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【IMSA】Vinicius Ramos:Toda lattice, billiards&the Viterbo conjecture
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https://www.youtube.com/watch?v=A2nGYYJffLg IMSA Dates: April 17-21, 2023 The Toda lattice is one of the earliest examples of non-linear completely integrable systems. Under a large deformation, the Hamiltonian flow can be seen to converge to a billiard flow in a simplex. In the 1970s, action-angle coordinates were computed for the standard system using a non-canonical transformation and some spectral theory. In this talk, I will explain how to adapt these coordinates to the situation to a large deformation and how this leads to new examples of symplectomorphisms of Lagrangian products with toric domains. In particular, we find a sequence of Lagrangian products whose symplectic systolic ratio is one and we prove that they are symplectic balls. This is joint work with Y. Ostrover and D. Sepe. Vinicius Gripp B. Ramos是一位世界著名的巴西数学家,现任巴西国家纯粹与应用数学研究所IMPA(Instituto Nacional de Matemática Pura e Aplicada)的副教授/Associate Professor。Vinicius Gripp B. Ramos的研究兴趣是辛几何和切触几何(contact geometry)。他研究不同种类的Floer同调,即embedded contact homology、Seiberg-Witten theory和Heegaard Floer homology。 他也对symplectic embeddings、billiard dynamics、Viterbo conjecture和Mahler conjecture感兴趣。Vinicius Gripp B. Ramos于2013年数学博士毕业于美国加州大学伯克利分校(UC Berkeley),导师是美国著名辛几何大师Michael Hutchings。他曾任美国普林斯顿高等研究院的von Neumann fellow。 Vinicius Ramos Homepage:https://vgbramos.impa.br/ Vinicius G. B. Ramos, Daniele Sepe——《On the rigidity of lagrangian products》: https://doi.org/10.48550/arXiv.1710.01753 Yaron Ostrover, Vinicius G. B. Ramos——《Symplectic embeddings of the ℓp-sum of two discs》: https://doi.org/10.48550/arXiv.1911.06062 Yaron Ostrover, Vinicius G. B. Ramos, Daniele Sepe——《From Lagrangian Products to Toric Domains via the Toda Lattice》:https://doi.org/10.48550/arXiv.2309.10912
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