Modular linear differential equations (MLDEs) are differential equations
involving Serre derivatives, with coefficients that are modular forms.
In this talk, I will explain the role of MLDEs in the theory of vertex
algebras and discuss how they can be used in the classification of
vertex algebras. Specifically, I will present our result on the
classification of vertex algebras whose characters are solutions of
third-order MLDEs.
This talk is based on joint work with Kiyokazu Nagatomo and Yuichi Sakai.