Piotr Mormul

Title: Special multi-flags at the crossroads of algebraic geometry and differential geometry

Abstract:
There exist different approaches to the singularities of special multi-flags, also called "generalized 
Goursat flags". They live in Monster Towers, also called Semple Towers. Colley, Kennedy et al have concluded 
in Michigan Math. J. 166 (2017) a series of earlier algebro-geometric constructions, by several authors, 
of fine stratifications of the stages of Semple Towers, eventually producing so-called "RV-classes of
singularities". In the meantime the author constructed in the stages of Monster Towers, in SIGMA 5 (2009),
the so-called "singularity classes", using purely differential and Lie-algebraic tools. It had been generally
believed that the former classes (much more numerous) were a refinement of the latter ones. This belief
now turns out to be false. The two approaches appear, to a sizeable degree, to mutually complement each other.