Related papers: Module constructions for certain subgroups of the …
Several situations are known when a holomorphic 2-form on a moduli space of sheaves over some base S is induced by a holomorphic 2-form on S. Moreover, the closedness of the 2-form on the base implies the closedness on the moduli space,…
We study spaces of conformal blocks associated with line bundles over elliptic curves, with coefficients in a vertex algebra. For vertex algebras satisfying suitable finiteness and semisimplicity conditions, which are met by all admissible…
By the theory of Eisenstein series, generating functions of various divisor functions arise as modular forms. It is natural to ask whether further divisor functions arise systematically in the theory of mock modular forms. We establish,…
We study moduli spaces of mirror non-compact Calabi-Yau threefolds enhanced with choices of differential forms. The differential forms are elements of the middle dimensional cohomology whose variation is described by a variation of mixed…
Modular, Jacobi, and mock-modular forms serve as generating functions for BPS black hole degeneracies. By training feed-forward neural networks on Fourier coefficients of automorphic forms derived from the Dedekind eta function, Eisenstein…
In this article, we discuss the relation between Kac-Moody algebras, the monstrous moonshine, Jacobi forms and infinite products. We also review Borcherds' solution of the Moonshine Conjecture and his work of constructing automorphic forms…
Using the framework relating hypergeometric motives to modular forms, we define an explicit family of weight 2 Hecke eigenforms with complex multiplication. We use the theory of ${}_2F_1(1)$ hypergeometric series and Ramanujan's theory of…
The purpose of this paper is to describe explicitly the modules of (Siegel-)Jacobi forms of degree two of index one of any scalar valued weight with respect to some congruence subgroups of small levels $N\leq 4$. Such a structure for the…
This article is an overview of Zagier's and Kim's work on traces of singular moduli. We give more detailed or new proofs to some of their results and also describe some algorithms to compute spaces of Jacobi forms and weight $3/2$ modular…
We consider a set of measures on the real line and the corresponding system of multiple orthogonal polynomials (MOPs) of the first and second type. Under some very mild assumptions, which are satisfied by Angelesco systems, we define…
Generalizing the theory of parity sheaves on complex algebraic stacks due to Juteau-Mautner-Williamson, we develop a theory of twisted equivariant parity sheaves. We use this formalism to construct a modular incarnation of Lusztig and Yun's…
We study moduli spaces of nonlinear sigma-models on Calabi-Yau manifolds, using the one-loop semiclassical approximation. The data being parameterized includes a choice of complex structure on the manifold, as well as some ``extra…
We present a new framework for a broad class of affine Hecke algebra modules, and show that such modules arise in a number of settings involving representations of $p$-adic groups and $R$-matrices for quantum groups. Instances of such…
In this paper we give a trace formula for Hecke operators acting on the cohomology of a Fuchsian group of finite covolume, with coefficients in a module $V$. The proof is based on constructing an operator whose trace on $V$ equals the…
Motivated by the appearance of penumbral moonshine, and by evidence that penumbral moonshine enjoys an extensive relationship to generalized monstrous moonshine via infinite products, we establish a general construction in this work which…
Consider a complex projective space with its Fubini-Study metric. We study certain one parameter deformations of this metric on the complement of an arrangement (=a finite union of hyperplanes) whose Levi-Civita connection is of Dunkl…
In this paper, we consider the Fourier coefficients of meromorphic Jacobi forms of negative index. This extends recent work of Creutzig and the first two authors for the special case of Kac-Wakimoto characters which occur naturally in Lie…
We study the second quantized version of the twisted twining genera of generalized Mathieu moonshine, and prove that they give rise to Siegel modular forms with infinite product representations. Most of these forms are expected to have an…
We show a few basic results about moduli spaces of semistable modules over Lie algebroids. The first result shows that such moduli spaces exist for relative projective morphisms of noetherian schemes, removing some earlier constraints. The…
\textit{Weak moonshine} for a finite group $G$ is the phenomenon where an infinite dimensional graded $G$-module $$V_G=\bigoplus_{n\gg-\infty}V_G(n)$$ has the property that its trace functions, known as McKay-Thompson series, are modular…