A categorical CohFT

Organizers

Kenji Fukaya, Honghao Gao, Hang Yuan(BIMSA)

Speaker

Yash Deshmukh

Institute for Advanced Study

Time

Monday, 16:50-17:50

July 13, 2026

Venue

B725, Shuangqing Complex Building A

A categorical CohFT

Costello and Caldararu-Tu constructed categorical enumerative invariants associated to a smooth and proper Calabi-Yau category equipped with a splitting of the non-commutative Hodge-de Rham spectral sequence. I will discuss an extension of this to a chain-level cohomological field theory (CohFT) structure on the Hochschild homology of the category. This construction will be universal in a precise sense, and I will explain how to exploit this to compare the categorical CohFT of a Fukaya category with the geometric CohFT of the underlying symplectic manifold whenever a chain-level open-closed Gromov-Witten CohFT satisfying suitable properties exists.

About the Speaker

I am a postdoctoral fellow at the Institute for Advanced Study. During 2023-24 I was a visiting fellow at the Max Planck Institute for Mathematics, Bonn. Before that I received my PhD from Columbia University in May 2023 under the supervision of Mohammed Abouzaid. My research focuses on Symplectic topology and Floer theory. Specifically, I am interested in the study of algebraic structures underlying various Floer theoretic invariants. Currently, I'm thinking about relations between algebraic invariants defined using Floer theory and Symplectic Field theory.