NSCPHD1272 Representation theory of groups, quantum groups and operator algebras

Volume 2014/2015
Content

Overview of the topic

 

Representation theory studies abstract groups of symmetries by representing them as concrete symmetries of the simplest geometric objects, linear spaces. The spaces which naturally arise, both from theoretical considerations and in applications (to geometry, dynamical systems, number theory, physics, … ) are often infinite-dimensional, and the study of infinite-dimensional group representations has been a major driving force in the development of operator algebra theory since the 1940s. This course will introduce students to some of the current trends in the overlap of representation theory and operator algebras.

 

Course structure and content

 

The five-day course will include three series of lectures by prominent international experts:

1. Operator algebras and representations of reductive groups (Prof. Nigel Higson, Penn State University)

2. Representation theory of quantum groups (Dr Christian Voigt, University of Glasgow)

3. The Mackey Machine and C*-algebras (Prof. Siegfried Echterhoff, University of Münster)

Each course will be complemented by suggestions for background and further reading, exercises and problems.

Additional research presentations by local and invited speakers will round out the scientific program, giving the participants a broad sampling of current research directions and open problems in this area.

Learning Outcome

Knowledge: students will learn how problems in representation theory have influenced the development of operator algebra theory, and how operator-algebraic methods are currently finding applications in representation theory.

Skills: Understanding how to combine concepts and techniques from representation theory and operator algebras to formulate and solve problems.

Competences: By the end of the course the students will be able to approach the research literature in the overlap of representation theory and operator algebars: both seminal papers and current work.

Research articles selected by the lecturers.

Lectures and exercises.
  • Category
  • Hours
  • Lectures
  • 25
  • Preparation
  • 25
  • Total
  • 50
Credit
2 ECTS
Type of assessment
Course participation
Aid
All aids allowed
Marking scale
passed/not passed
Censorship form
No external censorship
Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.