MMA150 Complex Analysis in Several Variables Spring 24
This page contains the program of the course: lectures, homework assignments and recommended exercises. Other information, such as learning outcomes, teachers, literature and examination, are in a separate course PM.
Preliminary program
The schedule of the course is in TimeEdit.
Lectures
| Lecture | Date (Who) | Sections | Content |
|---|---|---|---|
| 1 |
19/3 (EW) |
L 1.1-1.3 | Overview, basic definitions and properties of holomorphic functions |
| 2 |
21/3 (EW) |
L 1.1-1.3 |
Basic definitions and properties of holomorphic functions |
| 3 |
22/3 (EW) |
L 1.4 |
Inequivalence of ball and polydisc |
| 4 | 26/3 (EW) | L 1.6 | Riemann extension theorem |
| 5 |
9/4 (RL) |
KW 2.3-2.4 |
Reinhardt domains and power series |
| 6 |
11/4 (RL) |
L 2.1 |
Domains of holomorphy |
| 7 |
12/4 (RL) |
L 2.2 |
Convexity |
| 8 |
16/4 (RL) |
L 2.3 |
Levi pseudoconvexity |
| 9 |
18/4 (RL) |
L 2.3 |
Convexity and pseudoconvexity |
| 10 |
19/4 (RL) |
L 2.4 KW 8.1-8.3 |
Subharmonicity |
| 11 |
23/4 (RL) |
L 2.4 KW 8.1-8.3 |
Subharmonicity |
| 12 |
25/4 (RL) |
L 2.4 |
Plurisubharmonicity |
| 13 |
26/4 (RL) |
L 2.5 |
Hulls, Hartogs pseudoconvexity |
| 14 |
30/4 (RL) |
L 2.5 |
Hartogs pseudoconvexity |
| 15 |
2/5 (RL) |
L 2.6 |
Holomorphic convexity |
| 16 |
7/5 (RL) |
L 4.1 |
The dbar-equation, the Cauchy-Pompeiu formula |
| 17 |
14/5 (RL) |
L 2.6 |
Levi problem for Reinhardt domains |
| 18 |
16/5 (RL) |
L 4.2-4.3 |
Solvability of dbar for (0,1)-forms with compact support, Hartogs phenomenon |
| 19 |
17/5 (RL) |
L 4.6 KW 7.1, 7.3-5 |
Cousin I problem |
| 20 |
21/5 (RL) |
L 4.4-4.5 KW 7.5-7.6 (supplementary material: H) |
The local dbar-equation The dbar-equation on polydiscs and pseudoconvex domains |
| 21 |
23/5 (RL) |
L 4.4-4.5 KW 7.5-7.6 (supplementary material: H) |
The local dbar-equation The dbar-equation on polydiscs and pseudoconvex domains |
Homework assignments
You hand in the assignment by uploading your solutions under "Assignments" here in Canvas.
Note: The homework assignments are supposed to be handed in individually. You are free to cooperate with other students and to read whatever literature you can find about the subject. However, you are expected to formulate your solutions independently and it is neither allowed to copy from other students nor to copy solutions form any other source.
Recommended exercises
Course summary:
| Date | Details | Due |
|---|---|---|