MAT9810 - Introduction to Several Complex Variables
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Course content
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.
Learning outcomes
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.
Admission
To participate in this course you must have an admission to a Ph.D.-programme at a Norwegian University or University College.
If you do not have an admission to the Ph.D.-Programme in Science at The Faculty of Mathematics and Natural Sciences at UiO, you have to apply for hospitantstatus (norwegian text) . For more information, please contact the Department.
The examination in this course is not available for external candidates. Only students admitted to the course may sit for the examination.
Prerequisites
Recommended prior knowledge
MAT4800 - Complex Analysis/MAT9800 - Complex Analysis.
Overlap
4 credits against MAT4310 - Complex analysis. 4 credits against MAT9310 - Complex analysis. 4 credits against MA365. 4 credits against MAT4320 - Several complex variables I. 4 credits against MAT9320. 4 credits against MAT365.
For information about the potential partial overlap with other courses, contact the Department.
Teaching
4 hours of lectures/exercises per week.
If few students apply for the course, it may be given as self-tuition with one hour of common academic supervision each week.
Exam information
Oral exam.
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.
Exam resources
No special exam resources are allowed.
Language of examination
Students may, on subjects taught in Norwegian and the examination form is written exam, ask for the exam paper in Bokmål, Nynorsk or English. Closing date for registering the chosen examination language is September 1st for the fall semester and February 1st for the spring semester.
Please view the web page of the Faculty of Mathematics and Natural Sciences on how to proceed
Subjects taught in English will offer the exam paper in English only.
This rule also applies for subjects where the exam form is dependent on the number of students and written exam is chosen by the teaching staff.
Assessment and grading
Students are awarded either a passing or a failing grade. Read more about the grading system .
An external auditor regularly evaluates the academic quality of the course, including the form of exam used on the course.
Explanations and appeals
A student may appeal against an awarded grade and/or file a formal complaint about exam procedures
Possibility of make-up exams and re-takes
Students who due to illness or other valid reason of absence were unable to sit for their final exams may apply for participation in deferred examinations. Deferred examinations are arranged either later in the same semester or early in the semester following the exam in question. Documentation of valid reasons for absence from the regular exam must be submitted upon application to participate in deferred examinations.
Students who have failed an exam, who withdraw during an exam, and students who wish to retake an exam to achieve a better grade may not participate in deferred exams, but may retake the exam when it is regularly scheduled.
Information about deferred and new examination (also called repeat examination) is found here
Withdrawing from exams and limits on re-takes
A student can sit for this exam up to 3 times. If a student wishes to withdraw from the exam, s/he must do this in StudentWeb at least two weeks prior to the first day of the exam. Failure to do so will be counted as one of the three opportunities to sit for the exam.
Exam options for students with special needs
Students may apply for access to alternative exam resources or exam forms on the basis of chronic illness and/or special needs that create a marked disadvantage to other students in the exam situation. Mothers who are breastfeeding may apply for extra time to complete the exam.
Evaluation of this course
Feedback from our students is essential to us in our efforts to ensure and further improve the high quality of our programmes and courses. As a student at the University of Oslo you will therefore be asked to participate in various types of evaluation of our courses, facilities and services. All courses are subject to continuous evaluation. At regular intervals we also ask students on a particular course to participate in a more comprehensive, in-depth evaluation of this course, a so called "periodic evaluation".
Contact us
Department of Mathematics
Visiting address:
Niels Henrik Abel's building, Moltke Moes vei
Visiting hours:
Monday-friday 09:00-14:30
Postal address:
P.O.box 1053, Blindern
NO-0316 Oslo
Fax: +47 22 85 43 49
E-mail: studieinfo@math.uio.no
Web: http://www.mn.uio.no/math/english/