Symplectic Geometry Seminar

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...

In joint work with Bulent Tosun, it was shown that Heegaard Floer theory provides an obstruction for a contact 3-manifold to embed as a contact type hypersurface in standard symplectic 4-space. As one consequence, no Brieskorn homology sphere admits...

In their 2001 paper, Hofer, Wysocki and Zehnder conjectured that every autonomous Hamiltonian flow has either two or infinitely many simple periodic orbits on any compact star-shaped energy level; in the same paper, the authors prove this assuming...

I will give a construction of certain Q-valued deformation invariants of (in particular) complete non-positively curved Riemannian manifolds. These are obtained as certain elliptic Gromov-Witten curve counts. As one immediate application we give the...

Dimitroglou-Rizell-Golovko constructs a family of Legendrians in prequantization bundles by taking lifts of monotone Lagrangians. These lifted Legendrians have a Morse-Bott family of Reeb chords. We construct a version of Legendrian Contact Homology...

I'll explain joint work in progress with Abbondandolo and Kang concerning the Clarke dual action functional of convex domains and pseudoholomorphic planes. In dimension 4, I'll explain applications to the knot types of periodic Reeb orbits.

The dynamics associated with mechanical Hamiltonian flows with smooth potentials that include sharp fronts may be modeled, at the singular limit, by Hamiltonian impact systems: a class of generalized billiards by which the dynamics in the domain’s...