Joint IAS-PU Symplectic Geometry Seminar

One of the fundamental problems in contact topology is to classify contact structures on a given 3-manifold. In particular, classifying contact structures on surgeries along a given knot has been very poorly studied. The only fully understood case...

A closed hypersurface in a contact manifold is convex if it admits a transverse contact vector field. A closed hypersurface is robustly non-convex if it cannot be smoothly approximated by a convex hypersurface. The existence of such hypersurfaces...

For closed symplectic manifolds, the Gromov width is among the most fundamental symplectic capacities: it measures the size of the largest embedded symplectic ball and is sensitive to the perturbation of the symplectic forms. A natural question...

A classical construction of Mitsumatsu, later generalized by Hozoori, associates to any (oriented) Anosov flow on a closed 3-manifold M a Liouville structure on the thickening [−1,1]×M. This construction also extends to suitable taut foliations.

From...

We compute the subleading asymptotics of the ECH and elementary ECH capacities of toric domains and show that they recover the perimeter in the liminf, without any genericity required.  As an application, we give the first examples of the failure of...

Complex lines are a class of pseudoholomorphic curves which generalize rational curves. Applications of complex lines to symplectic geometry have been proposed, but they remain poorly understood. In this talk, I will describe a framework for...

Lagrangian correspondences between symplectic manifolds are generalizations of symplectomorphisms and are expected to give the morphisms in the 2-category of symplectic manifolds under geometric compositions. For the (wrapped) Fukaya categories of...

An exact Lagrangian in a cotangent bundle that coincides with

a cotangent fiber outside a compact set, and is disjoint from at least

one cotangent fiber is called a nearby Lagrangian fiber. I will explain

joint work in preparation with Yash Deshmukh...