Description:

This is the continuation of the Fall 2024 course Math 703. We will discuss more advanced topics in complex analysis with some emphasis on the geometric viewpoint. They include zeros of holomorphic functions, interpolation and approximation theorems, the holomorphic extension problem, ranges of holomorphic functions, holomorphic branched covering maps, and the uniformization theorem.

Picture: A conformal grid and tiling associated with the modular group acting on the upper half plane. See Arnuad Cheritat's gallery at
http://www.math.univ-toulouse.fr/~cheritat

Lecturer: Saeed Zakeri
Office: Room 4301
Office hours: By appointment
Class meetings: Mon/Fri 12:00-1:30, Room 6417
email: saeed DOT zakeri AT qc DOT cuny DOT edu

Syllabus

References

Homework

Announcements:

• 1/27: Welcome! Based on the GC academic calendar, our class meets every Monday and Friday from 1/27 to 5/12 except for the following four dates: 2/17 (moved to Tuesday 2/18), 3/31, 4/14, 4/18.

General Information and Ground Rules:

• Homework will be assigned roughly every week and is an absolutely essential part of the course. You are strongly advised to work on all the homework problems to make sure you are keeping pace with the class. You are also encouraged to work together on these problems, but the work that you hand in must be your own write up.

• Course grade is based on the following scheme:
  
  

  Homework	Midterm	Final
  20%	30%	50%

• Exams are tentatively scheduled as follows:
  
  

  Midterm	Final
  Friday April 4	Friday May 16

• If the midterm exam is missed because of a documented illness or valid emergency, the course grade will be determined on the basis of the other work done during the semester. Exams missed for other reasons will count as failures.

• At the end of the semester, everyone who has not withdrawn from the class will receive a grade. Incompletes will not be given to avoid unsatisfactory grades.