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Vertex operator algebra bundles on modular curves and their associated modular forms
Daniel Barake, Owen Chuchman, Cameron Franc +2
This paper describes the vector bundle on the elliptic modular curve that is associated to a vertex operator algebra (VOA) or more generally a quasi-vertex operator algebra (QV…
An Improved Lower Bound on the Image of the 2-adic Character Map for the Heisenberg Algebra via Modular Linear Differential Equations
Daniel Barake, Cameron Franc
We describe families of MLDEs whose solutions are modular forms of level one that converge, -adically, to a Hauptmodul on by using a theorem of Serre. Then, we apply th…
The moduli space of representations of the modular group into
Angelica Babei, Andrew Fiori, Cameron Franc
In this paper we construct a large four-dimensional family of representations of the modular group into . Precisely, this family is an etale cover of degree of an open su…
Density formulas for -adically bounded primes for hypergeometric series with rational and quadratic irrational parameters
Cameron Franc, Nathan Heisz, Hannah Nardone
We study densities of -adically bounded primes for hypergeometric series in two cases: the case of generalized hypergeometric series with rational parameters, and the case of $_…
Invitation to -adic vertex algebras
Cameron Franc, Geoffrey Mason
An overview of the authors' ideas about the process of completing a -adically normed space in the setting of vertex operator algebras. We focus in particular on the -adic Hei…
On -adic modularity in the -adic Heisenberg algebra
Cameron Franc, Geoffrey Mason
We establish existence theorems for the image of the normalized character map of the -adic Heisenberg algebra taking values in the algebra of Serre -adic modular forms $M…