14 problems

Let $\mathfrak{H}^0$ be the admissible word space, let $\mathfrak{H}^0_\ast$ denote its harmonic-product algebra, and define…

Let $\mathcal{E}^f$ be the formal multiple Eisenstein-series algebra, let $\mathcal{G}^f$ be the ambient formal algebra, and let $\theta=-\mathcal{D}\circ\varphi$ on the relevant w…

The derivative and relations conjecture for multiple Eisenstein series. For every $w\in\mathfrak{H}^{\geq2}$,

The $\mathfrak{sl}_2$-algebra conjecture for multiple Eisenstein series. These maps should be well-defined $\mathbb{Q}$-linear maps on $\mathcal{E}$, should be derivations, and sho…

Let $\mathcal{E}_k$ be the weight-$k$ component of the algebra of multiple Eisenstein series. Define the generating series for modular forms and cusp forms by … Here…

The weight-grading conjecture for multiple Eisenstein series. One should have

Let the combinatorial (bi-)multiple Eisenstein series be the $q$-series in ${\mathbb Q}\llbracket q\rrbracket$ introduced by Bachmann and Burmester through Bachmann's stuffle regul…

For each weight $k$, let … and let $\mathcal{E}=\sum_{k\geq 2}\mathcal{E}_k$. The dimension conjecture for multiple Eisenstein series. The Hilbert–Poincaré series of these spaces i…

Let $\mathcal{E}^{\!f}$ be the subspace of $\operatorname{Fil}^{\mathrm{lwt}}_0\mathcal{G}^{\!f}$ spanned by $G^{\!f}(k_1,\dots,k_r)$ with $r\geq0$ and $k_1,\dots,k_r\geq2$, and le…

Let $\mathcal{G}^{\!f}$ be the space of formal multiple Eisenstein series, equipped with the lower-weight and depth filtrations $\operatorname{Fil}^{\mathrm{lwt}}_d$ and…

Let $\mathcal{G}^{\!f}$ be the commutative $\mathbb{Q}$-algebra of formal multiple Eisenstein series, with elements $G^{\!f}(k_1,\dots,k_r)$ and double-indexed elements…

For $k1,dots,kr eq 1$ and $d1,dots,dr eq 1$, let $gbi{k1,dots,kr}{d1,dots,dr}$ denote the double-indexed $q$-series defined by the corresponding sum over $m1dotsmr0$ and…

Let $\mathcal{Z}_q$ be the algebra of multiple $q$-zeta values, and let the combinatorial bi-multiple Eisenstein series $G\binom{k_1,\ldots,k_d}{m_1,\ldots,m_d}$ form a spanning se…

Let $\operatorname{q\mathcal{M}\mathcal{Z}}$ be the space of multiple Eisenstein series and $\operatorname{q\mathcal{M}\mathcal{Z}}^\shuffle$ the space spanned by shuffle multiple…