turkmath.org

Teichmüller theory is primarily concerned about studying the moduli for hyperbolic structures on a given topological surface. It is subject where different branches of mathematics such as complex analysis, hyperbolic geometry, algebraic topology, low dimensional topology and several others intersect. In this talk, we will motivate and define the Teichmüller space and introduce several geometries on this space. Time permitting, we will discuss certain results about the comparison of these geometries and some open problems on the same topic.