Related papers: A note on mock automorphic forms and the BPS index
In this paper we investigate the Fourier coefficients of harmonic Maass forms of negative half-integral weight. We relate the algebraicity of these coefficients to the algebraicity of the coefficients of certain canonical meromorphic…
Harmonic weak Maass forms of half-integral weight are the subject of many recent works. They are closely related to Ramanujan's mock theta functions, their theta lifts give rise to Arakelov Green functions, and their coefficients are often…
We study the holomorphic projection of mixed mock modular forms involving sesquiharmonic Maass forms. As a special case, we numerically express the holomorphic projection of a function involving real quadratic class numbers multiplied by a…
Let $R$ be a commutative ring and $M$ a non-zero $R$-module. We introduce the class of \emph{pseudo strongly hollow submodules} (\emph{PS-hollow submodules}, for short) of $M$. Inspired by the theory of modules with \emph{secondary…
We introduce a new class of representations of the cohomological Hall algebras of Kontsevich and Soibelman, which we call cohomological Hall modules, or CoHM for short. These representations are constructed from self-dual representations of…
The exact degeneracies of quarter-BPS dyons in Type II string theory on $K3 \times T^2$ are given by Fourier coefficients of the inverse of the Igusa cusp form. For a fixed magnetic charge invariant $m$, the generating function of these…
We review briefly the thermodynamical interpretation of black hole physics and discuss the problems and inconsistencies in this approach. We provide an alternative interpretation of black holes as quantum objects and investigate the…
Zagier introduced special bases for weakly holomorphic modular forms to give the new proof of Borcherds' theorem on the infinite product expansions of integer weight modular forms on $\SL_2(\ZZ)$ with a Heegner divisor. These good bases…
We give a geometric interpretation for superconformal quantum mechanics defined on a hyper-Kahler cone which has an equivariant symplectic resolution. BPS states are identified with certain twisted Dolbeault cohomology classes on the…
We first give a relative flexible process to construct torsion cohomology classes for Shimura varieties of Kottwitz-Harris-Taylor type with coefficient in a non too regular local system. We then prove that associated to each torsion…
The article covers developments in the representation theory of finite group schemes over the last fifteen years. We start with the finite generation of cohomology of a finite group scheme and proceed to discuss various consequences and…
Motivated by the recently proposed connection between N=2 BPS black holes and topological strings, I study the attractor equations and their interplay with the holomorphic anomaly equation. The topological string partition function is…
We construct a natural basis for the space of weak harmonic Maass forms of weight 5/2 on the full modular group. The non-holomorphic part of the first element of this basis encodes the values of the ordinary partition function p(n). We…
Over the past few years the arithmetic Langlands program has proven useful in addressing physical problems. In this paper it is shown how Langlands' reciprocity conjecture for automorphic forms, in combination with a representation…
In this article, we introduce the concept of weakly uniquely stationary representations. This framework enables us to investigate the complementability of closed subspaces within the context of continuous cohomology with coeffcients in…
The quantum mechanics of $N$ slowly-moving BPS black holes in five dimensions is considered. A divergent continuum of states describing arbitrarily closely bound black holes with arbitrarily small excitation energies is found. A…
Given a non-holomorphic Saito-Kurokawa lift we construct a preimage under the vector-valued lowering operator. In analogy with the case of harmonic weak elliptic Maa{\ss} forms, this preimage allows for a natural decomposition into a…
We consider the spectrum of BPS states of the heterotic sigma model with $(0,8)$ supersymmetry and $T^8$ target, as well as its second-quantized counterpart. We show that the counting function for such states is intimately related to…
Any four-dimensional Supersymmetric Quantum Field Theory with eight supercharges can be associated to a monoidal category of BPS line defects. Any Coulomb vacuum of such a theory can be conjecturally associated to an ``algebra of BPS…
Recent progress in the understanding of the statistical nature of black hole entropy shows that the counting functions in certain classes of models are determined by automorphic forms of higher rank. In this paper we combine these results…