Vertex operator algebras on modular curves

Vertex operator algebras (VOAs) are algebraic objects that arose in the study of infinite dimensional lie algebras, mathematical physics, and in the classification of finite simple groups. These days they are understood to give rise to vector bundles on moduli spaces of algebraic curves that are useful in a variety of areas of mathematics and physics. In number theory one frequently encounters them via their incarnation on modular curves. In this talk we will recall background on VOAs and modular forms, and we will give a concrete description of the corresponding VOA bundles in terms of modular forms. We will also describe their connection with quasi-modular forms, which arises naturally from the VOA structure.