Cohomology of arithmetic groups

University of Copenhagen - 8-11 May 2017

The cohomology of arithmetic groups is an important mathematical topic, that lies at the intersection of a number of mathematical fields. In particular, these cohomology groups are algebro-topological invariants, but the information they contain is of deep number-theoretic significance. To study them, mathematicians draw from such diverse fields as algebraic topology, harmonic and complex analysis, and number theory. Our goal is to give students and early career researchers an introduction to these ideas, and to foster future research.

The Masterclass will consist of a lecture series by Andy Putman as well as a few contributed talks about current research.

Lecture series:

  • Andy Putman (Notre Dame)
    "Buildings, duality, and the high-dimensional cohomology of arithmetic groups."
    Abstract and references.


  • David Sprehn (Copenhagen University)
    "Stable modular cohomology"
  • Orsola Tommasi (Chalmers University of Technology and University of Gothenburg)
    "Cohomological stabilization of toroidal compactifications of Ag"
  • Alexander Kupers (Copenhagen University)
    "Computing K8(Z)"
  • Bena Tshishiku (Harvard University)
    "Geometric cycles"


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


A solid background in group theory and algebraic topology.

Schedule and abstracts:

There will be two lectures series consisting of four talks, and a few contributed talks. The schedule of the lectures can be found here.

References, lecture material, and notes:

For references, see the abstract and references for Andy Putman's lecture series. Notes will appear during the workshop. Notes from the lectures are linked from the schedule.

Registration and Participants:

The registration has closed. A list of participants can be found here.

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 Alexander Kupers and Nathalie Wahl.