Asymptotics of cells in Riemann's moduli space

In earlier work with Greg McShane, we had described the
stable curves to which a given cell in moduli space can degenerate; this involved explicit and rather involved computations which depend upon new properties of Ptolemy transformations. More recent work with Volodya Fock demonstrates the analogous result for measured
foliations using tropical techniques and rely on MUCH easier computations.