Pure Maths Colloquium - Systols on Origami Translation Surfaces - Prof Gabriela Weitze-Schmithüsen (Saarbrücken) Seminar

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Abstract: Translation surfaces are obtained by a charming concrete construction: Take finitely many polygons in the Euclidean plane and glue pairs of their edges via translations such that you obtain a connected surface. Although translation surfaces have been intensively studied since the 1980’s, there are still many natural questions wildly open. One of these questions is: Which translation surface of genus g has the largest shortest curve and how long is this curve? We describe an algorithmic approach to this question using a special class of translation surfaces called origamis or square-tiled surfaces.