MM805: Dirac operators (5 ECTS)

STADS: 13003201

Level
Master's level course approved as PhD course

Teaching period
The course is offered in the autumn semester.
Offered when needed

Teacher responsible
Email: svensson@imada.sdu.dk

Timetable
There is no timetable available for the chosen semester.

Comment:
Kører ikke F2010.

Ubegrænset deltagerantal. 4. kvartal.

Prerequisites:
None

Academic preconditions:
Material from MM804 Riemanian geometriy og Einstein metrics is assumed known.

Course introduction
Dirac operators first appeared in physical descriptions of the electron. Since then they have been used as a tool connecting analysis and topology on manifolds. The course gives a modern description of this theory with applications to properties of the Laplace operator.

Expected learning outcome
At the end of the course the student should be able to:

• reproduce definitions and results, including their proofs, from the theory of Dirac operators within the scope of the course syllabus
• apply these results to problems in differential geometry based on the course syllabus
• compare and related central results from the course
• explain the spectral properties of Dirac operators on compact Riemannian manifolds

Subject overview
Clifford algebras, principal bundles, spin structuers, Dirac operators and their spectrum, eigenvalues and twistor spinors.

Literature

Meddeles ved kursets start.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
Oral exam. Danish 7 mark scale, external examiner.
30 minutes preparation for the oral exam.

Terms for re-exam according to the rules decided by the Study Board.

Expected working hours
The teaching method is based on three phase model.

Forelæsninger, antal timer 32.
Eksaminatorietimer/opgaveregning, antal timer 18.
Educational activities

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.