Symplectic Geometry Seminar

This talk is based on joint work with Yang Li. I will discuss the problem of counting special Lagrangians in Calabi-Yau 3-folds and Fueter sections to define new numerical and Floer-theoretic invariants. The key challenges are the non-compactness...

In this talk, we will present a proof of contact big fiber theorem, based on invariants read off from contact Hamiltonian Floer homology. The theorem concludes that any contact involutive map on a Liouville fillable contact manifold admits at least...

In this talk we discuss a relation between the contact version

of the Hofer norm and positive loops of contactomorphisms.

This leads to a new criterion for the existence of contractible positive

loops in terms of open book decompositions and previously...

(joint work with Shaoyun Bai) Using a new version of transversality condition (the FOP transversality) on orbifolds, one can construct Hamiltonian Floer theory over integers for all compact symplectic manifolds. In this talk I will first describe...

The open Gromov-Witten (OGW) potential is a function defined  on the Maurer-Cartan space of a closed Lagrangian submanifold in a  symplectic manifold with values in the Novikov ring. From the values  of the OGW potential, one can extract so-called...

In a series of papers with Alexander Ritter, we construct a symplectic cohomology for open non-convex symplectic manifolds that admit pseudo-holomorphic C*-actions. Out of this construction, we get a filtration on ordinary cohomology of these...

We will explore certain C0-rigidity and flexibility phenomena in the study of contact transformations. In particular, we will show how the dichotomy between contact squeezing and non-squeezing is reflected in the group of contact homeomorphisms. We...

We show that skein valued counts of open holomorphic curves in a symplectic Calabi-Yau 3-fold with Maslov zero Lagrangian boundary condition are invariant under deformations and discuss applications (Ooguri-Vafa conjecture and simple recursion...

The spectral norm on the group of Hamiltonian diffeomorphisms of a symplectic manifold is defined via a homological min-max process on the filtered Floer homology. Based on the spectral norm one defines the spectral capacity of domains which is...

Let Y be a symplectic divisor of X, ω. In the Kahler setting, Givental's Quantum Lefschetz formula relates certain Gromov-Witten invariants (encoded by the G function) of X and Y. Given an Lagrangian L in (Y, ω|Y), we can lift it to a Lagrangian L'...