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MM832: Groups and operator algebras (5 ECTS)

STADS: 13011801

Master's level course approved as PhD course

Teaching period
The course is offered in the autumn semester.

Teacher responsible

Additional teachers

There is no timetable available for the chosen semester.

Ubegrænset deltagerantal.


Academic preconditions:
Basic knowledge of Hilbert and Banach spaces (MM815) and, ideally, a basic knowledge of operator algebras (MM819).

Course introduction
The interplay between operator algebras and group theory goes back to the seminal papers by Murray and von Neumann. Various group-theoretical properties, such as amenability and Kazhdan's property (T), have provided fundamental insights into the nature of C_-algebras and von Neumann algebras and is currently a very active research area. However, recent developments have also provided evidence that relationship is equally fruitful the other way around: certain aspects of group theory are best understood by operator algebraic means. In the course the student will be introduced to some of these results and the methods used to prove them.

The overall goal is to introduce the student to the vast interplay between group theory and operator algebras.

Expected learning outcome
  • Obtain a general understanding of the usage of operator algebras in group theory and vice versa
  • Be able to present advanced material related to the topics covered
  • Get acquainted with certain aspects of current mathematical research
Subject overview
The course will include one or several of the following topics based on the number of students and their individual prerequisites: Group C_- and von Neumann algebras, von Neumann dimension, L2-Betti numbers, amenability, property (T), the conjectures by Atiyah and Kaplansky.

    Meddeles ved kursets start.

This course uses e-learn (blackboard).

Prerequisites for participating in the exam

Assessment and marking:
  1. Active participation and delivering of one lecture, evaluated by internal censorship by the danish 7 mark scale (5 ECTS). (13011802)
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 Study phase: 28 hours

This course is taught in English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.