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Abstract: The Teichmüller space of a differential surface S is the space of marked complex structures on S, equivalently the space of marked hyperbolic
metrics on S. The aim of this course will be to study the geometry and topology of this space and its quotient: the moduli space of complex algebraic curves with underlying toplogical surface S, equivalently the moduli space of hyperbolic metrics on S. In particular, the end goal will be to prove Mirzakhani's recurrence for the Weil-Petersson volumes of these moduli spaces.
Prerequisites: Linear algebra, complex analysis, basic differential geometry, a bit of algebraic topology, a bit of algebraic geometry. |
