2018 Spring
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MM807: von Neumann algebras (5 ECTS)

STADS: 13003901

Level
Master's level course approved as PhD course

Teaching period
The course is held twice a year, once in the autumn semester and once in the spring semester.
Offered according to needs.

Teacher responsible
Email: dkyed@imada.sdu.dk

Timetable
Group Type Day Time Classroom Weeks Comment
Common I Tuesday 14-16 U161 15-22
H1 TE Wednesday 10-12 IMADA semi 15-22
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 Show personal time table for this course.

Comment:
Ubegrænset deltagerantal

Prerequisites:
MM548 and MM549 (or similar courses)

Academic preconditions:
Students taking the course are expected to:
  • Have a basic knowledge of topology and functional analysis, corresponding the contents of the courses MM548 and MM549.
  • Be able to use basic arguments from topology.
  • Be able to work independently with linear algebra.
  • Have a basic knowledge of the theory of groups and rings.
 


Course introduction
The aim of the course is to enable the student to work with operators on Hilbert spaces and algebras of such operators.
The course builds on the knowledge acquired in the courses MM548 and MM549 and will enable the student to follow more advanced courses in operator algebras.

In relation to the competence profile of the degree it is the explicit focus of the course to:
  • Give the competence to take responsibility for the academic development and specialization.
  • Give the competence to develop an overview of the interplay between different mathematical disciplines.
  • Give skills to work concretely with Hilbert spaces and their operators.
  • Give skills to use different operator topologies and their interactions.
  • Give knowledge and understanding of concrete examples of operator algebras.
  • Give knowledge of the theory of von Neumann algebras.
 


Expected learning outcome
The learning objectives of the course is that the student demonstrates the ability to:
  • Reproduce definitions and results, including their proofs, covered in the course.
  • Be able to use these results to analyse concrete examples.
  • Formulate and present definitions, proofs and calculations in a mathematically rigorous way.
 


Subject overview
The following main topics are contained in the course:
  • Basic operator theory
  • operator topologies
  • von Neumann algebras
 


Literature
There isn't any litterature for the course at the moment.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
  1. Written assignments and giving one of the lectures. Internal marking, 7-mark scale. (5 ECTS). (13003902).
Expected working hours
The teaching method is based on three phase model.
Intro phase: 14 hours
Skills training phase: 14 hours, hereof:
 - Tutorials: 14 hours

Educational activities
  • The students are expected to familiarize themselves with the material covered in the lectures.
  • To acquire knowledge of selected topics independently.
Educational form

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.

Remarks
Alle studerende der opfylder forudsætninger/krav kan tage kurset.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.