7 problems

Let $X$ and $Y$ be the complete intersections associated with the matrix data in the source, and let $G$, $V^\Lambda$, $\,{}^TG$, and $\,{}^TV^\Lambda$ denote the corresponding gro…

Generic nonvanishing and component conjecture. One has

Hayashi's quiver quotient conjecture. Every finite-dimensional weak bialgebra $H$ with commutative counital subalgebras is isomorphic to a weak bialgebra quotient of $\hay$ for som…

Let $\Gamma$ be a strongly connected graph. Its Perron–Frobenius eigenspace is the eigenspace corresponding to the Perron–Frobenius eigenvalue of its vertex matrix. Quantum vertex-…

Let $M$ be a compact connected smooth manifold, and let a compact quantum group act smoothly and faithfully on $C(M)$. A compact quantum group is genuine if it is not of the form…

For each $n\in\mathbb N$, let $H_n^+=G^+(I_n)$ be the quantum symmetry group of the $n$-segment graph, and consider the universal flat model for $C(H_n^+)$. Inner-faithfulness conj…

For each $n\in\mathbb N$, let $O_n^{-1}$ be the quantum group identified with the quantum symmetry group $G^+(K_n)$ of the $n$-cube graph, and consider the universal flat model for…