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Special Colloquium: The Toda lattice, billiards and symplectic geometry

Special Events

Speaker: Vinicius G.B. Ramos, IAS
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Location: 1147 MSB
Start time: Thu, Jan 19 2023, 3:10PM

The Toda lattice is one of the earliest examples of a non-linear completely integrable system. Under a large deformation, the corresponding Hamiltonian flow can be seen to converge to a billiard flow in a simplex. In the 1970s, action-angle coordinates were computed for this system using a non-canonical transformation and some spectral theory. In this talk, I will explain how these coordinates lead to a very interesting symplectomorphism that provides evidence for an important conjecture of Viterbo. I will also speak about the history of symplectic embeddings and how billiard dynamics provide beautiful sharp embeddings.