TITLE: Big finitistic dimension of finite dimensional algebra
QUESTION [5 upvotes]: Let $A$ be a finite dimensional algebra. The big finitistic dimension of $A$
is 
$$\operatorname{FinDim}(A)=\sup\{\operatorname{pd}(M)\mid M\in \text{Mod-}A \text{ and } \operatorname{pd}(M)<\infty\},$$
where $\operatorname{pd}(M)$ is the projective dimension of $M$, $\text{Mod-}A$ is the category of right $A$-modules.
Problem: Does there exist a finite dimensional algebra $A$ such that $\operatorname{FinDim}(A)=\infty?$
http://cn.arxiv.org/abs/1804.09801 (see Definition 4.1.)

REPLY [11 votes]: You quoted a very recent arxiv article, where it is stated that this is an open problem. No progress has been made towards this open problem since then.
The only big progress in the questions sourounding the finitistic dimension conjecture was made 1992 in https://link.springer.com/article/10.1007/BF02100610 where it was proven that the first finitistic dimension conjecture is wrong.