Weak and strong nilpotentizability in the monster towers hosting flag distributions

Weak nilpotentizability (of a distribution = subbundle in the tangent bundle to a manifold) means the existence of a (local) nilpotent basis of sections.

Strong nilpotentizability of a point, say p, is the equivalence of the distribution germ at p to the nilpotent approximation of that distribution at p. (This notion of 'strong nilpotentizability at a point' is relatively new, and fairly delicate.)

Strong implies weak (for germs), but not vice versa.

The talk will review these two properties, and formulate open questions, for distributions living in the so-called monster towers. These are classical flag distributions going back conceptually to von Weber and E. Cartan.