9:30 AM — 10:30 AM
Speaker: Robert Lipshitz, University of Oregon
Location: McDonnell A10

The Pairing Theorem and the Fukaya Category

We will discuss a Fukaya-categorical interpretation of bordered HF^- with torus boundary and, using it, sketch a proof of the Pairing Theorem.

11:00 AM — 12:00 PM
Speaker: Jonathan Zung, MIT
Location: McDonnell A02

Pseudo-Anosov flows and transverse foliations

Thurston proposed a program to construct a pseudo-Anosov flow transverse to a given taut foliation. We study the converse problem: given a pseudo-Anosov flow, when is there a transverse taut foliation? I will present some combinatorial methods to construct and obstruct such foliations. Parts work in progress with Siddhi Krishna and Thomas Massoni.

1:30 PM — 2:30 PM
Speaker: Luya Wang, IAS
Location: McDonnell A02

Spinal open books and symplectic fillings with exotic fibers

An evolving theme in symplectic topology has been the classification of symplectic manifolds, where pseudoholomorphic curves are often useful for establishing uniqueness and finiteness results. In the closed case, this traces back to Gromov and McDuff. In a series of works, Wendl used punctured pseudoholomorphic foliations to classify symplectic fillings of contact three-manifolds supported by planar open books, turning it into a problem about monodromy factorizations. In a joint work with Hyunki Min and Agniva Roy, we build on the recent works of Lisi--Van Horn-Morris--Wendl in using spinal open books to further study the classification problem of symplectic fillings of higher genus open books. In particular, we provide the local model of the mysterious "exotic fibers" in a generalized version of Lefschetz fibrations, which captures a natural type of singularity at infinity. We will give some applications to classifying symplectic fillings via this new phenomenon.

3:00 PM — 4:00 PM
Speaker: Rohil Prasad, UC Berkeley
Location: McDonnell A02

Low-action holomorphic curves and invariant sets

Holomorphic curves are a very useful tool for studying the topology and dynamics of symplectic manifolds. I will start with an overview of how holomorphic curves can detect periodic orbits of symplectic diffeomorphisms, taking the viewpoint pioneered by Hofer in 1993. Then, I will discuss a new method using “low-action” holomorphic curves to detect closed invariant subsets that might be more general than periodic orbits. This has a few applications. I will mention one of them: a generalization to higher genus surfaces of a theorem by Le Calvez and Yoccoz. The talk is based on joint work with Dan Cristofaro-Gardiner.