14 problems

Let $\mathcal{M}_{g,P}$ be the moduli space of smooth genus-$g$ curves with marked points $P$, and let $W_{m_*,P}$ denote the combinatorial class associated with ribbon graphs havi…

Let $G$ be a bridgeless connected graph and let $\Gamma$ be a signed ribbon diagram of $G$. For $n$ a positive integer, write $T(\Gamma,n,t)$ for the total face color polynomial. T…

Let $\Omega(\overline{\textsf N}^{fr})$ be the cobar construction of the properad of framed curves, let $\Omega(\textsf{Frob}^*)$ be the cobar construction of the dual Frobenius pr…

Let $d$ be an integer, and let $\textsf{OGC}_{2d+1}^{{\:\raisebox{3pt}{\text{\circle*{1.5}}}}}$ be the oriented graph complex and…

A ribbon graph is orientable if its associated ribbon surface is orientable, and its partial duality polynomial is the generating function that enumerates its partial duals by Eule…

Let $G$ be a ribbon graph, and let $~^{\partial}{\mathscr{E}}^{*}_{G}(z)$ denote its partial-$*$ polynomial. A polynomial is odd or even when all terms with nonzero coefficients ha…

Baker and Wang's conjecture. There exists a vertex $q$ of $G$ such that

Baker–Wang conjecture. The torsors $b_v$ and $r_v$ agree for all vertices $v$ if and only if $G$ is planar.

A ribbon graph is orientable if its underlying surface is orientable, and its partial-dual genus polynomial records the genera of all partial duals. A polynomial is non-constant if…

Let $G$ be a non-orientable ribbon graph. Its partial-dual Euler-genus polynomial is the generating function … where $G^A$ is the partial dual of $G$ with respect to…

Căldăraru's conjecture. For every genus $g\geq 2$, there is a natural identification

Let $G$ be a non-orientable ribbon graph, and define its partial-dual Euler-genus polynomial by … A polynomial is interpolating when its non-zero coefficients are all equal to $1$.…

Let $(G,\rho)$ be a ribbon graph. Write $V(G)$ for its vertices, $E(G)$ for its edges, $\operatorname{Pic}^0(G)$ for its degree-zero Picard group, and $\mathcal{T}(G)\subset E(G)$…

Let $(G,S)$ be a ribbon graph embedded in $S^3$, and let $H_i$ denote its homology groups. Planar graph detection conjecture. The ribbon graph $(G,S)$ is isotopic to a planar graph…