We consider the partition function of a general vertex operator algebra V on a genus two Riemann surface formed by sewing together two tori. We consider the non-trivial degeneration limit where one torus is pinched down ...

We discuss the partition function for the Heisenberg vertex operator algebra on a genus g Riemann surface formed by sewing handles to a Riemann sphere. In particular, it is shown how the partition can be computed by means ...

We discuss recent work of the authors concerning correlation functions and partition functions for free bosons/fermions and the b-c or ghost system. We compare and contrast the nature of the 1-point functions at genus 1, ...

We define the partition and $n$-point correlation functions for a vertex operator superalgebra on a genus two Riemann surface formed by sewing two tori together. For the free fermion vertex operator superalgebra we obtain ...

We consider the extension of the Heisenberg vertex operator algebra by all its irreducible modules. We give an elementary construction for the intertwining vertex operators and show that they satisfy a complex parametrized ...

We continue our program to define and study $n$-point correlation functions for a vertex operator algebra $V$ on a higher genus compact Riemann surface obtained by sewing surfaces of lower genus. Here we consider Riemann ...

We consider all genus zero and genus one correlation functions for the Virasoro vacuum descendants of a vertex operator algebra. These are described in terms of explicit generating functions that can be combinatorially ...

We consider a number of generalizations of the $\beta$-extended MacMahon Master Theorem for a matrix. The generalizations are based on replacing permutations on multisets formed from matrix indices by partial permutations ...

We consider the application of Abelian orbifold constructions in Meromorphic Conformal Field Theory (MCFT) towards an understanding of various aspects of Monstrous Moonshine and Generalised Moonshine. We review some of the ...

We consider exceptional vertex operator algebras for which particular Casimir vectors constructed from the primary vectors of lowest conformal weight are Virasoro descendants of the vacuum. We discuss constraints on these ...