Schedule, syllabus and examination date

Course content

Applications of the residue theorem, Montel's theorem, Cauchy-estimates, solutions to d-bar, Runge's theorem, Cousin I and II, Ahlfors-Schwarz-Pick Lemma, Riemann Mapping Theorem, Möbius transformations, hyperbolicity, metrics of negative curvature, Picard's Theorem, Schottky's Theorem, periodic functions in the plane, compact Riemann surfaces, some sheaf-theory and cohomology, divisors, meromorphic functions and Riemann-Roch.

Learning outcome

The course gives an introduction to classical results in function theory of the complex plane, and an analytic approach to some basic notions in complex/algebraic geometry via compact Riemann surfaces.

Admission to the course

PhD candidates from the Faculty of Mathematics and Natural Sciences at 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.

Overlapping courses

Teaching

4 hours of lectures/exercises per week throughout the semester.

The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.

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.

Examination

Final written exam or final oral exam, which counts 100 % towards the final grade.

The form of examination will be announced by the lecturer by 1 October/1 March for the autumn semester and the spring semester respectively.

This course has 1 mandatory assignment that must be approved before you can sit the final exam.

In addition, each PhD candidate is expected to give an oral presentation on a topic of relevance chosen in cooperation with the lecturer. The presentation has to be approved by the lecturer before you can sit the final exam.

It will also be counted as one of the three attempts to sit the exam for this course, if you sit the exam for one of the following courses: MAT4800 – Complex Analysis

Examination support material

No examination support material is allowed.

Language of examination

Courses taught in English will only offer the exam paper in English. You may submit your response in Norwegian, Swedish, Danish or English.

Grading scale

Grades are awarded on a pass/fail scale. Read more about the grading system.

Resit an examination

This course offers both postponed and resit of examination. Read more:

More about examinations at UiO

You will find further guides and resources at the web page on examinations at UiO.

Last updated from FS (Common Student System) Mar. 19, 2024 7:48:18 AM

Facts about this course

Level
PhD
Credits
10
Teaching
Autumn

Taught according to demand and resources. Contact studieinfo@math.uio.no if you are interested in this course.

Examination
Autumn
Teaching language
English