Studying symplectic structures up to deformation equivalences is
a fundamental question in symplectic geometry. Donaldson asked:
given two homeomorphic closed symplectic four-manifolds, are they
diffeomorphic if and only if their stabilized...
The C0 distance on the space of contact forms on a contact
manifold has been studied recently by different authors. It can be
thought of as an analogue for Reeb flows of the Hofer metric on the
space of Hamiltonian diffeomorphisms. In this talk, I...
Given a grid diagram for a knot or link in the three-sphere, we
construct a spectrum whose homology is the knot Floer homology of .
We conjecture that the homotopy type of the spectrum is an
invariant of . Our construction does not use holomorphic...
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...
