Symplectic Geometry Seminar

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.

Apart from the usual transversality problems in defining curve counting invariants, when defining the open Gromov-Witten invariants of a Lagrangian one has to deal with the fact that the moduli spaces have boundary. Thus a homological (virtual)...

Distinct Hamiltonian isotopy classes of monotone Lagrangian tori in $\mathbb{C} P^2$ can be associated to Markov triples. With two exceptions, each of these tori are symplectomorphic to exactly three Hamiltonian isotopy classes of tori in the ball...

Symplectic manifolds exhibit curious behaviour at the interface of rigidity and flexibility. A non-squeezing phenomenon discovered by Gromov in the 1980s was the first manifestation of this. Since then, extensive research has been carried out into...

I will introduce a new structure on (relative) Symplectic Cohomology defined in terms of a PROP called the “Plumber’s PROP.” This PROP consists of nodal Riemann surfaces, of all genera and with multiple inputs and outputs, satisfying a condition...

Algebraic torsion is a means of understanding the topological complexity of certain homomorphic curves counted in some Floer theories of contact manifolds.  This talk focuses on algebraic torsion and the contact invariant in embedded contact...

In 1987, Hofer and Zehnder showed that for any smooth function H

on ℝ2n, almost every compact and regular level set contains at least one closed characteristic. I'll show that, when n=2, almost every compact and regular level set contains at least...