5 problems

Let $P_m$ be the $m$-prism with ladder perfect matching $L$, and let $H^{i,j}(P_m,L)$ denote the associated bigraded cohomology. Prism graph cohomology conjecture. If $(P_m,L)$ is…

Let $T$ be the tetrahedron graph, and let $\Sigma_{g=3}$ be the genus-three surface bounding a tubular neighborhood of $T$. Let $x_1,x_2,x_3,x_4,x_{12},x_{23}$ be the holonomy coor…

Let $\Theta$ be the theta graph, and let $\Sigma_{g=2}$ be the genus-two boundary surface of its tubular neighborhood. Let $x_a,x_b,x_c$ and $y_a,y_b,y_c$ be the holonomy and twist…

Generalized volume conjecture. The equations defining this character variety can be obtained by taking the large-color limit of the $U_q(\mathfrak{sl}_2)$ quantum invariant of the…

Let $\Gamma$ be either the theta graph or the tetrahedron graph, with $E$ edges, and let $J_{n_1,\ldots,n_E}(\Gamma;q)$ denote its $U_q(\mathfrak{sl}_2)$ colored quantum invariant.…