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
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
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,
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