Random veering triangulations are not geometric

Every pseudo-Anosov mapping class phi defines an associated veering triangulation tau(phi) of a punctured mapping torus. We show that generically, tau(phi) is not geometric. Here, the word "generic" can be taken either with respect to random walks in mapping class groups or with respect to counting geodesics in moduli space. Tools in the proof include Teichmfiller theory, the Ending Lamination Theorem, study of the Thurston norm, and rigorous computation.