Kollár–Shokurov inversion of adjunction conjecture

Let $(X,Y)$ be a pair, where $Y$ is a formal rational or real linear combination of closed subvarieties of $X$. For a log resolution $f:X'\xrightarrow{\ \ } X$, write

$$f^{-1}Y=\sum a_iE_i,\qquad K_{X'/X}=\sum b_iE_i,$$

and define the minimal log discrepancy along a subvariety $W\subseteq X$ by

$$\operatorname{mld}(W;X,Y)=\begin{cases} \min\{b_i-a_i+1\mid f(E_i)\subseteq W\},&\text{if this minimum is non-negative},\\ -\infty,&\text{otherwise.} \end{cases}$$

Let $D$ be a normal effective Cartier divisor on $X$ with $D\not\subseteq Y$, and let $W\subset D$ be a proper closed subset. Kollár–Shokurov's inversion of adjunction conjecture. Then

$$\operatorname{mld}(W;X,Y+D)=\operatorname{mld}(W;D,Y|_D).$$

The conjecture describes how the singularities of a pair behave under restriction to a Cartier divisor: log canonicity near $W$ should be equivalent to the corresponding condition on the restricted pair on $D$.