Maxwell, Airy and Hill walk into a bar, here is the theorem they write

The lemma of Hill (or of Hill-Mandel) is crucial to the consistent treatment of effective properties in the theory of composites. Building on various classical results (notably by Maxwell and Airy), I've recently applied the lemma sort of "out of context" to characterize (count really) the (infinitesimal) isometric deformations of periodic surfaces.

My work on this topic started some 10 years ago at École des Ponts (with Arthur Lobée and Laurent Monasse) motivated by then recent work by two groups at Cambridge (under S. Guest) and Harvard (under L. Mahadevan). But the direct inspiration is more recent and took place at two highly interdisciplinary workshops: one at ICERM (Brown) and one at IMAG (Granada). Kudos to the organizers for bringing together mechanicians, geometers, architects, artists and computer scientists.

For the short version of the theorem, see the attached abstract to a talk I've had the pleasure of presenting at SNP Glasgow recently.

For the full detail, see the published paper.