# Vertex algebras of divisors in toric Calabi-Yau threefolds from perverse coherent extensions

### APA

Butson, D. (2022). Vertex algebras of divisors in toric Calabi-Yau threefolds from perverse coherent extensions. Perimeter Institute. https://pirsa.org/22110046

### MLA

Butson, Dylan. Vertex algebras of divisors in toric Calabi-Yau threefolds from perverse coherent extensions. Perimeter Institute, Nov. 04, 2022, https://pirsa.org/22110046

### BibTex

@misc{ pirsa_22110046, doi = {10.48660/22110046}, url = {https://pirsa.org/22110046}, author = {Butson, Dylan}, keywords = {Mathematical physics}, language = {en}, title = {Vertex algebras of divisors in toric Calabi-Yau threefolds from perverse coherent extensions}, publisher = {Perimeter Institute}, year = {2022}, month = {nov}, note = {PIRSA:22110046 see, \url{https://pirsa.org}} }

Dylan Butson University of Oxford

## Abstract

I'll explain work in progress, joint with Miroslav Rapcak, on geometric constructions of vertex algebras associated to divisors in toric Calabi-Yau threefolds, in terms of moduli stacks of objects in certain exotic abelian subcategories of complexes of coherent sheaves on the underlying threefold. These vertex algebras were originally proposed by Gaiotto-Rapcak, and constructed mathematically in the example of affine space by Rapcak-Soibelman-Yang-Zhao, building on Schiffmann-Vasserot's proof of the AGT conjecture. We give a geometric explanation and generalization of the quivers with potential that feature in the latter results, and outline the analogous construction of vertex algebras in this setting.

Zoom link: https://pitp.zoom.us/j/93749710253?pwd=Y3NUTHBXZ3FPQUdPU0E0d0ttVzFFdz09