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Colloquium: Daryl Cooper—Symmetry, Old and New

Wednesday, April 05
4:00 PM
203 TMCB

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.