  Associated varieties of vertex algebras are analogue of the associated
varieties of primitive ideals of the universal enveloping algebras of
semisimple Lie algebras. They not only capture some of the important properties
of vertex algebras but also have interesting relationship with the Higgs
branches of four-dimensional $N=2$ superconformal field theories (SCFTs). As a
consequence, one can deduce the modular invariance of Schur indices of 4d $N=2$
SCFTs from the theory of vertex algebras.
