Related papers: Elliptic modular graph forms, equivariant iterated…

Banks--Panzer--Pym have shown that the volume integrals appearing in Kontsevich's deformation quantization formula always evaluate to integer-linear combinations of multiple zeta values (MZVs). We prove a sort of converse, which they…

Scattering amplitudes at loop level can be reduced to a basis of linearly independent Feynman integrals. The integral coefficients are extracted from generalized unitarity cuts which define algebraic varieties. The topology of an algebraic…

The small elliptic quantum group $e_{\tau,\gamma}(sl_N)$, introduced in the paper, is an elliptic dynamical analogue of the universal enveloping algebra $U(sl_n)$. We define highest weight modules, Verma modules and contragradient modules…

The theories of hypergeometric functions and modular forms are highly intertwined. For example, particular values of truncated hypergeometric functions and hypergeometric character sums are often congruent or equal to Fourier coefficients…

About ten years ago, Katz, Klemm and Huang conjectured that topological string amplitudes on compact, elliptically fibered Calabi-Yau threefolds at fixed base degree could be expressed in terms of meromorphic Jacobi forms for…

We express all the newforms of weight $2$ and levels $30$, $33$, $35$, $38$, $40$, $42$, $44$, $45$ as linear combinations of eta quotients and Eisenstein series, and list their corresponding strong Weil curves. Let $p$ denote a prime and…

We study the de Rham fundamental group of the configuration space $E^{(n)}$ of $n+1$ marked points on an elliptic curve $E$, and define multiple elliptic polylogarithms. These are multivalued functions on $E^{(n)}$ with unipotent monodromy,…

For each open subgroup $G$ of ${\rm GL}_2(\hat{\mathbb{Z}})$ containing $-I$ with full determinant, let $X_G/\mathbb{Q}$ denote the modular curve that loosely parametrizes elliptic curves whose Galois representation, which arises from the…

We identify a class of "semi-modular" forms invariant on special subgroups of $GL_2(\mathbb Z)$, which includes classical modular forms together with complementary classes of functions that are also nice in a specific sense. We define an…

Modular graph functions arise in the calculation of the low-energy expansion of closed-string scattering amplitudes. For toroidal world-sheets, they are ${\rm SL}(2,\mathbb{Z})$-invariant functions of the torus complex structure that have…

Let g be a complex semisimple Lie algebra, tau a point in the upper half-plane, and h a complex deformation parameter such that the image of h in the elliptic curve E_tau is of infinite order. In this paper, we give an intrinsic definition…

In this article we define an elliptic double shuffle Lie algebra $ds_{ell}$ that generalizes the well-known double shuffle Lie algebra $ds$ to the elliptic situation. The double shuffle, or dimorphic, relations satisfied by elements of the…

Modular symmetries naturally combine with traditional flavor symmetries and $\mathcal{CP}$, giving rise to the so-called eclectic flavor symmetry. We apply this scheme to the two-dimensional $\mathbb{Z}_2$ orbifold, which is equipped with…

We describe iterated integrals as unipotent periods on families of marked elliptic curves in terms of multiple zeta values and elliptic multiple zeta values.

Multiple zeta values arise as special values of polylogarithms defined on Riemann surfaces of various genera. Building on the vast knowledge for classical and elliptic multiple zeta values, we explore a canonical extension of the formalism…

In this paper we consider weakly holomorphic modular forms (i.e. those meromorphic modular forms for which poles only possibly occur at the cusps) of weight $2-k\in 2\Z$ for the full modular group $\SL_2(\Z)$. The space has a distinguished…

In a series of papers \cite{KS,MR}, Krawitz, Milanov, Ruan, and Shen have verified the so-called Landau-Ginzburg/Calabi-Yau (LG/CY) correspondence for simple elliptic singularities $E_N^{(1,1)}$ ($N=6,7,8$). As a byproduct it was also…

Adaptive multilevel finite element methods are developed and analyzed for certain elliptic systems arising in geometric analysis and general relativity. This class of nonlinear elliptic systems of tensor equations on manifolds is first…

Machine-learning interatomic potentials (MLIPs) have made a significant contribution to the recent progress in the fields of computational materials and chemistry due to the MLIPs' ability of accurately approximating energy landscapes of…

Enhancing and essentially generalizing previous results on a class of (1+1)-dimensional nonlinear wave and elliptic equations, we apply several new techniques to classify admissible point transformations within this class up to the…