MAT4551 – Symplectic geometry
Schedule, syllabus and examination date
The course gives an introduction to symplectic geometry. It covers different classes of symplectic manifolds, contact manifolds and interactions between them. The main focus will be on local structures, Hamiltonian dynamics and some special types of submanifolds. Symplectic geometry is a relatively new field in mathematics, and has connections to algebraic geometry, dynamical systems, geometric topology, and theoretical physics.
After completing the course you:
- understand well the concepts of symplectic and contact manifolds, and can give examples of some main classes of them and how some of them interact
- know what an almost complex structure is and are familiar with how these can be used to gain information about the geometry of a symplectic manifold in some examples
- know about Moser's trick and can use this in the local theory
- are familiar with Lagrangian and Legendrian submanifolds, and know some techniques to study their properties
- understand some of the questions regarding Hamiltonian dynamics on symplectic manifolds and Reeb dynamics on contact manifolds
- know some standard constructions in symplectic geometry, such as Lefschetz fibrations and Weinstein handle attachments
Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.
If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.
10 credits overlap with MAT9551 – Symplectic geometry
4 hours lectures/exercises each week, throughout the semester.
1 mandatory assignment to be approved before the final exam. Final oral examination that counts 100 % of the grade.
Examination support material
No examination support material is allowed.
Language of examination
You may write your examination paper in Norwegian, Swedish, Danish or English.
Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. 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.
The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.