Shokurov's ascending chain conjecture for log canonical thresholds

Let $X$ be a variety of dimension $n$ and let $Y\subset X$ be a subvariety. The log canonical threshold of the pair $(X,Y)$ is denoted by $\operatorname{lc}(X,Y)$. Shokurov's conjecture. For every $n$, the set

$$\{\operatorname{lc}(X,Y)\mid \dim(X)=n,\ Y\subset X\}$$

satisfies the ascending chain condition; that is, it contains no strictly increasing sequences. This is presented as a central open problem about log canonical thresholds and concerns the birational-geometric behavior of these singularity invariants.