MAT9830 – Topics in complex analysis and dynamics

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.

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