27 problems

Let $M(\bs;\varepsilon)$ denote a multiple mixed value and $T(\bs)$ a multiple t-value. Classify indices as wide, slender, or narrow according to whether their largest component is…

Let $M(\bs;\varepsilon)$ denote a multiple mixed value and $T(\bs)$ a multiple t-value. Classify indices as wide, slender, or narrow according to whether their largest component is…

Let $M(\bs;\varepsilon)$ denote a multiple mixed value of depth $4$, let $T(\bs)$ denote a multiple t-value, and classify indices as wide, slender, or narrow by whether their large…

Let $\bfs$ be an index, let $T(\bfs)$ be a multiple t-value (MTV), and let $\bfs^*$ be its dual. Define the width $\operatorname{wth}(\bfs)$ as the largest component of $\bfs$; cal…

Let $d$ be a positive integer with $d\ge 3$. Write $1_{d-3}$ for a string of $d-3$ entries equal to $1$, let $\zeta^\sharp$ denote the Euler sharp sum, and let $\zeta(m,n)$ denote…

Maximal transcendence-degree conjecture. The transcendence degree of the $\mathbb Q$-extension field generated by this set is maximal.

Let $K\subset\mathbb{C}$ be a number field. The ring $\mathcal{H}(K)$ is the ring of effective motivic periods of the category of mixed Tate motives over $K$, and motivic iterated…

Let $F$ be a number field. For elements $a_0,\ldots,a_{n+1}\in F$, let … be the motivic iterated integral associated with the corresponding motivic fundamental groupoid, and let…

Unramified MtV conjecture. For $m,n,e\text{\in}N$ and with all components of $q$ at least two, the MtV

Kaneko–Tsumura's conjecture. For even weights, the values $T(k,l,m)$ with $k,r$ odd and at least $3$ and $q$ even, together with their duals, are in $MZV$. Together with the single…

Let $a\in\mathbb{N}_0$, $\ell\in\mathbb{N}$, and let $u_j,v_j\in X:=\{1,\bar2,3,\bar4,\dots\}$ for $j=1,\dots,\ell$, with … For $\mathfrak S_\ell$ the symmetric group on $\ell$ let…

Let $p_{a,b,c}$ and $q_{a,b,c}$ be the polynomials and let $r_{a,b,c}$ and $r'_{a,b,c}$ be the integers defined in the statement. Let $I_{\mathrm{bl}}^{\mathfrak{m}}$ denote the mo…

Let $I^{\mathfrak{m}}(0,a_1,\ldots,a_k,1)$ denote the motivic iterated integral along the specified tangential path from $0$ to $1$. For an odd index $(l_1,\ldots,l_d)$, define…

Let $G$ be a primitive log-divergent Feynman graph, and let $[H_G,\omega_G,\sigma]^{\rm m}$ denote the motivic realisation of its Feynman integral $I_G^{\rm m}$. Let $\Delta$ denot…

Brown's coaction conjecture. The space $\mathcal{P}_{g}^{\rm m}$ is stable under the Galois coaction:

Panzer–Schnetz coaction conjecture. The Galois coaction closes on $\phi^4$-periods:

The period conjecture. The period map is an isomorphism.

Invertibility conjecture. For any $r\geq3$, $N\geq r+2$, and $N-r\equiv0\pmod 2$, the order $|T_{N,r}|$ matrix

Let $I\subset\mathcal{P}\times\mathbb{N}$, and let $\widehat{\operatorname{per}}_{\operatorname{har}_I}$ be the period map on weight-adically convergent sums of motivic multiple ha…

Let $a_i,c_i\in\mathbb{N}^{\ast}$ with $c_i\neq 2$, and define … where $\delta_c=\delta_{c=1}$ equals $1$ if $c=1$ and $0$ otherwise. Define … … and … Here \text{\boldmath 1…

Analytic coefficient conjecture. The equalities for the real multiple zeta values are satisfied with

Loop-number weight conjecture. The weight of $I_G^{\mathfrak{m}}$ is less than or equal to $4h_G$.

Let $\xi\in\mathcal{P}^{\mathfrak{m},+}$ be a motivic period, and let $P_{\xi}\subset\mathbb C$ be the $\mathbb Q$-algebra generated by the images under the period homomorphism of…

Motic-descendant degree conjecture. The amplitude of $G$ is a regularised period of motic descendants of $G$ of degree at most $dh$.

Weight bound conjecture. The amplitude integrand satisfies