Math 220C - Complex Analysis

Course description: This is the third in a three-sequence graduate course on complex analysis, picking up where Math 220B left off. Topics to be presented include: Mittag-Leffler's theorem, Schwarz reflection principle, analytic continuation, sheaves of analytic functions, analytic manifolds (Riemann surfaces), harmonic/subharmonic/superharmonic functions, order of entire functions, the big Picard theorem. If time permits, we may say more about Riemann surfaces in the direction of the Riemann-Roch theorem.

Instructor: Kiran Kedlaya, kedlaya [at] ucsd [etcetera]. Office hours: Thu 11-12 or by appointment.

Lectures: MWF 9-10, in APM 7421.

Textbook: Required: J.B. Conway, Functions of One Complex Variable, Second Edition (same text as for Math 220B). From any UCSD computer, the book is available as a legal free download via this link.

Prerequisites: Math 220B or equivalent (with instructor's permission).

Homework: Weekly assignments, due on Fridays.

Final exam: None. Instead, the qualifying exam will be held Wednesday, May 31, 9am-12pm.

Grading: 100% homework.