MAST 90056: Riemann Surfaces and Complex Analysis
Lecturer: Christian Haesemeyer
Office: Richard Berry 171
Consultation: Wednesday 14:00 - 17:00 in Richard Berry 171.
Times and location: Lecture Monday 10 - 11, Richard Berry G03 (Evan Williams Theatre); Lecture Wednesday 10 - 11, Richard Berry G03; Lecture/Practical Friday 10 - 11, Richard Berry G03.
- Lectures will not be recorded.
- The start of semester pack includes: Housekeeping (pdf), Plagiarism (pdf), Plagiarism declaration (pdf), Academic Misconduct (pdf), SSLC responsibilities (pdf).
Subject outline: See the handbook entry here. A bit more specifically: The first part of this course will study holomorphic functions in regions of the complex plane and meromorphic functions in the plane beyond the material of a basic complex analysis course. we will prove the Riemann mapping theorem and discuss the Cauchy-Riemann equations. The second part of this course will provide a quick introduction to the notion of complex manifold, holomorphic functions on a complex manifold, and differential forms on complex manifolds. In the third part, we will introduce Riemann surfaces as the natural domains of multi-valued functions in the plane; complex elliptic curves will be studied more closely as an example. The fourth and final part of the course will discuss holomorphic and meromorphic differentials, residues and periods on Riemann surfaces.
Assessment: A total of three assignments will be posted, accounting for 60% of the subject assessment. They will be due at the beginning of lecture on Wednesday, September 9; Wednesday October 7; and Wednesday, October 21. Assignments will be posted approximately 4 weeks before they are due. No extensions will be granted. In addition there will be a two-hour exam during the final exam period, accounting for 40% of the assessment.
- Assignment 1.
- Assignment 2.
- Assignment 3.
- Sources: The lectures will not follow a set textbook; attendance is therefore highly encouraged. Sources used by the instructor for the first part include Walter Rudin, Real and Complex Analysis (3rd ed.), McGraw-Hill 1987; and for the second through fourth parts, Otto Forster, Lectures on Riemann Surfaces, Springer 1999. The books listed in the handbook entry for this subject are also excellent sources for most of the material covered. Please find below scans of the handwritten lecture notes: