# 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)

`rpenner@math.usc.edu`

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.