5 problems

Mutation-generation conjecture. All exceptional bundles and sheaves on $X$ can be obtained by mutations of the helix ${\cal R}$. In particular, there exists a mutated helix

Ordovician lattice structure conjecture. The following hold:

Let $\mathcal N$ be a lattice and let $f itslashin i mathbb C[mathcal N]$ be a Laurent polynomial such that $operatorname{Newt}(f)$ is a Fano polytope and the constant term of $f$…

Let $X$ be a Fano variety, and let $f$ and $g$ be Laurent-polynomial mirror partners to $X$. A mutation connectivity conjecture asserts that $f$ and $g$ are connected by a finite s…

Let $\tau$ be a tangle, and let $\alpha_0$ and $\alpha_1$ be sites for a rational subtangle replacement (RSR) on $\tau$. Suppose their lifts to the branched double cover of $\tau$…