2018 Spring
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Dansk English

MM844: Introduction to noncommutative geometry. (10 ECTS)

STADS: 13017101

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.

Teacher responsible
Email: kaad@imada.sdu.dk

Timetable
Group Type Day Time Classroom Weeks Comment
Common I Thursday 10-12 IMADA semi 5
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Comment:
Ubegrænset deltagerantal. Udbydes til matematik-økonomi

Prerequisites:
A bachelor’s degree in mathematics or applied mathematics.

Academic preconditions:
Students taking the course are expected to:
  • Have a basic knowledge of topology and functional analysis, corresponding to the contents of the courses MM549 and MM548.
  • 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, rings and modules and be able to work comfortably with these objects.
  • Basic knowledge of C*-algebra theory corresponding to the content of the course MM819.
 


Course introduction
The aim of the course is to introduce the student to one or more topics in non-commutative geometry and present them with the relevant tools and techniques. This will enable the student to investigate current research topics in noncommutative geometry on his or her own. 
 
The course primarily builds on the knowledge acquired in the course MM548 (Measure and integration and Banach spaces) and the course MM819 (Introduction to operator algebras).
 
The course is not necessarily offered every semester, but according to the demand and need of the students.
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 new mathematical tools and objects.
• Give skills to learn and understand advanced mathematical theories at a more independent level.
• Give knowledge and understanding of one or more concrete disciplines within analysis
• Bring perspective into the student’s mathematical knowledge.
 


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: Introduction to one or more topics in noncommutative geometry. This could, for example, be:
  • Hilbert C*-modules.
  • KK-theory.
  • Quantum groups.
  • Spectral triples.
  • Cyclic theory and index theory.
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:


Expected working hours
The teaching method is based on three phase model.
Intro phase: 60 hours
Skills training phase: 20 hours, hereof:
 - Tutorials: 20 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
If there are only a few students signed up for the course, the course will be taught as a reading-course, possibly with a few introductory lectures.

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.