Is it possible to find an embedded Lagrangian disk in \C^n - B^2n, so that the boundary is a Legendrian in S^{2n-1}? When n=2 the answer is no, but in all higher dimensions such disks exist in abundance. This follows from a more general existence theorem for Lagrangian embeddings with loose concave boundary; in this two-part talk we precisely state and prove this theorem. The proof has two main components: an action-balancing lemma for Lagrangian immersions, and a Lagrangian Whitney trick. We discuss the proof of both, in particular discussing how they both rely on the
In this two-part talk, we will discuss the classification of loose Legendrians in high dimensional contact manifolds. The full classification of Legendrian embeddings up to isotopy is likely an
Nous parlerons d'un travail joint avec Roman Golovko et Georgios Rizell où l'on démontre des restrictions fortes sur la topologie des cobordismes lagrangiens d'une variété legendrienne vers elle-même lorsque les variété legendriennes considérées ont des augmentations.
Everyone knows that a cat dropped upside downcan turn around and fall on his legs. This ability, which at first glance would seem to contradict the conservation of angular momentum, it is instead a consequence of it and is based on the cat's ability to change shape over the course of the fall. In the first part of the seminar we will discuss the kinematics of a deformable body (the cat, but it could also be a satellite or a robotic arm) from the points of view of differential geometryfollowing R. Montgomery.