Symplectic Dynamics

Distinguishing fillings via dynamics of Fukaya categories

Yusuf Baris Kartal
Massachusetts Institute of Technology
November 12, 2018
Given a Weinstein domain $M$ and a compactly supported, exact symplectomorphism $\phi$, one can construct the open symplectic mapping torus $T_\phi$. Its contact boundary is independent of $\phi$ and thus $T_\phi$ gives a Weinstein filling of $T_0\times M$, where $T_0$ is the punctured 2-torus. In this talk, we will outline a method to distinguish $T_\phi$ from $T_0\times M$ using dynamics and deformation theory of their wrapped Fukaya categories.

Structures in the Floer theory of Symplectic Lie Groupoids

James Pascaleff
University of Illinois, Urbana-Champaign
October 15, 2018
A symplectic Lie groupoid is a Lie groupoid with a
multiplicative symplectic form. We take the perspective that such an object is symplectic manifold with an extra categorical structure. Applying the machinery of Floer theory, the extra structure is expected to yield a monoidal structure on the Fukaya category, and new operations on the closed string invariants. I will take an examples-based approach to working out what these structures are, focusing on cases where the
Floer theory is tractable, such as the cotangent bundle of a compact manifold.

Semitoric families

Joseph Palmer
Rutgers University
October 8, 2018
Semitoric systems are a type of 4-dimensional integrable system which has been classified by Pelayo-Vu Ngoc in terms of five invariants, one of which is a family of polygons generalizing the Delzant polygons which classify 4-dimensional toric integrable systems. In this talk we present one-parameter families of integrable systems which are semitoric at all but finitely many values of the parameter, which we call semitoric families, with the goal of developing a strategy to find a semitoric system associated to a given partial list of semitoric invariants.