Donovan–Wemyss classification conjecture for simple formal flopping contractions

Let $({\widehat{Y}},{\widehat{f}},R)$ and $({\widehat{Y}}^{\prime},{\widehat{f}}^{\prime},R^{\prime})$ be two three-dimensional simple formal flopping contractions, with associated Calabi–Yau tilted algebras $\Lambda$ and $\Lambda^{\prime}$. Donovan–Wemyss classification conjecture. The following are equivalent:

$$R\text{ is isomorphic to }R^{\prime}.$$ $$\Lambda\text{ is isomorphic to }\Lambda^{\prime}.$$

Equivalently, the analytic isomorphism type of the contraction is determined by, and determines, the isomorphism type of its Calabi–Yau tilted algebra. The implication from (2') to (1) is one of the main open problems in the homological minimal model program for threefolds.