7 problems

Let $\mathcal{Z}_q$ be the algebra of balanced multiple $q$-zeta values, generated by elements $\zeta_q(s_1,\ldots,s_l)$ with $s_1\geq1$ and $s_2,\ldots,s_l\geq0$. The balanced qua…

Let $QSym(\mathbb Z)$ denote the universal ring of quasi-symmetric functions, identified with $J^{\vee}(\mathbb Z[y])=H^*(\Omega\Sigma\mathbb CP^{\infty};\mathbb Z)$, where $|y|=2$…

Balanced multiple q-zeta relation conjecture. All algebraic relations in $\mathcal{Z}_q$ are induced by the balanced quasi-shuffle product and the $\tau$-invariance of balanced mul…

Let $\mathcal{B}=\{b_i\mid i\geq0\}$ and let $\mathbb{Q}\langle\mathcal{B}\rangle^0$ be the subspace spanned by words that do not end in $b_0$. The balanced quasi-shuffle product i…

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…

Let $\mathcal{Z}_q$ be the $\mathbb{Q}$-algebra spanned by Schlesinger–Zudilin multiple $q$-zeta values … The stuffle–tau conjecture. All algebraic relations in $\mathcal{Z}_q$ are…

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…