Date:	Tue, March 3, 2015
Time:	14:15
Place:	Research I Seminar Room

Abstract: We extend Thurston’s famous characterization theorem of rational maps to the family of exponential maps, which provides the first (and to this day: only) transcendental extension of Thurston’s theorem. One fundamental ingredient is a decomposition theorem of quadratic differentials on Riemann surfaces, similar to a different result by McMullen. This decomposition theorem gives an “almost” compact model of the cotangent space to Teichmüller space. This decomposition was developed with the goal of extending Thurston’s theorem to larger spaces of transcendental maps, and we will outline where the obstacles are. We might remark that part of the work was the Bachelor thesis of our former students Bastian Laubner and Vlad Vicol