A Lagrangian cobordism between Legendrian knots is an important
notion in symplectic geometry. Many questions, including basic
structural questions about these surfaces are yet unanswered. For
instance, while it is known that these cobordisms form a...
Contact homology is a Floer-type invariant for contact
manifolds, and is a part of Symplectic Field Theory. One of its
first applications was the existence of exotic contact structures
on spheres. Originally, contact homology was defined only
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
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 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...