIAM Richard C. DiPrima Prize, the 2017 SIAM Gábor Szegő Prize and earned an NSF CAREER award. He coauthored the book 'Riemann-Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions' (2016) with Sheehan Olver.

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• 1. Introduction; 2. Hamiltonian mechanics and integrable systems; 3. The Toda lattice; 4. Toda without Hamiltonian structure; 5. Random matrix ensembles; 6. Universality for the Toda algorithm; References; Notation and Abbreviations; Index.

Percy Deift is Silver Professor of Mathematics at New York University. He is a Fellow of the American Mathematical Society, a member of the American Academy of Arts and Sciences, a member of the National Academy of Sciences and a member of the American Academy of Sciences and Letters. He is a winner of the George Pólya Prize, a Guggenheim Fellow and a winner of the Henri Poincare Prize. Guillaume Dubach is Professeur Monge at École Polytechnique, Paris. He was awarded the 2019 Wilhelm Magnus Prize and the 2024 Shiing-Shen Chern Young Faculty Award. Carlos Tomei is Professor in the Department of Mathematics at the Pontifical Catholic University of Rio de Janeiro (PUC-Rio). He is a member of the Brazilian Academy of Sciences and a SIAM Fellow. Thomas Trogdon is Professor in the Department of Applied Mathematics at the University of Washington. He won the 2013 SIAM Richard C. DiPrima Prize, the 2017 SIAM Gábor Szegő Prize and earned an NSF CAREER award. He coauthored the book 'Riemann-Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions' (2016) with Sheehan Olver.

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• 1. Introduction; 2. Hamiltonian mechanics and integrable systems; 3. The Toda lattice; 4. Toda without Hamiltonian structure; 5. Random matrix ensembles; 6. Universality for the Toda algorithm; References; Notation and Abbreviations; Index.