Teichmüller spaces, quadratic differentials, and cluster coordinates

Abstract: In the late 1980s, Nigel Hitchin and Michael Wolf independently discovered a parametrization of the Teichmüller space of a compact surface by holomorphic quadratic differentials. In this talk, I will describe a generalization of their result. I will explain how, by replacing holomorphic differentials by meromorphic differentials, one is naturally led to consider an object called the enhanced Teichmüller space. The latter is an extension of the classical Teichmüller space which is important in mathematical physics and the theory of cluster algebras.

mathematical physicsalgebraic geometrygeometric topologyquantum algebra

Audience: researchers in the discipline

( video )

Geometry, Algebra and Physics at KIAS