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...
I will discuss a recent work constructing quasimorphisms on the
group of area and orientation preserving homeomorphisms of the
two-sphere. The existence of these quasimorphisms answers a
question of Entov, Polterovich, and Py. As an
immediate...
If G is a Lie group whose adjoint representation preserves a
nondegenerate symmetric bilinear form on its Lie algebra (e.g. a
semisimple group) and F is the fundamental group of a closed
oriented surface S, then the spaces of equivalence classes
of...
I will discuss some recent work showing that a generic
area-preserving diffeomorphism of a closed surface has an
equidistributed sequence of periodic orbits. The proof uses several
properties of spectral invariants from periodic Floer
homology...
I will talk about ongoing work with S. Venugopalan on computing
disk potentials (which are counts of holomorphic disks with
boundary on a Lagrangian) via multi-directional neck stretching.
The focus will be on examples.
We describe two extensions, called the virtual Morse-Bott index
and circle-equivariant virtual Morse-Bott index, of the classical
Morse-Bott index of a Morse-Bott function on a smooth manifold to
the setting of (a) suitably defined analytic...
