Homotopy Theory and Algebraic and Arithmetic Geometry
In more detail my research interests include: algebraic and étale cobordism; chromatic, profinite, étale and motivic homotopy theory; algebraic cycles; Deligne cohomology theories; anabelian geometry.
Publications and Preprints
Profinite and discrete G-spectra and iterated homotopy fixed points
with Daniel G. Davis - preprint - submitted - arXiv:1401.7150 - pdf
Existence of rational points as a homotopy limit problem
preprint - submitted - arXiv:1309.0463 - pdf
Homotopy theory of smooth compactifications of algebraic varieties
New York Journal of Mathematics 19 (2013) 533-544 - pdf
Hodge filtered complex bordism
with Michael J. Hopkins - preprint - submitted - arXiv:1212.2173 - pdf
Continuous homotopy fixed points for Lubin-Tate spectra
Homology, Homotopy and Applications 15 (2013) 191-222 - pdf
Profinite G-spectra
Homology, Homotopy and Applications 15 (2013) 151-189 - pdf
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 - pdf
Torsion algebraic cycles and étale cobordism
Advances in Mathematics 227 (2011) 962-985 - preprint
Continuous group actions on profinite spaces
Journal of Pure and Applied Algebra 215 (2011) 1024-1039 - preprint
Profinite homotopy theory
Documenta Mathematica 13 (2008) 585-612 - pdf
Stable étale realization and étale cobordism
Advances in Mathematics 214 (2007) 730-760 - pdf
Editorial work
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
Lecture Notes of a lecture series on étale homotopy theory in Heidelberg in March 2014:
Lecture 1: Motivation
Lecture 2: Constructions
Lecture 3: Applications
Homotopical Methods in Algebraic Geometry, May 28-June1, 2013 at University of Southern California, Los Angeles, organized by A. Asok, E. Friedlander, C. Haesemeyer, M. Walker, and C. Weibel.
University of Heidelberg: Workshop on Motivic and étale homotopy theory, March 2014: Abel-Jacobi maps and homotopy theory
University of Tokyo: International Workshop on Motives, November 2013: Algebraic cycles and cobordism
Université de Strasbourg: Séminaire Algèbre et Topologie, November 2013: Hodge filtered complex bordism
Institut de Mathématiques de Jussieu, Paris: Séminaire de géométrie algébrique de Jussieu, November 2013: Algebraic cycles and cobordism
USC Los Angeles: Conference on Homotopical Methods in Algebraic Geometry, May 2013: Generalized Deligne-Beilinson cohomology theories
Technical University of Munich: Seminar in Algebraic Geometry, January 2013: Hodge filtered complex bordism
University of Regensburg: GK-Kolloquium, January 2013: Hodge filtered complex bordism
Harvard University: Thursday Topology Seminar,
November 2012: The smooth cycle map in generalized Deligne cohomology
Imperial College London: Workshop on Arithmetic Geometry and Homotopy Theory,
May 2012: Existence of rational points as a homotopy limit problem
Wayne State University Detroit: Topology Seminar,
February 2012: Hodge filtered complex cobordism
University of Virginia: Topology Seminar,
October 2011: Hodge filtered complex cobordism
USC Los Angeles: Algebra Seminar,
August 2011: Algebraic cycles, étale cobordism and differential cohomology theories
University of Regensburg: Summer School on Rigidity theorems in A^{1}-homotopy theory, August 2011: Introduction to the A^{1}-homotopy category of Morel-Voevodsky
MIT: Topology Seminar,
May 2011: Homotopy fixed points of profinite spectra
University of Regensburg: Workshop on Arithmetic and Motivic Algebraic Geometry, February 2011: Galois actions on étale homotopy types
University of Tokyo: International Workshop on Motives, December 2010: Torsion algebraic cycles and étale cobordism
RIMS Kyoto University: RIMS Camp-style Seminar on Galois-theoretic Arithmetic Geometry, October 2010: Galois actions on étale homotopy types
University of Coimbra: GAeL XVIII, June 2010: Torsion algebraic cycles and étale cobordism
University of Essen: Algebraic Geometry Seminar, May 2010: Torsion algebraic cycles and étale cobordism
Alfred Renyi Institute of Mathematics Budapest: April 2010: Torsion algebraic cycles and étale cobordism
University of London Ontario: March 2010: Torsion algebraic cycles and étale cobordism
University of Heidelberg: PIA 2010 The arithmetic of
fundamental groups, February 2010: Torsion algebraic cycles and étale
cobordism
University of Regensburg: Colloquium in Arithmetic Geometry, December 2009: Torsion algebraic cycles and étale cobordism
MIT: Topology Seminar,
October 2009: Some applications of profinite homotopy theory
Short CV
01-06/2014: Research Associate and Lecturer at Harvard University
08-09/2013: Postdoctoral Fellow at Harvard University
06/2013: Habilitation in Mathematics at Math. Department, University of Münster
since 09/2012: Postdoctoral Fellow at Math. Department, University of Münster
10/2010-08/2012: Postdoctoral Fellow at Harvard University
02-03/2010: Visitor at the Institute for Advanced Study in Princeton
09-10/2009: Postdoctoral Fellow at Harvard University
09/2007: EU-Research Fellow at University of Tokyo
07/2005-09/2010: Postdoctoral Fellow at Math. Department, University of Münster
07/2005: PhD in Mathematics with a thesis on profinite étale
cobordism, advisor: Prof. Dr. C. Deninger
03/2004-06/2004: Marie Curie Fellowship, Institut Henri Poincaré in
Paris
10/2001-06/2005: Scientific assistant at Math. Department,
University of Münster
09/2000-06/2001: DEA des Méthodes algébriques, Université Pierre et Marie Curie in Paris, advisor: Prof. Dr. B. Kahn
10/1999-06/2000: Certificate of Advanced Study in Mathematics,
University of Cambridge, UK
10/1997-09/1999: Studies in Mathematics, Philosophy and Physics,
University of Heidelberg