Joint IAS-PU Symplectic Geometry Seminar

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...

Higher-dimensional Heegaard Floer homology (HDHF) is defined by extending Lipshitz's cylindrical reformulation of Heegaard Floer homology from surfaces to arbitrary Liouville domains. The HDHF also serves as a model for Lagrangian Floer homology of...

Given a Hamiltonian H∈C∞(S1×M), what is the relationship between the dynamics of the isotopy generated by H and the various Floer-theoretic invariants associated to H? In this talk I will discuss how — in the case where M is a closed surface —one...

Legendrian Contact Homology (LCH) was among the first, and is still among the most important, non-classical invariants of Legendrian knots. In this talk, I will tell a story that builds up ever more sophisticated analogues of Poincare Duality in LCH...

In the late '90s, Eliashberg and Thurston established a remarkable connection between foliations and contact structures in dimension three: any co-oriented, aspherical foliation on a closed, oriented 3-manifold can be approximated by positive and...