  This paper focuses on the connection of holomorphic two-dimensional
factorization algebras and vertex algebras which has been made precise in the
forthcoming book of Costello-Gwilliam. We provide a construction of the
Virasoro vertex algebra starting from a local Lie algebra on the complex plane.
Moreover, we discuss an extension of this factorization algebra to a
factorization algebra on the category of Riemann surfaces. The factorization
homology of this factorization algebra is computed as are the correlation
functions. We provide an example of how the Virasoro factorization algebra
implements conformal symmetry of the beta-gamma system using the method of
effective BV quantization.
