In only sixteen pages, thearticle gives a panoramic viewof the theory of translationsurfaces and of the recentbreakthrough by Alex Eskin,Maryam Mirzakhani, and Amir Mohammadi on the structureof the orbit closure of a translation surface. Wright’saccount combines brevity with clarity. It is a considerablefeat: this active and highly technical research area comprisesthe work of many. The article gives nonspecialists a goodentry point and a guide to further reading.
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