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Abstract: I will present in this lecture some of the works of Maryam
Mirzakhani. Maryam Mirzakhani was a mathematician working in hyperbolic
geometry, studying curves on surfaces and more precisely their
distribution.
Rather than giving a precise account of her numerous and amazing results,
I will use one of her work as a thread — or a pretext — to present some
basic ideas of geometry as well as a little history of the subject: What
is a surface? What is hyperbolic geometry? How do mathematicians count
curves on surfaces?
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