Comments on Vertex Operator Algebras for N=2 SCFTs

Every N=2 SCFT in four dimensions comes equipped with a vertex operator algebrathat encodes the spectrum
and OPE coefficients of an infinite class of 1/4 BPS operators knownas Schur operators. I will discuss a number
of results as well as open questions regarding thestructural properties of the VOAs that appear in this
correspondence and their relationship to four-dimensional physics. I will discuss a proposal for how to recover of
the Higgs branch ofvacua from the VOA and the consequences of this proposal for the behaviour of Schur superconformal
indices under modular transformations. This leads to a surprising relationship between the a-type Weyl
anomaly coefficient and the spectrum of surface operators in an N=2 SCFT.