MAT9810 – Introduction to Several Complex Variables
Holomorphic functions and mappings. Hartog's extension phenomenon, domains of holomorphy and holomorphic convexity. Plurisubharmonic functions. The d-bar equation and the Levi problem. Oka's approximation theorem, Runge pairs and the Cousin problems. Polynomial convexity and applications.
The course gives an introduction to the most central aspects and methods in the theory of holomorphic functions of several complex variables, and applications of these to approximation- and mapping problems.
PhD candidates from the University of Oslo should apply for classes and register for examinations through Studentweb.
If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.
PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.
- 10 credits overlap with MAT4810 – Introduction to Several Complex Variables
- 4 credits overlap with MAT4310
- 4 credits overlap with MAT9310 – Complex analysis (discontinued)
- 4 credits overlap with MAT4320 – Several complex variables I (discontinued)
- 4 credits overlap with MAT9320
- 4 credits overlap with MA365
- 4 credits overlap with MAT365
For information about the potential partial overlap with other courses, contact the Department.
4 hours of lectures/exercises per week.
Upon the attendance of three or fewer students, the lecturer may, in conjunction with the Head of Teaching, change the course to self-study with supervision.
Final oral examination.
In addition, each PhD student is expected to give a one hour oral presentation on a topic of relevance chosen in cooperation with the lecturer. The presentation has to be approved by the lecturer for the student to be admitted to the final exam.
Examination support material
No examination support material is allowed.
Language of examination
Subjects taught in English will only offer the exam paper in English.
You may write your examination paper in Norwegian, Swedish, Danish or English.
Grades are awarded on a pass/fail scale. Read more about the grading system.
Explanations and appeals
Resit an examination
Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.
Re-scheduled examinations are not offered to students who withdraw during, or did not pass the original examination.
Withdrawal from an examination
It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.
Special examination arrangements
Application form, deadline and requirements for special examination arrangements.
The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.