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...
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...
