Related papers: Twisting moduli for GL(2)

Let $k$ be a positive integer such that $k\equiv3\mod4$, and let $N$ be a positive square-free integer. In this paper, we compute a basis for the two-dimensional subspace $S_{\frac{k}{2}}(\Gamma_{0}(4N),F)$ of half-integral weight modular…

Motivated by logarithmic conformal field theory and Gromov-Witten theory, we introduce a notion of a twisted module of a vertex algebra under an arbitrary (not necessarily semisimple) automorphism. Its main feature is that the twisted…

We establish Flat Torus Theorem type results for groups acting on small cancellation complexes satisfying C(6), C(4)-T(4) and C(3)-T(6) conditions. For C(3)-T(6) complexes the result closely parallels the CAT(0) setting. For C(6) complexes…

Let $A$ be the ring of elements in an algebraic function field $K$ over a finite field $F_q$ which are integral outside a fixed place $\infty$. In an earlier paper we have shown that the Drinfeld modular group $G=GL_2(A)$ has automorphisms…

Suppose l=2m+1, m>0. We introduce m "theta-series", [1],...,[m], in Z/2[[x]]. It has been conjectured that the n for which the coefficient of x^n in 1/[i] is 1 form a set of density 0. This is probably always false, but in certain cases,…

In a previous paper \cite{BorGunn}, we defined the space of toric forms $\TTT(l)$, and showed that it is a finitely generated subring of the holomorphic modular forms of integral weight on the congruence group $\Gamma_1(l)$. In this article…

Let $G_{2n}$ be the Eisenstein series of weight $2n$ for the full modular group $\Gamma=SL_2(\ZZ)$. It is well-known that the space $M_{2k}$ of modular forms of weight $2k$ on $\Gamma$ has a basis $\{G_{4}^\alpha G_{6}^\beta\ |\…

It is shown that any irreducible analytic 1-flat $G$-structure as well as any analytic torsion-free affine connection with irreducibly acting holonomy group can, in principle, be contstructed by twistor methods.

Let $\rho$ denote an irreducible two-dimensional representation of $\Gamma_{0}(2)$. The collection of vector-valued modular forms for $\rho$, which we denote by $M(\rho)$, form a graded and free module of rank two over the ring of modular…

We consider a class of heterotic N=2 -> 0 super no-scale Z_2-orbifold models. An appropriate stringy Scherk-Schwarz supersymmetry breaking induces tree level masses to all massless bosons of the twisted hypermultiplets and therefore…

We set up an algebraic framework for the study of pseudoholomorphic discs bounding nonorientable Lagrangians, as well as equivariant extensions of such structures arising from a torus action. First, we define unital cyclic twisted…

Modular graph forms (MGFs) are a class of non-holomorphic modular forms which naturally appear in the low-energy expansion of closed-string genus-one amplitudes and have generated considerable interest from pure mathematicians. MGFs satisfy…

Let f be a newform of weight at least 3 with Fourier coefficients in a number field K. We show that the universal deformation ring of the mod lambda Galois representation associated to f is unobstructed, and thus isomorphic to a power…

We prove that the complement of a toric arrangement has the homotopy type of a minimal CW complex. As a corollary we obtain that the integer cohomology of these spaces is torsion free. We use Discrete Morse Theory, providing a sequence of…

Let $N(\Gamma,G)$ be the number of homomorphisms from $\Gamma$ to $G$ up to conjugation by $G$. Physics of four-dimensional $\mathcal{N}=4$ supersymmetric gauge theories predicts that $N(\Gamma,G)=N(\Gamma , \tilde G)$ when $\Gamma$ is a…

This paper presents a worldsheet theory describing holomorphic maps to twistor space with N fermionic directions. The theory is anomaly free when N=8. Via the Penrose transform, the vertex operators correspond to an N=8 Einstein…

Non-commutative torsors (equivalently, two-cocycles) for a Hopf algebra can be used to twist comodule algebras. After surveying and extending the literature on the subject, we prove a theorem that affords a presentation by generators and…

We study sums of additively twisted Fourier coefficients of a holomorphic cusp form, a Maass cusp form, and the symmetric-square lift of a holomorphic cusp form. We obtain bounds that are uniform with respect to both the form and the terms…

Given a supermanifold equipped with an odd distribution of maximal dimension and constant symbol, we construct the formal moduli problem of deformations of the distribution. This moduli problem is described by a local super dg Lie algebra…

In this article we perform an extensive study of the spaces of automorphic forms for GL(2) of weight two and level N, for N an ideal in the ring of integers of the quartic CM field generated by the twelfth roots of unity. This study is…