JOINT COLLOQUIUM Friday, August 14, 2 PM Room 3084 in the Red Centre, University of New South Wales Stephan Tillman, University of Queensland The complexity of 3 manifolds The complexity of a 3-manifold is the minimum number of tetrahedra in a triangulation of the manifold. It was defined and first studied by Matveev in 1990. The complexity is generally difficult to compute, and various upper and lower bounds have been derived during the last decade using fundamental group, homology or hyperbolic volume. Effective bounds have only been found recently in joint work with Jaco and Rubinstein. Our bounds not only allowed us to determine the first infinite classes of minimal triangulations of closed 3-manifolds, but they also lead to a structure theory of minimal triangulations. In this talk, I will give a general introduction to complexity of 3-manifolds and explain its ramifications for algorithmic problems in the study of 3-manifolds. please contact me firstname.lastname@example.org if you are planning to attend and either need or can offer a lift. We will take the Speaker to lunch beforehand; exact lunch plans are yet to be determined.