We introduce an SFT-type invariant for Legendrian knots in R^3,
which is a deformation of the Chekanov-Eliashberg differential
graded algebra. The differential includes components that count
index zero pseudoholomorphic disks with up to two positive...
One of the earliest achievements of mirror symmetry was the
prediction of genus zero Gromov-Witten invariants for the quintic
threefold in terms of period integrals on the mirror. Analogous
predictions for open Gromov-Witten invariants in closed...
We show that two generic, open, convex or concave toric domains
in R4 are symplectomorphic if and only if they agree up to
reflection. The proof uses barcodes in positive S1-equivariant
symplectic homology, or equivalently in cylindrical contact...
Given an anticanonical divisor in a projective variety, one
naturally obtains a monotone Kähler manifold, and the divisor
complement is naturally a Liouville manifold. For certain kinds of
singular divisors, we will outline a result obtaining rigid...
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...
First considered by Lee in the 40s, locally conformally
symplectic (LCS) geometry appears as a generalization of symplectic
geometry which allows for the study of Hamiltonian dynamics on a
wider range of manifolds while preserving the local...
Associated to a star-shaped domain
in ℝ2nR2n are two increasing sequences of
capacities: the Ekeland-Hofer capacities and the so-called
Gutt-Hutchings capacities. I shall recall both constructions and
then present the main theorem that they are the...
Given a path-connected topological space X, a differential
graded (DG) local system (or derived local system) is a module over
the DGA of chains on the based loop space of X. I will explain how
to define in the symplectically aspherical case...
Chen and Ruan constructed symplectic orbifold Gromov-Witten
invariants more than 20 years ago. In ongoing work with Alex
Ritter, we show that moduli spaces of pseudo-holomorphic curves
mapping to a symplectic orbifold admit global Kuranishi
charts...
It is conjectured that every Reeb flow on a closed
three-manifold has either two, or infinitely many, simple periodic
orbits. I will survey what is currently known about this
conjecture. Then, I will try to explain some of the key ideas
behind...
