Given an area-preserving surface diffeomorphism, what can one
say about the topological properties of its periodic orbits? In
particular, a finite set of periodic orbits gives rise to a braid
in the mapping torus, and one can ask which isotopy...
I will discuss work in progress with Morgan Weiler on knot
filtered embedded contact homology (ECH) of open book
decompositions of S^3 along T(2,q) torus knots to deduce
information about the dynamics of symplectomorphisms of the genus
(q-1)/2 pages...
The four dimensional ellipsoid embedding function of a toric
symplectic manifold M measures when a symplectic ellipsoid embeds
into M. It generalizes the Gromov width and ball packing numbers.
This function can have a property called an infinite...
ECH capacities have found many applications to symplectic
embedding problems, most of which in the toric setting. I will
discuss a new application of ECH to studying optimal embeddings for
non-toric rational surfaces. The key convex geometric...
An Anosov flow Φ on a closed 3-manifold M gives rise to a
non-Weinstein Liouville structure on V:=[−1,1]×M. Building upon the
work of Hozoori, we establish a homotopy correspondence between
Anosov flows and certain pairs of contact forms. Moreover...
I shall present two billiard-like systems associated with
a convex hypersurface in a symplectic space, the outer and an
inner ones. The talk will survey the known results and
focus on open problems.
I will discuss an idea of constructing a category associated
with a pair of holomorphic Lagrangians in a hyperkahler manifold,
or, more generally, a manifold equipped with a triple of almost
complex structures I,J,K satisfying the quaternionic...
Most work on Lagrangian fillings of Legendrian knots to date has
concentrated on orientable fillings, but instead I will present
some first steps in constructions of and (especially) obstructions
to the existence of (decomposable exact) non...
Because of the presence of non-trivial automorphisms of stable
maps, Gromov-Witten invariants of a general symplectic manifold are
usually rational-valued. Realizing a proposal of Fukaya-Ono back in
the 1990s, I will explain how to construct integer...
Given a trivalent plane graph embedded in the Euclidean plane
(up to isotopy), Treumann and Zaslow constructed and studied a
certain associated Legendrian surface embedded in standard contact
R5, nowadays referred to as a Legendrian 2-weave. Using...
