Results of Matveev, Piergallini, and Amendola show that any two triangulations of a three-manifold with the same number of vertices are related to each other by a sequence of local combinatorial moves (namely, 2-3 and 3-2 moves). For some applications however, we need our triangulations to have certain properties, for example that all edges are essential. (An edge is inessential if both ends are incident to a single vertex, into which the edge can be homotoped.) We show that any two triangulations with all edges essential can be related to each other by a sequence of 2-3 and 3-2 moves, keeping all edges essential as we go. This is joint work with Tejas Kalelkar and Saul Schleimer.

**Note the non-standard time for the seminar, 1:30-2:30 Wednesday.**