A uniform geometric construction of chiral differential operators

Geometric Representation Theory Seminar

Organizers：

Lin Chen, Will Donovan, Penghui Li, Peng Shan, Changjian Su, Wenbin Yan

Speaker：

Xuanzhong Dai 戴烜中 (RIMS)

Time：

Fri., 10:30-11:30 am, Nov. 28, 2025

Venue：

B627, Shuangqing Complex Building A

Title:

A uniform geometric construction of chiral differential operators

Abstract:

In this talk, we present a uniform geometric framework that connects the representation theory of vertex algebras with symplectic geometry and invariant theory. We construct chiral analogues of differential operators acting on classical invariant rings, realized as global sections of sheaves of chiral differential operators associated with vector bundles on smooth open subvarieties of affine GIT quotients, using the BRST reduction. Within this framework, we develop a localization theory for modules over these global sections, following Borisov’s approach, and prove that the resulting vertex algebras are simple, with the category of $C_1$-cofinite, lower-bounded modules equivalent to the category of vector spaces. As an application, we construct new infinite families of simple conformal quasi-lisse vertex algebras. This is joint work with Tomoyuki Arakawa and Bailin Song.