25/11, UFF. Campus do Gragoatá, Bloco H, sala 407 (como de chegar)
10:3011:30 
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 McDuffSchlenk relating the Fibonacci numbers with the sharp symplectic embeddings of fourdimensional ellipsoids into balls. I will also talk about a recent result relating these sharp bounds to lengths of billiards in a disk.
 12:0013:00 
Letterio Gatto (Torino),
On the Equations of Plücker Quadrics
Resumo. Let G(r,n) be the complex Grassmann manifold parametrizing rdimensional subspaces of C^{n}, understood as the locus of decomposable tensors in rth exterior product of C^{n}. 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 rth exterior product of C^{n} with H^{*}(G(r,n),C), to be described in the talk. The formula, obtained within a familiar finitedimensional context, asymptotically recovers the celebrated KPhierarchy, a system of infinitely many quadratic PDEs eventually seen, in yet another way, as the Plücker equations of a Grassmannian parametrizing infinitedimensional 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.

