MAT4830 – Topics in complex analysis and dynamics

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.

Students admitted at UiO must apply for courses in Studentweb. Students enrolled in other Master's Degree Programmes can, on application, be admitted to the course if this is cleared by their own study programme.

Nordic citizens and applicants residing in the Nordic countries may apply to take this course as a single course student.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures for international applicants.

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.

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.

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: MAT9830 – Topics in complex analysis and dynamics

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.