MAT9830 – Topics in complex analysis and dynamics

Schedule, syllabus and examination date

Choose semester

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).

The course builds on MAT4800 – Complex AnalysisMAT4810 – Introduction to Several Complex Variables and MAT4820 – Complex Dynamics.

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

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.

Prerequisites

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 lectures/exercises per week.

Examination

mandatory assignment.

Final oral examination. 

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 for the student to be admitted to the final exam

Examination support material

No examination support material is allowed.

Language of examination

The examination text is given in English, and you submit your response in English.

Grading scale

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.

Evaluation

The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.

Facts about this course

Credits

10

Level

PhD

Teaching

Examination

Teaching language

English