Symplectic Geometry Seminar

(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'...

The growth of an autonomous Hamiltonian flow in Hofer's metric is not yet well understood. A result of Polterovich and Rosen shows that generically this growth is asymptotically linear, and in all known cases where it is not, it appears to be...

Consider a contact three-manifold, and within it a symplectic surface with boundary on Reeb orbits. We show that assuming a certain inequality on the rotation numbers of the boundary Reeb orbits, there must exist Reeb orbits which intersect the...

I will discuss the occurrence of some notions and results from contact topology in the context of equilibrium and non-equilibrium thermodynamics. Based on joint works with Michael Entov and Lenya Ryzhik.