SNYM

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.

Columbia University, December 5, 2025

• 09:00-10:00 Bagels&Coffee

• 10:00-12:00 Ivan Danilenko

• 12:00-02:00 Lunch

• 02:00-04:00 Elise LePage

• 04:00-05:00 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).