Finite generation of log canonical rings for projective lc pairs

Let $(X,\Delta)$ be a projective log canonical (lc) pair defined over $\mathbb C$, where $\Delta$ is a $\mathbb Q$-divisor on $X$. Its log canonical ring is

$$R(X,\Delta):=\bigoplus_{m\geq 0}H^0(X,\mathcal O_X(\lfloor m(K_X+\Delta)\rfloor)).$$

Finite-generation conjecture. The ring $R(X,\Delta)$ is a finitely generated $\mathbb C$-algebra.

Finite generation of log canonical rings is a central open problem in the minimal model program for log canonical pairs. The source states that this conjecture is thought to be a very difficult open problem.