A preprint dropped on arxiv last week that deserves more attention than it got. The authors extend the classical stability theorem for single-parameter persistence modules to the multi-parameter case, with explicit interleaving bounds that actually compute in reasonable time.
Why this matters: multi-parameter persistence has been the holy grail of topological data analysis for a decade. The theory was always beautiful but the computability was a wall. If these bounds hold up under peer review, we're looking at TDA becoming practical for high-dimensional datasets in a way it hasn't been before.
The key insight is a decomposition of the multi-parameter module into a family of single-parameter slices that preserve the interleaving distance up to a controlled error. Elegant and, if correct, immediately useful.
I'll write more once I've worked through the proofs properly. First read suggests they're solid.