MAT 626. Teichmuller Theory
Samuel Grushevsky, Fall 2012, Stony Brook University
TuTh 1:00pm - 2:20pm, in Physics P123

Overview: We will develop the analytic and geometric approach to Teichmuller theory, by reviewing the definition of Riemann surfaces (aka complex algebraic curves), defining quasiconformal maps, studying Beltrami differentials, and defining the Teichmuller space with its Teichmuller metric. We will discuss the identification of the cotangent space to the Teichmuller space with the space of quadratic differentials, and the Weil-Petersson metric on the Teichmuller space. Further topics may include: completion of the Teichmuller space, and projectivity of the moduli space of curves; Mirzakhani's hyperbolic geometry proof of Witten's conjecture; geometry of, and towards the dynamics on, moduli of abelian differentials.

Prerequisites: Core graduate courses in complex analysis and geometry/topology. Further knowledge of complex or algebraic geometry would be helpful, but not required. If in doubt, please ask me.

Grading: Please see me if you have not passed your orals yet.

Textbook: While there is no one textbook, here is a selection of textbooks from which I'll draw some of the material:

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