Sums of self-adjoint operators: Kasparov products and applications

The University of Copenhagen 
August 22nd to August 26th, 2016

This master class will introduce the necessary technical tools for constructing Kasparov products in the unbounded picture of KK as well as discussing the many open problems related to sums of self-adjoint operators, the standard model in physics, topological insulators and operator spaces. 

Lecture series:

  • Johannes Kellendonk (University Lyon I)
    "Introduction to topological insulators"
  • Matthias Lesch (University of Bonn)
    "Sums of regular self-adjoint operators"
  • Bram Mesland (University of Hannover)
    "Frames and connections in KK-theory"
  • Adam Rennie (University of Wollongong)
    "Applications of KK-theory in non-commutative geometry and physics"
  • Fedor Sukochev (University of New South Wales)
    "Introduction to double operator integration and quantum differentiability of essentially bounded functions on euclidean space"


  • Francesca Arici (Radboud University Nijmegen)
    "Mapping cone exact sequences for Cuntz-Pimsner algebras"
  • Chris Bourne (University of Erlangen-Nuremberg),
    "Disordered topological states and Kasparov theory"
  • Jens Kaad (University of Southern Denmark)
    "Descent and index pairings in weighted KK-theory"
  • Koen van Dungen (SISSA, Trieste)
    "Locally bounded perturbations and (odd) unbounded KK-theory"
  • Walter van Suijlekom (Radboud University Nijmegen)
    "Factorizations in KK-theory and applications to physics"


The master class will take place at the Department of Mathematical Sciences, University of Copenhagen, with support from the Centre for Symmetry and Deformation. Detailed instructions on how to reach Copenhagen and the conference venue are given here. A map over the venues for social activities is found here.

Schedule, Abstracts, Slides and Notes:

The schedule is available here and the abstracts there. You can also access the slides from some of the talks:

  • The first part and the second part of the course by Fedor Sukochev
  • Jens Kaad's talk.
  • Lecture notes from the talks by Bram Mesland (the notes are from a more extensive lecture series given by Bram Mesland a few weeks earlier and thanks are due to Francesca Arici for making the notes available).
  • Lecture notes by Matthias Lesch from his talk.

Financial support:

Participants 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.

Registration and Participants:

Registration is closed. A list of participants is available.

Accommodation and public transportation:

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). 

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.

Organised by Olivier GabrielMagnus Goffeng and Ryszard Nest.