Stratifications of algebraic sets over R and C can be used to yield information about their singularities. I. Halupczok previously introduced the notion of definable t-stratification for definable sets in valuative extensions. As well as establishing their existence, he uses them to obtain a new kind of stratification induced on the definable subsets of R and C. While they exist, a t-stratification of X is not typically uniquely determined.

To remedy this, in ongoing joint work with I. Halupczok, we introduce a related yet also canonical invariant called the riso-tree of X in a spherically complete valuative extensions K of R and C. Using Hensel minimality of K, as introduced by Cluckers-Halupczok-Rideau, we prove that the canonical riso-tree of X is itself definable. Then using the canonical riso-tree, we go on to obtain a new kind of definable stratification for algebraic subsets of R and C.

I will give an informal introduction to these new notions, and present our central main results for their construction.