My research is mainly focused on homotopy theory and its applications in algebraic and arithmetic geometry. For more information, please see my research articles and notes from talks and lecture series below.
My research is supported by the project Motivic Hopf equations financed by the Research Council of Norway. I am also associated to the DFG-Priority Program 1786 Homotopy Theory and Algebraic Geometry. Previously, my research was supported by the German Research Foundation (DFG) in project QU 317/1.
If you are interested in working on a project which may lead to a Bachelor or Master Theses or if you would like to work on a StudForsk-Project, I would be very happy to talk to you. You find some suggestions for possible topics here. Please contact me for more information.
Since 2020 I am the study adviser (studieveileder) for the Bachelor (3 year) and Master (2 year) programs in Mathematics at NTNU. Please contact me if you need any academic advice on how to navigate through these study programs.
Publications, Preprints, Notes
Examples of non-algebraic classes in the Brown-Peterson tower
Mathematische Zeitschrift 293 (2019) 25-37
Unstable splittings in Hodge filtered Brown-Peterson cohomology
Journal of Homotopy and Related Structures 14 (2019)
349-369
An Abel-Jacobi invariant for cobordant cycles
Documenta Mathematica 21 (2016) 1645-1668
Profinite and discrete G-spectra and iterated homotopy fixed points (with Daniel G. Davis)
Algebraic & Geometric Topology 16 (2016) 2257-2303
Existence of rational points as a homotopy limit problem
Journal of Pure and Applied Algebra 219 (2015) 3466-3481
Homotopy theory of smooth compactifications of algebraic varieties
New York Journal of Mathematics 19 (2013) 533-544
Continuous homotopy fixed points for Lubin-Tate spectra
Homology, Homotopy and Applications 15 (2013) 191-222
Profinite G-spectra
Homology, Homotopy and Applications 15 (2013) 151-189
Some remarks on profinite completion of spaces 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
Advances in Mathematics 227 (2011) 962-985
Continuous group actions on profinite spaces
Journal of Pure and Applied Algebra 215 (2011) 1024-1039 - updated version
Profinite homotopy theory
Documenta Mathematica 13 (2008) 585-612
Stable étale realization and étale cobordism
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
to appear in Springer - Book Series Abel Symposia
Eric M. Friedlander, Paul Arne Østvær, Gereon Quick (as special editors): Special Issue on motivic A^{1}-homotopy theory
Journal of K-Theory, Volume 7, Issue 3, 2011