My research is mainly focused on homotopy theory and its applications in algebraic, complex and arithmetic geometry.

I am currently supported by the project Equations in Motivic Homotopy financed by the Research Council of Norway, and I am a research partner in the LPP-RIMS International Research Network Arithmetic & Homotopic Galois Theory.

Prior my research was supported by RCN project Motivic Hopf equations and by the German Research Foundation in various forms.

ORCID iD icon https://orcid.org/0000-0003-1898-1647

Publications and Preprints

  • Geometric representation of cohomology classes for the Lie groups Spin(7) and Spin(8) pdf (with Eiolf Kaspersen)
    preprint - arXiv:2409.06491 - 8 pages

  • A note on the Thom morphism for the classifying space of certain Lie groups and gauge groups pdf (with Eiolf Kaspersen)
    preprint - arXiv:2405.12717 - 11 pages

  • Real projective groups are formal pdf (with Ambrus Pál)
    preprint - arXiv:2206.14645 - 38 pages

  • Making the motivic group structure on the endomorphisms of the projective line explicit pdf
    (with Viktor Balch Barth, William Hornslien and Glen M. Wilson)
    Advances in Mathematics 461 (2025) Paper No. 110080 - 65 pages

  • On the cokernel of the Thom morphism for compact Lie groups pdf (with Eiolf Kaspersen)
    accepted for publication in Homology, Homotopy and Applications - 30 pages

  • Geometric pushforward in Hodge filtered complex cobordism and secondary invariants pdf (with Knut Bjarte Haus)
    Documenta Mathematica 29 (2024), 457–509

  • A note on Real line bundles with connection and Real smooth Deligne cohomology pdf
    (with Peter Marius Flydal and Eirik Eik Svanes) - Acta Mathematica Vietnamica 49 (2024) 187–199

  • Formality and strong Massey vanishing for real projective groups pdf (with Ambrus Pál)
    Oberwolfach Reports 20 (2023), no. 3

  • Geometric Hodge filtered complex cobordism pdf (with Knut Bjarte Haus)
    Advances in Mathematics 431 (2023), Paper No. 109244, 58 pages

  • Representability of the local motivic Brouwer degree pdf (with Therese Strand and Glen M. Wilson)
    Mathematica Scandinavica 128 (2022), 54–77

  • Examples of non-algebraic classes in the Brown-Peterson tower pdf
    Mathematische Zeitschrift 293 (2019), 25–37

  • Unstable splittings in Hodge filtered Brown-Peterson cohomology pdf
    Journal of Homotopy and Related Structures 14 (2019), 349–369

  • Algebraic cycles in generalized cohomology theories (with Michael J. Hopkins)
    Oberwolfach Reports vol. 15 (2018), no. 2

  • An Abel-Jacobi invariant for cobordant cycles pdf
    Documenta Mathematica 21 (2016), 1645–1668

  • Profinite and discrete G-spectra and iterated homotopy fixed points pdf (with Daniel G. Davis)
    Algebraic & Geometric Topology 16 (2016), 2257–2303

  • Existence of rational points as a homotopy limit problem pdf
    Journal of Pure and Applied Algebra 219 (2015), 3466–3481

  • Hodge filtered complex bordism pdf (with Michael J. Hopkins)
    Journal of Topology 8 (2015), 147–183

  • Homotopy theory of smooth compactifications of algebraic varieties pdf
    New York Journal of Mathematics 19 (2013), 533–544

  • Continuous homotopy fixed points for Lubin-Tate spectra pdf
    Homology, Homotopy and Applications 15 (2013), 191–222

  • Profinite G-spectra pdf
    Homology, Homotopy and Applications 15 (2013), 151–189

  • Some remarks on profinite completion of spaces pdf
    Galois-Teichmüller theory and Arithmetic Geometry (Hiroaki Nakamura, Florian Pop, Leila Schneps, and Akio Tamagawa, eds.), Advanced Studies in Pure Mathematics, vol. 63, Mathematical Society of Japan, 2012, pp. 413–448

  • Torsion algebraic cycles and étale cobordism pdf
    Advances in Mathematics 227 (2011), 962–985

  • Continuous group actions on profinite spaces corrected version
    Journal of Pure and Applied Algebra 215 (2011), 1024–1039

  • Profinite homotopy theory pdf
    Documenta Mathematica 13 (2008), 585–612

  • Stable étale realization and étale cobordism pdf
    Advances in Mathematics 214 (2007), 730–760

Editorial Work

  • Nils A. Baas, Gunnar E. Carlsson, Gereon Quick, Markus Szymik, Marius Thaule (as editors):
    Topological Data Analysis - The Abel Symposium 2018
    Abel Symposia, volume 15, Springer-Verlag 2020 - Preface to the book

  • Eric M. Friedlander, Gereon Quick, Paul Arne Østvær (as special editors):
    Special Issue on motivic A1-homotopy theory
    Journal of K-Theory, volume 7, issue 3, 2011 - Preface to the special issue

Other writing

  • Mixed Hodge structure on \(\pi_1\) (with Gabriel Herz)
    Extended abstract - Arbeitsgemeinschaft mit aktuellem Thema: Polylogarithms
    Oberwolfach Reports vol. 1, no. 4 (2004), 2551–2553