## Geometry Seminar - Abstracts

### Talk

Wednesday 20 December 2017, 16:00-17:00 in HG03.085

**Daniele Sepe** (Universidade Federal Fluminense)

*Rigidity of symmetric Lagrangian products*

### Abstract

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.

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