Quantum dispersionless KdV hierarchy and vertex algebra

Date
2025/01/23 Thu 10:30 - 12:00
Room
RIMS006号室
Speaker
Zhe Wang
Affiliation
Kyoto
Abstract

We consider the quantization of the dispersionless KdV hierarchy with respect to its first Poisson structure, which was first considered by Y. Eliashberg as an algebraic model for the symplectic field theory of a disk. This quantization problem is then further generalized by Buryak-Rossi to general cohomological field theories. In this talk, we will approach this problem in a combinatorial way. We will first establish a general framework for such quantization problems using vertex algebras, and then construct the quantum dispersionless KdV hierarchy via a non-associative Weyl quantization, which allows us to prove various properties of this quantum integrable system. The talk is based on the preprint arXiv:2410.16747.