For open problems/conjectures in combinatorial and discrete geometry, there's the journal Geombinatorics focusing on "live mathematics," i.e., research in progress.

One big title is Aubrey de Grey's 2018 "The chromatic number of the plane is at least 5."

The explanation of the journal's topical parameters includes the advice, "We encourage mathematicians in other areas to start similar lively publications." It seems there are some further examples now.