MM854: Graduate seminar
Study Board of Science
Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N310054102
Assessment: Second examiner: None
Grading: Pass/Fail
Offered in: Odense
Offered in: Autumn
Level: Master
STADS ID (UVA): N310054101
ECTS value: 5
Date of Approval: 07-04-2021
Duration: 1 semester
Version: Approved - active
Comment
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.
- 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 and be able to work comfortably with these objects, corresponding to the contents of the courses MM539 and MM551.
Course introduction
The aim of the course is to introduce the student to one or more topics either in modern analysis or in modern algebra and present them with the relevant tools and techniques. This will prepare the student for writing a master’s thesis within modern analysis or algebra.
The course primarily builds on the knowledge acquired in the course MM548 (Mål- integralteori og Banachrum) and knowledge from the course MM845 (Funktional analyse) can also be included. The course gives the student a deeper insight into the many aspects of analysis.
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 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.
- Give knowledge and understanding of one or more concrete disciplines within analysis or algebra.
- 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.
- select and structure relevant mathematical material within a given topic and present the material to fellow students in a lecture.
- Communicate and explain mathematical insights to fellow students in a clear and well-structured fashion.
- Formulate and present definitions, proofs and calculations in a mathematically rigorous way.
Content
The following main topics are contained in the course:
Introduction to one or more topics in analysis. This could, for example, be:
- Representation theory.
- Cohomology theory for groups and/or algebras.
- Introduction to K-theory.
- Important classes of discrete groups.
- Von Neumann algebras.
- Index theory.
- Unbounded operators and their spectral theory.
- Introduction to noncommutative geometry.
- Hilbert C*-modules.
- Quantum groups.
- Symplectic geometry.
- Quantum field theory and classical field theory.
- Algebraic geometry.
- Deformation quantization.
- Geometric quantization.
- Cluster algebras.
- Gauge theory.
- Moduli space theory.
- Homological mirror symmetry.
- Micro local sheaf theory.
Literature
Examination regulations
Exam element a)
Timing
Autumn
Tests
Oral presentation
EKA
N310054102
Assessment
Second examiner: None
Grading
Pass/Fail
Identification
Full name and SDU username
Language
Normally, the same as teaching language
Duration
2 hours
Examination aids
Allowed
ECTS value
5
Additional information
Students give a lecture during course. Teacher and other students participate in the examination lectures thus the given lectures is a part of the overall learning outcome. The subject of the lecture is agreed in advance.
Indicative number of lessons
Teaching Method
The teaching method is based on the three-phase model. The hours are for guidance purposes.
- Intro phase: 28 hours
- Skills training phase: 28 hours, hereof tutorials: 28 hours
- Activities during the study phase:
- The students are expected to familiarize themselves with the material covered in the lectures.
- To acquire knowledge of selected topics independently.
- Select and structure mathematical material and prepare to present this material in lecture form to fellow students.