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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)


    Research papers


  1. The quantum metric structure of quantum SU(2) arXiv:2205.06043
    Preprint
    with Jens Kaad

  2. The Podleś spheres converge to the sphere arXiv:2102.12761
    Communications in Mathematical Physics 392(3), (2022),
    with Konrad Aguilar and Jens Kaad

  3. Polynomial approximation of quantum Lipschitz functions arXiv:2104.04317
    Documenta Mathematica 27, (2022)
    with Konrad Aguilar and Jens Kaad

  4. Gromov-Hausdorff convergence of quantised intervals arXiv:2007.09694
    Journal of Mathematical Analysis and Applications 500(2), (2021)
    with Thomas Gotfredsen and Jens Kaad

  5. Cohomological induction and uniform measure equivalence arXiv:1904.03862
    Fundamenta Mathematicae 255(1), (2021)
    with Thomas Gotfredsen
    The Maple worksheets referred to in the paper can be downloaded here

  6. Dynamics of compact quantum metric spaces arXiv:1904.13278
    Ergodic Theory and Dynamical Systems 41(7), (2021)
    with Jens Kaad

  7. Measure equivalence for non-unimodular groups arXiv:1805.09063
    Transformation Groups 26(1), (2021)
    with Juhani Koivisto and Sven Raum

  8. Measure equivalence and coarse equivalence for unimodular locally compact groups arXiv:1703.08121
    Groups, Geometry, and Dynamics 15(1), (2021)
    with Juhani Koivisto and Sven Raum

  9. Polynomial cohomology and polynomial maps on nilpotent groups arXiv:1503.04068
    Glasgow Mathematical Journal 62(3), (2020)
    with Henrik Densing Petersen

  10. Uniquness questions for C*-norms on group rings arXiv:1806.10983
    Pacific Journal of Mathematics 298(2), (2019)
    with Vadim Alekseev.

  11. Higher ℓ²-Betti numbers of universal quantum groups arXiv:1612.07706
    Canadian Mathematical Bulletin 61(2), (2018)
    with Julien Bichon and Sven Raum

  12. 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

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

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

  15. 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

  16. 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

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

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

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

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

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

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

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

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

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


    Theses and other publications

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

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

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