Workshop on the h-principle and beyond

Ampleness up to avoidance

Abstract: In the first half of the talk I will review Gromov's work on convex integration for open differential relations. I will put particular emphasis on comparing various flavours of ampleness and, in particular, I will note that the different flavours require slightly different implementations of convex integration.

In the second half of the talk I will explain some recent joint work with F.J. Martínez Aguinaga: We define a notion of "ampleness up to avoidance" and we prove that convex integration applies to open relations satisfying it. Our main example is the differential relation defining hyperbolic (4,6)-distributions: it is not ample in the classic sense, but it is ample up to avoidance and thus abides by the h-principle.

Date & Time

November 04, 2021 | 11:45am – 12:45pm


Simonyi 101 and Remote Access


Alvaro del Pino Gomez

Speaker Affiliation

University of Utrecht