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Riemann Surfaces (M392C)

University of Texas at Austin, Spring semester, 2014

  • Course number: M 392C. Unique identifier: 53880

  • Monday, Wednesday, Friday, 1 - 2 pm, RLM 11.176

  • Instructor: Timothy Perutz (Assistant Professor)

  • Office hours: Tuesday, Wednesday, 4-5 p.m., RLM 10.136.

  • Email: perutz AT math DOT utexas DOT edu

  • Textbook: S.K. Donaldson, Riemann Surfaces, Oxford University Press, 2011. An electronic version is available from the University of Texas library here:

  • Information about this course can be found in PDF format here. Please download and read!

I'm happy to answer questions about this course by email or in person (RLM 10.136).


Review of basic complex analysis. (Last updated: Jan. 20, 2016)


There will be homework assignments every other week. They will largely be questions from Donaldson's text.

For students who are in candidacy already, or are preparing for a candidacy exam later this semester, homework is optional.

For other students, getting an A in this class requires substantial attempts at the homework assignments. Warning: grading will be cursory.

There will be no exams.

Homework 1.
Donaldson, chapter 1, questions 2, 3, 4, 5, 6. (Note: In q5, the indicial roots are 0 and 1-c, not 0 and c.) Due Friday, Feb. 5 (in my pigeonhole or by email by 5pm).

Homework 2.
Donaldson, chapter 3, questions 4, 5, 6, 7, 9, 10, 11. Also: A) in class I wrote down a characterization of the Riemann surface of a holomorphic function, and sketched its construction. Provide a full account. B) In the construction of plane projective curves, I omitted the check of compatibility of the charts coming from the three affine subsets of the projective plane. Carry it out. Due Wed., March 2 (in my pigeonhole or by email by 5pm).