Jaime Bustillo (ENS, Paris) : A coisotropic non-squeezing theorem in symplectic geometry

mercredi 27 juin 2018, 14:00 → 15:00 Europe/Paris

I will explain how generating functions and Viterbo's capacities can be used to prove a coisotropic non-squeezing theorem for compactly supported Hamiltonian diffeomorphisms in R^{2n}. We will then see that this rigidity also appears in some non-compact settings where the Hamiltonian $H$ is sub-quadratic and also in cotangent bundles of torus. Moreover, I will explain the relation of this theorem with the middle dimensional symplectic rigidity problem. Finally, if I have time, I will briefly explain how this type of rigidity extends to infinite-dimensional settings associated to certain types of Hamiltonian PDEs. As a particular example this result can be applied to the Sine-Gordon equation.