14 problems

Poisson equation conjecture. The Poisson equation

Let the low-energy expansion of the genus-one four-graviton amplitude be organized by derivative order, and assign transcendental weights to the constants and functions appearing i…

Let $\mathcal{M}\mathcal{I}^E$ be the subalgebra of modular functions generated over $\mathcal{Z}^{\rm sv}$ by the specified equivariant iterated Eichler integrals of Eisenstein se…

Brödel–Schlotterer–Zerbini's esv conjecture. For all graphs $\Gamma$,

Let $\Gamma$ be a graph with $l$ edges, and write its modular graph function as … where $\tau\in\mathbb{H}$, $q=\exp(2\pi i\tau)$, and $y=\pi\,\operatorname{Im}(\tau)$. The coeffic…

Elliptic single-valued map conjecture. Once a $B$-cycle graph function is suitably expressed in terms of $T$ and $\operatorname{\mathcal{E}_0}(\underline{k})$, applying the esv-map…

A graph has a number of loops, and its associated modular graph function has a depth, meaning the depth in the nested or iterated structure of the modular graph function. Loop-dept…

A-cycle differential-equation transfer conjecture. Such a differential equation is the open-string counterpart of a differential equation among the corresponding modular graph func…

Let $X$ be the space of terms discarded in the paper's relations, let $\mathcal{P}$ be a polynomial in $A$-cycle graph functions and MZVs, and let $\mathcal{G}$ be a collection of…

Let $\operatorname{\mathcal{E}_0}(k_1,k_2,\ldots,k_r)$ denote iterated Eisenstein integrals, let $T$ be the variable used in the $B$-cycle expressions, and let…

Vanishing conjecture. For $1\leq n\leq a_1-1$,

The differential relation conjecture for $D_5$.

Let $j^{(1,1)}(\tau)$ be the modular function occurring in the weight-five low-energy expansion, and let $D_{2,1,1,1}(\tau)=C_{3,1,1}(\tau)$ be the corresponding modular graph func…

Let $D_4$ be the weight-four modular graph function, let $E_2$ and $E_4$ be the non-holomorphic Eisenstein series of weights $2$ and $4$, and let $\tau$ lie in the upper half plane…