A parametrisation of the Teichmüller space by polygons

In this talk, we present a parametrizaion of the Teichmüller space of hyperelliptic curves by Euclidean polygons. There is a natural way to associate nonsingular Euclidean polygons to hyperelliptic curves. We shall introduce a notion of marked Euclidean cone manifold to extend such an association to general Euclidean polygons. Joint work with Kenichi Ohshika. (PDF file)