Manchester Geometry Seminar 2007/2008

Extraordinary session: Monday 22 October 2007. The Frank Adams Room (Room 1.212), the Alan Turing Building. 2pm

Asymptotics of the Cell Decomposition of Teichmueller Space

Robert Penner (University of Southern California)

Recent joint work with Greg McShane has answered the following question: Which curves can be short in a given cell of the cell decomposition of Teichmueller space? The answer involves a new combinatorial structure called "screens on fatgraphs" as we shall describe. The techniques of proof involve path-ordered product expansions of holonomies, Ptolemy transformations, and the triangle inequality. This is a main step in giving a combinatorial description of the Deligne-Mumford compactification of moduli space, which we shall also discuss as time permits.