Coordinates, canonicity, and cellularity

Abstract: 

I plan to discuss Penner's lambda coordinates on Teichmüller space. I plan to discuss Weeks's algorithm for determining canonical forms for hyperbolic surfaces of finite area, and how this leads to a cell decomposition of Teichmüller space. Finally, I plan to sketch recent work, joint with Stephan Tillmann, showing that Cooper and Long's decompositions of two similar moduli spaces are cell decompositions.