# Modular linear differential equations of fourth order and minimal W-algebras

Modular linear differential equations are differential equations invariant under modular transformations.

They play important roles in the study of 2D conformal field theory, vertex operator algebras and modular forms.

For example, characters of lisse (C_2-cofinite) vertex algebras and more generally, those of quasi-lisse vertex algebras,

satisfy modular linear differential equations. Moreover, they have also used in the attempt to classify lisse vertex algebras

from their characters. In this talk, we study a certain family of modular linear differential equations of fourth order

and discuss which vertex operator algebras satisfy

the differential equations.