MAT9830 – Topics in complex analysis and dynamics
Course description
Schedule, syllabus and examination date
Course content
The content of the course is various topics in complex analysis and dynamics. The concrete content will vary, but can include advanced methods and topics of high current interest in either complex analysis (in one or several variables, and interaction with dynamical systems and algebraic geometry) or complex dynamics (and interaction with algebraic dynamics and number theory).
Learning outcome
The course will cover one or more of the following topics
Andersen-Lempert theory of holomorphic automorphisms in the affine space, and applications to Fatou-Bieberbach domains and complex curves in the affine space
Riemann surfaces, Teichmuller spaces and applications to embedding of open Riemann surfaces
Dynamical properties of holomorphic maps of affine spaces in one and higher dimensions: Fatou and Julia sets, local and global theory of periodic points, wandering domains
Positive closed currents, intersections and relations to algebraic cycles, Monge-Ampere equations and dynamical currents of meromorphic maps
Cohomological properties of rational maps: birational invariants (dynamical degrees) and relations to topological entropy, periodic points and Weil’s Riemann hypothesis in positive characteristic.
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.
Recommended previous knowledge
MAT4800 - Complex Analysis and/or MAT4810 - Introduction to Several Complex Variables and/or MAT4820 - Complex Dynamics, or a similar course. MAT3440 - Dynamical systems og MAT4210 - Algebraic Geometry 1 are also useful courses to have done previously.
Overlapping courses
- 10 credits overlap with MAT4830 – Topics in complex analysis and dynamics.
Teaching
3 hours of lectures/exercises per week.
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 oral exam which counts 100 % towards the final grade.
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: MAT4830 – Topics in complex analysis and dynamics
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 write your examination paper 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
- Use of sources and citations
- Special exam arrangements due to individual needs
- Withdrawal from an exam
- Illness at exams / postponed exams
- Explanation of grades and appeals
- Resitting an exam
- Cheating/attempted cheating
You will find further guides and resources at the web page on examinations at UiO.