SNYM
Symplectic New York Meetings
Symplectic New York Meetings
SNYM is a series of one-day meetings for researchers in the New York area, focused on geometry with connections to symplectic structures in a broad sense. The goal is to foster interaction across career stages and scientific perspectives.
Rutgers University, May 1, 2026
Register here . Rooms are located on Busch campus.
10:15-11:15, Room SEC-117: Zihong Chen (Cambridge)
11:30-12:30, Room SEC-117: Yao Xiao (Rutgers)
12:30-02:00, Faculty Dining Hall: Lunch
02:00-03:00, Room SEC-117: Spencer Cattalani (Stony Brook)
03:00-03:30, Room TBD: Tea
03:30-04:30, Room SEC-117: Soham Chanda (USC)
Abstracts
(Chen) Steenrod operations, operads, and Lagrangian realization
It is classically known that the fundamental class of an algebraic cycle in a smooth projective complex variety has vanishing odd Steenrod powers; this leads to the first counterexample to the integral Hodge conjecture by Atiyah and Hirzebruch. Motivated by mirror symmetry, one may ask what obstructions are there for a middle homology class of a closed symplectic manifold to be realized by a rigid Lagrangian (i.e. supporting an object of the Fukaya category). In this talk, I would like to share some ongoing (and far from complete) attempts at this question that see interesting links to Fukaya category, E_2 operadic structures, and equivariant operations in Gromov-Witten theory.
(Xiao) Lagrangian Floer theory on multiplicity-free manifolds
Symplectic toric manifolds have long served as particularly effective examples in Floer theory. In this talk, we extend existing techniques to study the symplectic topology and the Fukaya category of a family of non-toric symplectic manifolds.
(Cattalani) Ahlfors Currents and symplectic non-hyperbolicity
The study of rational curves has revealed deep connections between symplectic and algebraic geometry. Complex lines are a more general class of curve that has the potential to connect symplectic and complex analytic geometry. Remarkably, as shown by Bangert in 1998, every almost complex structure on a 2n-torus tamed by a linear symplectic structure contains a complex line. These curves are non-compact, which presents a serious difficulty in understanding their symplectic aspects. In this talk, I will explain how Ahlfors currents can be used to resolve this difficulty and produce a theory parallel to that of rational curves.
(Chanda) A contact flow category
We adapt the construction of global Kuranishi charts to the moduli space of genus 0 SFT buildings. Using these charts, we associate a flow category with any non-degenerate contact manifold where the objects are collections of Reeb orbits and morphisms are moduli of buildings. This is joint work with Amanda Hirschi.
Columbia University, December 5, 2025
09:00-10:00, Room 508: Bagels&Coffee
10:00-12:00, Room 312: Ivan Danilenko (Yale)
12:00-02:00, Room 508: Lunch
02:00-04:00, Room 312: Elise LePage (Columbia)
04:00-05:00, Room 508: Cake&Tea
Abstracts
(Danilenko) Mirror symmetry for Coulomb branches
Recently, B. Gammage, M. McBreen, and B. Webster proved homological mirror symmetry for hypertoric varieties. One can consider hypertoric varieties in a more general framework of Coulomb branches as an abelian case. A non-abelian version of mirror symmetry for Coulomb branches was proved in a joint project with M. Aganagic, Y. Li, V. Shende, and P. Zhou. I will outline the main aspects of this case, focusing on the Fukaya side. The proof provided a close connection to diagrammatic algebras and Webster's link invariants.
(LePage) Aganagic’s invariant is Khovanov homology
Recently, Aganagic proposed a categorification of quantum link invariants (corresponding to U_q(g) where g is an ADE Lie algebra) using Lagrangian Floer theory in multiplicative Coulomb branches equipped with a potential. Her original proposal was based on insights from string theory, but the resulting definition of categorified link invariants can be made mathematically rigorous. In this talk, I will review her proposal for link invariants and explain my recent proof (joint with Vivek Shende) that Aganagic’s invariant recovers Khovanov homology in the case g=sl(2).