Complex Analysis in Several Variables

General entry requirements and the equivalent of 90 credits in mathematics, including the equivalent of the course MMG700 Analytic Function Theory. Knowledge of fundamental topological concepts for subsets of R^n is recommended, corresponding to relevant parts of the courses MMA100 Topology or MMG600 Real Analysis.

Holomorphic functions of several variables. Cauchy's integral formula in several variables. Reinhardt domains. Hartogs' phenomenon. Extension theorems. Pseudoconvexity. Plurisubharmonic functions. Domains of holomorphy. The Levi problem. The dbar-equation. Approximation theorems.

On successful completion of the course the student will be able to

• Account for fundamental results concerning holomorphic functions of several variables.
• Describe theory that generalizes from one to several complex variables, as well as theory that does not.
• Prove and apply various extension and approximation theorems for holomorphic functions.
• Explain and prove the equivalence of different formulations of pseudoconvexity.

The course is assessed by means of a written assignments and a written exam at the end of the course. During the course, there may be optional assignments that give bonus points on the exam. Examples of such assignemnts are tests, written assignments, laboratory sessions or project work. Information for the current course instance is given via the course homepage.

If a student who has been failed twice for the same examination element wishes to change examiner before the next examination session, such a request is to be granted unless there are specific reasons to the contrary (Chapter 6 Section 22 HF).

If a student has received a certificate of disability study support from the University of Gothenburg with a recommendation of adapted examination and/or adapted forms of assessment, an examiner may decide, if this is consistent with the course’s intended learning outcomes and provided that no unreasonable resources would be needed, to grant the student adapted examination and/or adapted forms of assessment.

If a course has been discontinued or undergone major changes, the student must be offered at least two examination sessions in addition to ordinary examination sessions. These sessions are to be spread over a period of at least one year but no more than two years after the course has been discontinued/changed. The same applies to placement and internship (VFU) except that this is restricted to only one further examination session.

If a student has been notified that they fulfil the requirements for being a student at Riksidrottsuniversitetet (RIU student), to combine elite sports activities with studies, the examiner is entitled to decide on adaptation of examinations if this is done in accordance with the Local rules regarding RIU students at the University of Gothenburg.

The grading scale comprises: Pass with Distinction (VG), Pass (G) and Fail (U).

The course is evaluated with an anonymous questionnaire and/or a discussion with the student representatives. The results of and possible changes to the course will be shared with students who participated in the evaluation and students who are starting the course.