Subfactors and Quantum Groups: a combinatorial approach to some problems in Operator Algebras

Participants, 2 May 2019. Click for large photo.

Masterclass, University of Copenhagen, 29 April -  3 May 2019

The celebrated theory of subfactors studied by V. Jones in the early 1980's finds a connection with discrete quantum groups (duals of compact quantum groups in the sense of Woronowicz) through the concept of rigid C*-tensor category thanks to works of S. Popa in the 1990's. The aim of this 5-days masterclass is to provide a comprehensive introduction to the subfactor theory as well as the combinatorics behind in order to understand this connection and highlight some recent applications.

The masterclass will consist of three lecture series by Michael Brannan, Amaury Freslon and Stefaan Vaes, accompained by several problem sessions. Besides, there will be three contributed talks which will complement the topics treated in the mini-courses. 

Lecture series:

  • Michael Brannan (Texas A&M University): rigid C*-tensor categories, monoidal equivalence, the Temperley-Lieb category, quantum channels, entanglement, non-local games and an application of CQG.
  • Amaury Freslon (Université Paris-Sud 11): compact and discrete quantum groups, categories of partitions, the representation theory of partition quantum groups and the Connes embedding property for quantum group von Neumann algebras
  • Stefaan Vaes (KU Leuven): subfactors theory, property (T) for discrete quantum groups and Zuk's criterion for property (T).

Research Talks:

  • Laura Mančinska (Centre for the Mathematics of Quantum Theory, QMATH)
  • Adam Skalski (Institute of Mathematics Polish Academy of Sciences, IMPAN)
  • Roland Vergnioux (Université de Caen Normandie)

Prerequisites and references:

A solid background in C*-algebras, von Neumann algebras and tensor categories will be appropriate in order to make the most of the lectures.

Some general literature that could be used as support is the following.

  • C*-algebras and finite dimensional approximations (Nathanial P. Brown & Narutaka Ozawa)
  • Compact Quantum Groups and their representation categories (Sergey Neshveyev & Lars Tuset)
  • Lectures on von Neumann algebras (Serban Stratila & Lázló Zsidó)
  • Introduction to subfactors (V. Jones & V. S. Sunder)


Here you can find the shedule of the masterclass together with the rooms where the lectures/talks will take place.

Here you can find a plan of the campus where the lectures/talks will take place.

Financial support:

Graduate students and other early career researchers can apply for financial support to partly cover local expenses. If you wish to apply for support, please indicate this on the registration form. The support should be roughly DKK 500 per day, at most DKK 2500 in total.


The masterclass will take place at the Department of Mathematical Sciences, University of Copenhagen. See detailed instructions on how to reach Copenhagen and the conference venue.


There are several canteens located in the campus. Namely, the canteen in the Biocenter Building and the canteen in the August Krogh Building. You will be free to choose the place where you will have lunch. Participants will be asked to pay for their own lunch, which typically costs around 25-50 kr.

Pizza reception and conference dinner:

  • There will be a lunch reception in the department with pizza on May 1st.
  • Conference dinner. It will take place in the Indian restaurant B’India on May 2nd at 7:30. It is located in Blegdamsvej 130, 2100 København Ø, which means 20 minutes by walking from the Department of Mathematical Sciences.

    Please, if you finally decide to not attending the conference dinner, you should warn us by mail as soon as possible.


We kindly ask the participants to arrange their own accommodation. We recommend Hotel 9 Små Hjem, which is pleasant and inexpensive and offers rooms with a kitchen. Other inexpensive alternatives are CabInn, which has several locations in Copenhagen: the Hotel City (close to Tivoli), Hotel Scandivania (Frederiksberg, close to the lakes), and Hotel Express (Frederiksberg) are the most convenient locations; the latter two are 2.5-3 km from the math department. Somewhat more expensive – and still recommended – options are Hotel Nora and  Ibsen's Hotel.

An additional option is to combine a stay at the CabInn Metro Hotel with a pass for Copenhagen (efficient and reliable) public transportation (e.g. FlexCard 7 days with 2 zones, CityPass 24 or 72 hours). 

Public transportation:

Tickets and passes for public transportation can be bought at the Copenhagen Airport and every train or metro station. You can find the DSB office on your right-hand side as soon as you come out of the arrival area of the airport. DSB has an agreement with 7-Eleven, so many of their shops double as selling points for public transportation. A journey planner in English is available. More information on the "find us" webpage.

Registration and Participants:

The deadline for registration and funding applications is March 20th, 2019.

Here you can find the list of participants to the masterclass

Registration form

This masterclass is supported by the PhD-school of the Faculty of SCIENCE, Copenhagen University and the Centre for Symmetry and Deformation.

Organized by Rubén Martos and Ryszard Nest.