4 problems

Non-toric NCCR extension conjecture. The statement of the theorem holds also if $\Lambda'$ is a non-toric NCCR.

Trichotomy conjecture. For every vertex $i\neq 0$, there is a unique $k(i)\in\\{-1,0\\}$ such that

Non-commutative crepant resolution conjecture. The algebra $\Lambda^1(Q)$ is a 2-dimensional non-commutative crepant resolution of its center, the ring of functions on…

Let $Q$ be the quiver associated with a noncommutative crepant resolution $A=\mathbb{C}\{Q,W\}$ of the threefold setup, let $C$ be the flopping curve, and let $\Phi(0,1)$ be its di…