11 problems

Kleppe–Ellia's conjecture. If $C$ is linearly normal, then every small deformation $C'$ of $C$ in $\mathbb P^3$ is contained in a cubic surface $S'\subset\mathbb P^3$; equivalently…

Chas–Phillips conjecture. The maximal self-intersection number of a closed curve of odd combinatorial length $L(\gamma)$ is

Universal k-equivalence descent conjecture. On the pair of pants, $k$-equivalence implies $(k-1)$-equivalence for all positive integers $k$.

The intersection-triple bound conjecture. For any curve $\alpha$ on the pair of pants,

The intersection-ratio conjecture. For any free homotopy class of curves $\alpha$ on the pair of pants, the ratio between the intersection numbers of $\alpha$ with one free homotop…

The k-equivalence descent conjecture. On the pair of pants, if two classes of curves $\alpha_1$ and $\alpha_2$ are $k$-equivalent for some positive integer $k\geq 2$, it follows th…

Let $\mathcal{Q}$ be an acyclic quiver, let $P_{\mathcal{Q}}$ be the relevant set of seeds, and for each $\sigma\in P_{\mathcal{Q}}$ let $\Gamma_{\sigma}$ be the set of isotopy cla…

Let $R$ be the path algebra of an acyclic quiver, let $g$ be the onto map from admissible curves to indecomposable modules corresponding to positive real roots, and let $M$ be an i…

Let a curve, or a multicurve, have $n$ crossings on an arbitrary surface, and let homotopy moves simplify it by removing reducible features. Quadratic simplification conjecture. An…

Let $X_n$ be the projective plane blown up at $n$ general points, and let $C$ be an irreducible curve of genus $g>0$ on $X_n$. Let $(3;1^9,0^{n-9})$ denote the indicated plane line…

Cobracket criterion conjecture. If