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Harmonic maps and cluster coordinates

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CARW03 - Interdisciplinary applications of cluster algebras

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 present work in progress on 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 equipped with an atlas of cluster Poisson coordinates.

This talk is part of the Isaac Newton Institute Seminar Series series.

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