MAT9551 – Symplectic geometry
Course description
Schedule, syllabus and examination date
Course content
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.
Learning outcome
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
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.
Overlapping courses
10 credits overlap with MAT4551 – Symplectic geometry
Teaching
4 hours lectures/exercises each week, throughout the semester.
Examination
1 mandatory assignment to be approved before the final exam. Final oral examination that counts 100 % of the grade.
In addition, each PhD student 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
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.
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.
The course MAT9551 – Symplectic geometry overlaps 10 ECTS with MAT4551 – Symplectic geometry and number of times one can take the exam applies to these courses combined.
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.