14 problems

Surjectivity conjecture. The map is an isomorphism:

Elliptic identity lifting conjecture. For any $j\in\{1,\ldots,h\}$ and any genus $h\geq1$, the corresponding higher-genus multiple zeta values satisfy

Weight-exchange reflection conjecture. At depth two, higher-genus multiple zeta values satisfy

Let $I^A(i_1,\ldots,i_n)$ denote an elliptic multiple zeta value, and consider the shuffle relations, reflection relations, and Fay relations satisfied by these values. Exhaustion…

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-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…

Let the non-planar part of the one-loop open-string amplitude be expanded at low energy in the inverse string tension $\alpha'$. The relevant iterated integrals are twisted ellipti…

Let $\mathfrak{e}_m(\tau)$ be the mould of the elliptic multiple zeta values, and let the $\Delta$-bialternal relations be the elliptic double shuffle relations imposed on it. Dept…

Let $\mathfrak{e}_m(\tau)$ denote the mould of the elliptic multiple zeta values, and let the elliptic double shuffle relations be the $\Delta$-bialternality relations satisfied by…

Let $\mathcal{EZ}^A_N$ be the $\mathbb{Q}$-vector space of A-elliptic multiple zeta values of weight $N$, and let…

Let $w_\omega$ denote the modular weight and $\ell_\omega$ the length of an elliptic multiple zeta value. An eMZV is called indecomposable when it represents a nontrivial class aft…

Elliptic multiple zeta values (eMZVs) satisfy shuffle relations from their iterated-integral definition and Fay identities generalizing partial-fraction identities. Fay–shuffle com…