A deformation of Penner's simplicial coordinate- Tian Yang

Conference Title: GEAR Retreat 2012 Theme: Junior Talks (11 of 12) Title: A deformation of Penner's simplicial coordinate Speaker: Tian Yang, Rutgers; Date and Time: Friday August 3, 15:50 Description: Decorated Teichmuller space of a punctured surface was introduced by R. Penner as a fiber bundle over the Teichmuller space of complete hyperbolic metrics with finite area. To give a cell decomposition of this space that is invariant under the action of the mapping class group, Penner defined the simplicial coordinate Ψ in which the cells can be easily described. The main result that I will be talking about is to find a one-parameter family of coordinates Ψsub-h that deforms Ψ. The decorated Teichmuller space turns out to be explicit convex open polytopes in these deformed coordinates. As an application, Bowditch-Epstein and Penner's cell decomposition is reproduced. Some further questions will be mentioned at the end of the talk. Sponsor: GEAR Network Local host: UIUC Department of Mathematics Funding provided by: National Science Foundation Research Networks in Mathematical Sciences programAbstract: Tian Yang, in this GEAR Retreat 2012 Junior Talk, will discuss how to find a one-parameter family of coordinates Ψsub-h that deforms Ψ in decorated Teichmuller space.