Symplectic Geometry Seminar

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...

Relative symplectic cohomology, an invariant of subsets in a symplectic manifold, was recently introduced by Varolgunes. In this talk, I will present a generalization of this invariant to pairs of subsets, which shares similar properties with the...

I will discuss a recent proof of new cases of the Hilbert-Smith conjecture for actions by homeomorphisms of symplectic nature. In particular, it rules out faithful actions of the additive p-adic group in this setting and provides further...

I will discuss an adaptation of Gromov's ideal-valued measures to symplectic topology. It leads to a unified viewpoint at three "big fiber theorems": the Centerpoint Theorem in combinatorial geometry, the Maximal Fiber Inequality in topology, and...

Since the beginning of the subject, it has been speculated that Gromov-Witten invariants should admit refinements in complex cobordism. I will propose a resolution of this question based on joint work-in-progress with Abouzaid, building on recent...

For the past 25 years, a key player in contact topology has been the Floer-theoretic invariant called Legendrian contact homology. I'll discuss a package of new invariants for Legendrian knots and links that builds on Legendrian contact homology and...

We discuss the shape invariant, a sort of set valued symplectic capacity defined by the Lagrangian tori inside a domain of R4. Partial computations for convex toric domains are sometimes enough to give sharp obstructions to symplectic embeddings...