Wednesday 20 December 2017, 16:00-17:00 in HG03.085
Daniele Sepe (Universidade Federal Fluminense)
Rigidity of symmetric Lagrangian products
The problem of finding obstructions to symplectic embeddings is one of the driving questions in symplectic topology. Recently, some symplectic submanifolds of the cotangent bundle to Euclidean space, known as Lagrangian products, have come to the fore in symplectic topology, primarily because of their connection to billiards. For instance, Ramos has calculated the optimal symplectic embeddings of the 4-dimensional Lagrangian bidisc into a ball and an ellipsoid. The aim of this talk is to show that for a large class of Lagrangian products of any dimension, the corresponding symplectic embedding problem is rigid, i.e. the natural inclusion is the best possible embedding. The proof of the result is inspired by Ramos' techniques and combines ideas from the theory of integrable systems with two symplectic capacities, namely the Gromov width and the cube capacity recently introduced by Gutt and Hutchings. This is joint work with Vinicius G. B. Ramos.