Spectral invariants defined via Embedded Contact Homology (ECH)
or the closely related Periodic Floer Homology (PFH) satisfy a Weyl
law: Asymptotically, they recover symplectic volume. This Weyl law
has led to striking applications in dynamics...
Arnold conjecture says that the number of 1-periodic orbits of a
Hamiltonian diffeomorphism is greater than or equal to the
dimension of the Hamiltonian Floer homology. In 1994, Hofer and
Zehnder conjectured that there are infinitely many periodic...
We show a new Hamiltonian fragmentation result for
four-dimensional symplectic polydisks. As an application to our
result, we prove C0-continuity of the spectral estimators defined
by Polterovich and Shelukhin for polydisks.
We discuss some properties of a pseudo-metric on the
contactomorphism group of a strict contact manifold M induced by
the maximum/minimum of Hamiltonians. We show that it is
non-degenerate if and only if M is orderable and that its metric
topology...
While convex hypersurfaces are well understood in 3d contact
topology, we are just starting to explore their basic properties in
high dimensions. I will describe how to compute contact homologies
(CH) of their neighborhoods, which can be used to...
The Toda lattice is one of the earliest examples of non-linear
completely integrable systems. Under a large deformation, the
Hamiltonian flow can be seen to converge to a billiard flow in a
simplex. In the 1970s, action-angle coordinates were...
A symplectic embedding of a disjoint union of domains into a
symplectic manifold M is said to be of Kahler type (respectively
tame) if it is holomorphic with respect to some (not a priori
fixed) integrable complex structure on M which is compatible...
Given a convex billiard table, one defines the set swept by
locally maximizing orbits for convex billiard. This is a remarkable
closed invariant set which does not depend (under certain
assumptions) on the choice of the generating function. I...
I will describe the construction of a global Kuranishi chart for
moduli spaces of stable pseudoholomorphic maps of any genus and
explain how this allows for a straightforward definition of GW
invariants. For those not convinced of its usefulness, I...
