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...

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Joint IAS-PU Symplectic Geometry Seminar

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...

## Generic equidistribution of periodic orbits for area-preserving surface diffeomorphisms

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...