Speaker: Daryl Cooper (UC Santa Barbara)
Title: Symmetry, Old and New: triangulations and 3-manifolds.
Abstract: The theme is that interesting classes of objects can be defined in a purely combinatorial way, defined by restricting the allowed triangulations. This turns out to be equivalent to studying those manifolds that immerse into a certain branched manifold = higher dimensional train track. They can also be characterized using a generalization of regular languages where the symbols are not linearly arranged, but label the vertices of a graph, like models of molecules.
These ideas are applied to give a combinatorial description of the geometric decomposition of 3-manifolds. In particular, there is a combinatorial characterization of hyperbolic 3-manifolds. I will endeavor to make the talk widely understandable.
Joint with Priyam Patel and Leslie Mavrakis.