On the one hand, as mentioned here, basically "everything" in algebraic geometry could be seen in the context of "moduli problems" - on the other hand, Grothendieck's few remarks on a possible "tame topology" tell that he wondered about some general principle behind the stratifications of known moduli "spaces".
This makes me wonderwhen reinterpretations :
When did re-interpretations as moduli problems turned turn out to be helpfull, if ?
How is "tame topology" was used there (then?
... and actually, how develops tame topologydeveloped, e.g. Grothendieck mentions in his "Esquisse" something on "tubular neighbourhoods of subtopoi" - what's that?), which that?
Which role play moduli problems play in derived (or else generalised ) geometry?
