Practical informationSemester: 2018/2019 - summer
Module code: V5D3 - Advanced Topics in Geometry
Times and rooms:
- Tuesdays 10:15 - 12:00 in SR-0.008, Endenicher Allee 60
- Thursdays 12:15 - 14:00 in SR-0.007, Endenicher Allee 60
There will be no more lectures for this course
ExamThe exams will be oral and will take place in office 2.003 at the Endenicher Allee 60. They will take place on July 11 and 12 and August 28, 29 and 30. If you haven't yet picked a time slot, please contact me by email.
ContentsThe Teichmüller space of a surface S is the deformation space of complex structures on S and can also be seen as a space of 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 hyperbolic metrics on S. In particular, the end goal will be to prove Mirzakhani's recurrence for the Weil-Petersson volumes of moduli spaces.
PreliminariesLinear algebra, analysis, complex analysis, basic differential geometry, point-set topology.
Lecture notesI will post my notes here after each lecture. The exercises for every week can be found on the last pages of each section.
DISCLAIMER: I do not guarantee in any way that these notes are correct. I will be happy to hear of any mistakes that are found.
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- Ernesto Girondo and Gabino González-Diez. Introduction to compact Riemann surfaces and dessins d’enfants volume 79 of London Mathematical Society Student Texts. Cambridge University Press, Cambridge, 2012.
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- Maryam Mirzakhani. Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces. Invent. Math., 167(1):179–222, 2007.
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- Jeff Cheeger and David G. Ebin. Comparison theorems in Riemannian geometry. AMS Chelsea Publishing, Providence, RI, 2008.
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