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“A large part of mathematics which becomes useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly know in what area it would become useful; and there were no general indications that it ever would be so.”

– John von Neumann (1903 - 1957)


    Preprints

  1. Measure equivalence and coarse equivalence for unimodular locally compact groups arXiv:1703.08121
    Preprint
    with Juhani Koivisto and Sven Raum

  2. Polynomial cohomology and polynomial maps on nilpotent groups arXiv:1503.04068
    Preprint
    with Henrik Densing Petersen


    Published and accepted papers

  3. Higher ℓ²-Betti numbers of universal quantum groups arXiv:1612.07706
    Canadian Mathematical Bulletin (to appear), (2017)
    with Julien Bichon and Sven Raum

  4. L²-Betti numbers of rigid C*-tensor categories and discrete quantum groups arXiv:1701.06447
    Analysis & PDE 10(7), (2017)
    with Sven Raum, Matthias Valvekens and Stefaan Vaes

  5. On the ℓ²-Betti numbers of universal quantum groups     [View only version] arXiv:1610.05474
    Mathematische Annalen 369(3), (2017).
    with Sven Raum

  6. Topologizing Lie algebra cohomology arXiv:1603.03691
    Differential Geometry and its Applications 49, (2016)

  7. L²-Betti numbers of locally compact groups and their cross section equivalence relations arXiv:1302.6753
    Transactions of the AMS 367, (2015)
    with Henrik Densing Petersen and Stefaan Vaes

  8. Measure continuous derivations on von Neumann algebras and applications to L²-cohomology arXiv:1110.6155
    Journal of Operator Theory 73(1), (2015)
    with Vadim Alekseev

  9. A groupoid approach to Lück's amenability conjecture arXiv:1205.1930
    Osaka Journal of Mathematics 51(4), (2014)
    with Henrik Densing Petersen

  10. Applications of Følner's condition to quantum groups arXiv:1003.5181
    Journal of Noncommuative Geometry 7(2), (2013)
    with Andreas Thom

  11. Amenability and vanishing of L²-Betti numbers: an operator algebraic approach arXiv:1105.3406
    Journal of Functional Analysis 263(4), (2012)
    with Vadim Alekseev

  12. Property (T) and exotic quantum group norms arXiv:1006.4044
    Journal of Noncommuative Geometry 6(4), (2012)
    with Piotr M. Sołtan

  13. An L²-Künneth formula for tracial algebras arXiv:0903.0931
    Journal of Operator Theory 67(2), (2012)

  14. A cohomological description of property (T) for quantum groups arXiv:1003.5181
    Journal of Functional Analysis 261(6) (2011)

  15. On the zeroth L²-homology of a quantum group arXiv:0906.0656
    Münster Journal of Mathematics 4, (2011)

  16. L²-Betti numbers of coamenable quantum groups arXiv:0704.1582
    Münster Journal of Mathematics 1, (2008)

  17. L²-homology for compact quantum groups arXiv:math/0605240
    Mathematica Scandinavica. 103(1), (2008)


    Theses and other publications

  18. Uniqueness of group-measure space Cartan subalgebras arXiv:1110.3508
    Expository notes following Adrian Ioana's IHP-lectures from May 2011

  19. L²-invariants for quantum groups
    PhD dissertation, University of Copenhagen, 2008

  20. Generalized Murray-von Neumann dimension and L²-homology for finite von Neumann algebras
    Master's thesis, University of Copenhagen, 2005