## Gereon QuickMailing address:Department of Mathematical Sciences Norwegian University of Science and Technology 7491 Trondheim NORWAY Office: 1246 in Sentralbygg 2 Gløshaugen in Trondheim Tel: +47 735 50287 Email: gereon.quick (at) ntnu.no |

I am an Associate Professor in the Department of Mathematical Sciences and member of the Geometry and Topology Group at NTNU.

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 activities are 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.

**Examples of non-algebraic classes in the Brown-Peterson tower**

preprint - arXiv:1611.09136

**Unstable splittings in Hodge filtered Brown-Peterson cohomology**

preprint - arXiv:1610.07912

**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

**Hodge filtered complex bordism**(with Michael J. Hopkins)

Journal of Topology 8 (2015) 147-183

**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

- E. M. Friedlander, P. A. Østvær, G. Quick (as special editors):

**Special Issue on motivic A**^{1}-homotopy theory

Journal of K-Theory, Volume 7, Issue 3, 2011

- Slides of a talk in Berlin in November 2017: Examples of non-algebraic classes in the Brown-Peterson tower

- Slides of a talk in Paris in September 2017: On detecting algebraic classes in generalised cohomology theories

- Slides of a talk at Institut Mittag-Leffler in April 2017: Examples of non-algebraic classes in the Brown-Peterson tower

- Slides of a talk at the Chern Institute in July 2016: From rational points to homotopy fixed points

- Slides of a talk in Paris in May 2016: Generalized Deligne-Beilinson cohomology and regulators

- Slides of a talk in Stockholm in March 2016: On topological invariants for algebraic cobordism

- Notes of a lecture series on étale homotopy theory in Heidelberg in March 2014:

Lecture 1: Motivation

Lecture 2: Constructions

Lecture 3: Applications