Analysis Seminar

The Teichmuller space of a closed surface carries a natural complex structure, whose analytic properties reflect the topology and geometry of the surface. In this talk, we discuss the problem of classifying the holomorphic retracts of Teichmuller space. Our approach hinges on the analysis of two dynamical flows - one in the moduli space of half-translation surfaces, and the other in the space of bounded holomorphic functions on the polydisk.