A Vertex Operator Algebra (VOA) is an algebraic system closely related to conformal field theory in physics. VOAs have a rich and well established connection with elliptic and modular functions through Zhu theory which describes the partition and correlation functions for a VOA on a torus. In this talk I will give an introduction to VOA theory and discuss higher genus Zhu theory and its relationship to the geometry of the Riemann surface. |

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