Symplectic Dynamics/Geometry Seminar

We will ask how many Lagrangian tori, say with an integral area class, can be `packed' into a given symplectic manifold. Similarly, given an arrangement of such tori, like the integral product tori in Euclidean space, one can ask about the...

Suppose L is a link with n components and the rank of Kh(L;Z/2) is 2^n, we show that L can be obtained by disjoint unions and connected sums of Hopf links and unknots. This result gives a positive answer to a question asked by Batson-Seed, and...

I will explain how coisotropic submanifolds of symplectic manifolds can be distinguished among all submanifolds by a criterion ("local rigidity") related to the Hofer energy necessary to disjoin open sets from them. This criterion is invariant under...

We prove several relations between spectrum and dynamics including wave trace expansion, sharp/improved Weyl laws, propagation of singularities and quantum ergodicity for the sub-Riemannian (sR) Laplacian in the four dimensional quasi-contact case...

I'll show a graphical user interface I wrote which explores the problem of inscribing rectangles in Jordan loops. The motivation behind this is the notorious Square Peg Conjecture of Toeplitz, from 1911.

I did not manage to solve this problem, but I...

Starting from a contact manifold and a supporting open book decomposition, an explicit construction by Bourgeois provides a contact structure in the product of the original manifold with the two-torus. In this talk, we will discuss recent results...

Certain `flexible' structures in symplectic and contact topology satisfy h-principles, meaning that their geometry reduces to underlying topological data. Although these flexible structures have no interesting geometry by themselves, I will show how...

I will explain a polyfold proof, joint with Katrin Wehrheim, of the Arnold conjecture: the number of 1-periodic orbits of a nondegenerate 1-periodic Hamiltonian on a closed symplectic manifold is at least the sum of the Betti numbers. Our proof is a...