The set of simple closed curves is of integral importance in the study of Riemann surfaces; passing to its completion, the space of measured laminations, often reveals new underlying structure. Measured laminations play many roles in Teichmüller theory, from geometric (compactifying Teichmüller space) to analytic (parametrizing quadratic differentials) to dynamic (describing Teichmüller geodesic flow). Beginning from first definitions, I will survey some of these applications, leading towards a discussion of two different analogues of unipotent flow adapted to a given lamination. This talk is meant as a prelude to my talk tomorrow.
Speaker(s): Aaron Calderon (Yale)