Let f be a polynomial over the complex numbers with an isolated
singular point at the origin and let d be a positive integer. To
such a polynomial we can assign a variety called the dth contact
locus of f. Morally, this corresponds to the space of d...
A transverse link in a contact 3-manifold forces topological
entropy if every Reeb flow possessing this link as a set of
periodic orbits has positive topological entropy. We will explain
how cylindrical contact homology on the complement of...
In this talk we will be addressing the question whether a given
Lagrangian torus in a toric monotone symplectic manifold can be
realized as the fixed point set of an anti-symplectic involution
(in which case it is called "real"). In the case of...
Gromov nonsqueezing tells us that symplectic embeddings are
governed by more complex obstructions than volume. In particular,
in 2012, McDuff-Schlenk computed the embedding capacity function of
the ball, whose value at a is the size of the smallest...
I will explain a duality theorem with products in Rabinowitz-Floer
homology. This has a bearing on string topology and explains a
number of dualities that have been observed in that setting. Joint
work in progress with Kai Cieliebak and Nancy...
Homological mirror symmetry predicts that the derived category of
coherent sheaves on a curve has a symplectic counterpart as the
Fukaya category of a mirror space. However, with the exception of
elliptic curves, this mirror is usually a symplectic...
This talk beings with a light introduction, including some
historical anecdotes to motivate the development of this Floer
theoretic machinery for contact manifolds some 25 years ago. I will
discuss joint work with Hutchings which constructs...
Given a smooth knot K in the 3-sphere, a classic question in knot
theory is: What surfaces in the 4-ball have boundary equal to K?
One can also consider immersed surfaces and ask a “geography”
question: What combinations of genus and double points...
There is growing interest in looking at operations on quantum
cohomology that take into account symmetries in the holomorphic
spheres (such as the quantum Steenrod powers, using a
Z/p-symmetry). In order to prove relations between them, one needs
to...
We discuss interactions between quantum mechanics and symplectic
topology including a link between symplectic displacement energy, a
fundamental notion of symplectic dynamics, and the quantum speed
limit, a universal constraint on the speed of...
