Hassler Whitney I know from matroid theory (in particular, antimatroids for the mathematical psychology of learning), so stratification theory might be interesting because that also was.
René Thom I know from catastrophe theory, so stratification theory might be interesting because that also was.
Boundaries of boundaries are interesting, as are their arrow-reversed variants, but that's likely 1*1=1 compared with this material? (which I take to have something to do with finding nice boundaries along which to slice wholes up to better study their parts?) For ML in particular, maybe it could provide a reasonable way to divide-and-conquer manifold learning?
In fact, as of this comment, although I'm pretty sure the vertices of my play are interesting, I have yet to learn whether its convex hull will also turn out to be interesting — if someone else can provide the ELI5, that'd be great!