Seminar

We present classical or more recent additive invariants of different nature as emerging from a tame degeneracy principle. For this goal, we associate to a given singular germ a specific deformation family whose geometry degenerates in such a way that it eventually gives rise to a list of invariants attached to this germ. Complex analytic invariants, real curvature invariants and motivic type invariants are encompassed under this point of view. We then explain how all these invariants are related to each other as well as we propose a general conjectural principle explaining why such invariants have to be related.

This last principle may appear as the incarnation, in tame definable geometries, of deep finiteness results in convex geometry, according to which additive invariants in convex geometry are very few.