MM868: Compact quantum metric spaces
The Study Board for Science
Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N310084102
Assessment: Second examiner: None
Grading: Pass/Fail
Offered in: Odense
Offered in: Autumn
Level: Master
STADS ID (UVA): N310084101
ECTS value: 5
Date of Approval: 22-04-2025
Duration: 1 semester
Version: Archive
Entry requirements
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 MM548 and MM549.
- Have a basic knowledge of the theory of groups and rings and be able to work comfortably with these objects, corresponding to the contents of the courses MM570 and MM567.
- Independently be able to carry out basic arguments of topological and algebraic nature.
- It is an advantage to have knowledge of basic C*-algebra theory (corresponding to the course MM819) which can be followed in parallel with MM868.
Course introduction
The aim of the course is to introduce the theory of compact quantum metric spaces and present them with the relevant tools and techniques.
The course primarily builds on the knowledge acquired in the courses MM548 (Measure and Integration and Banach spaces) and MM845 (Functional analysis).
The course primarily builds on the knowledge acquired in the courses MM548 (Measure and Integration and Banach spaces) and MM845 (Functional analysis).
The course will:
- Give the competence to take responsibility for the academic development and specialisation.
- 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.
- Bring perspective into the student’s mathematical knowledge.
Expected learning outcome
The learning objective of the course is that the student demonstrates the ability to:
- be able to use these results to analyse concrete examples.
- communicate and explain mathematical insights to fellow students in a clear and well-structured fashion
- select and structure relevant mathematical material within a given topic and present the material in the form of lectures.
- formulate and present definitions, proofs and calculations in a mathematically rigorous way.
Content
The following main topics are contained in the course:
- Operator systems and their state spaces
- Compact quantum metric spaces
- Spectral triples and their relation to quantum metric spaces
- Quantum Gromov-Hausdorff distance (if time permits)
Literature
Examination regulations
Exam element a)
Timing
Autumn
Tests
Oral exam
EKA
N310084102
Assessment
Second examiner: None
Grading
Pass/Fail
Identification
Full name and SDU username
Language
Normally, the same as teaching language
Duration
90 minutes
Examination aids
All common aids allowed
ECTS value
5
Additional information
The exam consists of a presentation of parts of the theoretical content and relevant exercises during the course.
Indicative number of lessons
Teaching Method
Planned lessons:
Total number of planned lessons: 56
Hereof:
Common lessons in classroom/auditorium: 56
During the planned lessons, the core curriculum will be presented in lectures, delivered partly by the students. The lectures are supplemented by relevant exercises that train the new concepts introduced.
Outside the planned lessons, the students are supposed to study the material on their own, solve relevant exercises, and work on the presentations of those parts of the curriculum that are planned for the student presentations.
Teacher responsible
| Name | Department | |
|---|---|---|
| David Kyed | dkyed@imada.sdu.dk | Institut for Matematik og Datalogi |
| Robin Kaarsgaard Sales | kaarsgaard@imada.sdu.dk | Institut for Matematik og Datalogi |