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...
Toric integrable systems, also known as symplectic toric
manifolds, arise as examples in different contexts within geometry
and related areas. Semitoric integrable systems are a
generalization of toric integrable systems in dimension four. In
this...
For the past 25 years, Legendrian contact homology has played a
key role in contact topology. I'll discuss a package of new
invariants for Legendrian knots and links that builds on Legendrian
contact homology and is derived from rational symplectic...
We discuss constraints on exact Lagrangian embeddings obtained
from considering bordism classes of flow modules over Lagrangian
Floer flow categories. This talk reports on joint work with Noah
Porcelli.
The presence of hyperbolic periodic orbits or invariant sets
often has an affect on the global behavior of a dynamical system.
In this talk we discuss two theorems along the lines of this
phenomenon, extending some properties of Hamiltonian...
