25/11, UFF. Campus do Gragoatá, Bloco H, sala 407 (como de chegar)
Vinicius Gripp Barros Ramos (IMPA),
Symplectic embeddings, number theory and billiards |
Resumo. The study of symplectic embeddings lies at the core of symplectic topology and its flexbility and ridigity properties has been shown to be very interesting and difficult to predict. In this talk, I will explain a theorem of McDuff-Schlenk relating the Fibonacci numbers with the sharp symplectic embeddings of four-dimensional ellipsoids into balls. I will also talk about a recent result relating these sharp bounds to lengths of billiards in a disk.
Letterio Gatto (Torino),
On the Equations of Plücker Quadrics|
Resumo. Let G(r,n) be the complex Grassmann manifold parametrizing r-dimensional subspaces of Cn, understood as the locus of decomposable tensors in r-th exterior product of Cn. The goal is to sketch the proof of a formula, obtained with P. Salehyan, that characterizes the image of G(r,n) in H*(G(r,n),C) via a natural isomorphism of the r-th exterior product of Cn with H*(G(r,n),C), to be described in the talk. The formula, obtained within a familiar finite-dimensional context, asymptotically recovers the celebrated KP-hierarchy, a system of infinitely many quadratic PDEs eventually seen, in yet another way, as the Plücker equations of a Grassmannian parametrizing infinite-dimensional subspaces of C∞. Most of the computations will be explicitly performed in the case of G(2,n) to simplify the combinatorial issues, although exactly the same arguments work to describe the Plücker embedding of G(r,n), for all 2≤ r≤ n at once.