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Institut für Mathematik

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Prof. Dr. rer. nat. Markus Spitzweck

Institut für Mathematik

Albrechtstr. 28a
49076 Osnabrück

Raum: 69/222
Telefon: +49 541 969 2555
Fax: +49 541 969 2770
E-Mail: markus.spitzweck@uni-osnabrueck.de
Homepage: http://www.mathematik.uni-osnabrueck.de/spitzweck
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Research Areas:

  • Algebraic geometry 14-XX

  • K-theory 19-XX

  • Algebraic topology 55-XX

Education and employment

Feb. 1999Diplom in Mathematics, Universität Bonn
March 1999 - Sept. 1999Research position in Cambridge/GB
Oct. 1999 - Nov. 1999Research position at IAS Princeton
Jan. 2000 - Dec. 2001Assistent position Universität Bonn
Jan. 2002 - Dec. 2002Scholarship holder at MPIM Bonn
Aug. 2003Ph.D. in Mathematics, Universität Bonn (Advisor: Prof. Dr. Günter Harder)
Oct. 2003 - Sept. 2007Assistent position Universität Göttingen
Oct. 2007 - Sept. 2009DFG-position Universität Regensburg with Prof. Ulrich Bunke
Oct. 2009 - March 2011Post-Doc position University Oslo
Apr. 2011 -- Aug. 2011 W3-Substitute Professor Universität Regensburg
Sept. 2011 - Sept. 2012Assistent position Universität Regensburg
Since Oct. 2012Juniorprofessor at the Universität Osnabrück 
Sept. 2015positively evaluated after 3 years of Juniorprofessorship


  1. M. Spitzweck:  Motivic approach to limit sheaves; Geometric Methods in Algebra and Number Theory, Band 235 von Progr. Math., Birkhäuser, Boston, MA, 2005.
  2. M. Spitzweck: S-modules; Rep. No. 46/2005 für Arbeitsgemeinschaft mit aktuellem Thema: Modern Foundations for Stable Homotopy Theory.
  3. M. Spitzweck: The FHT-Theorem I; Rep. No. 46/2006 für Arbeitsgemeinschaft mit aktuellem Thema: Twisted K-Theory.
  4. U. Bunke, T. Schick, M. Spitzweck and A. Thom: Duality for topological abelian group stacks and T-duality; Proceedings of the International Conference on K-theory and Non-commutative Geometry, Valladolid, 2006.
  5. U. Bunke, T. Schick and M. Spitzweck: Sheaf theory for stacks in manifolds and twisted cohomology for S1-gerbes; Alg. Geom. Topol., 7, 2007.
  6. N. Hoffmann and M. Spitzweck: Homological algebra with locally compact abelian groups; Adv. Math., 212(2), 2007.
  7. U. Bunke, T. Schick and M. Spitzweck: Inertia and delocalized twisted cohomology; Homology, Homotopy Appl., 10(1), 2008.
  8. N: Naumann, M. Spitzweck, P.A. Ostvaer: Chern classes, K-theory and Landweber exactness over nonregular base schemes; Proceedings of the conference on Motives and Algebraic Cycles: A Conference Dedicated to the Mathematical Heritage of Spencer J. Bloch (Edited by Rob de Jeu and James D. Lewis), 2008.
  9. U. Bunke, M. Spitzweck, T. Schick: Periodic twisted cohomology and T-dualit}; Astérisque 337, 2011.
  10. M. Spitzweck, P.A. Ostvaer: The Bott inverted infinite projective space is homotopy algebraic K-theory; Bull. Lond. Math. Soc., 41(2), 2009.
  11. M. Spitzweck, P.A. Ostvaer: A Bott inverted model for equivariant unitary topological K-theory; Math. Scand. 106(2), 2010.
  12. M. Spitzweck: Homotopy limits of model categories over inverse index categories,  J. Pure Appl. Algebra  214  (2010),  no. 6, 769--777.
  13. N. Naumann, M. Spitzweck,  P.A. Ostvaer: Motivic Landweber Exactness; Doc. Math.  14  (2009), 551--593.
  14. O. R\"ondigs, M: Spitzweck, P.A. Ostvaer: Motivic strict ring models for K-theory; Proc. Amer. Math. Soc. 138 (2010).
  15. M. Spitzweck: Slices of motivic Landweber spectra; Journal of K-theory, February 2012 - Volume 9, Issue 01, pp 103-117.
  16. M. Spitzweck: Relations between slices and quotients of the algebraic cobordism spectrum; Homology, Homotopy Appl. 12(2), 2010.
  17. M. Spitzweck, Ostvaer: Universality of mod-p cohomology; Topology Appl. 157(18), 2010.
  18. N. Naumann, M. Spitzweck: Brown representability in A1-homotopy theory; J. K-Theory 7(3), 2011.
  19. M. Spitzweck, P.A. Ostvaer: Motivic twisted K-theory; Algebraic & Geometric Topology 12 (2012) 565-599.
  20. J. Gutiérrez, O. Röndigs, M. Spitzweck, P. A. Ostvaer: Motivic slices and coloured operads; J. Topology, 5(3):727-755, 2012.  
  21. N. Naumann, M. Spitzweck, P.A. Ostvaer: Existence and uniqueness of E structures on motivic K-theory spectra;  J. Homotopy Relat. Struct. 10 (2015), no. 3, 333–-346.
  22. O. Röndigs, M. Spitzweck, P. A. Ostvaer: Cellularity of hermitian K-theory and Witt theory; will appear in Proceedings of the International Colloquium at TIFR held in January, Chief Editor Ravi A. Rao, 2016

Submitted articles

  1. O. Röndigs, M. Spitzweck, P. A. Ostvaer:  The first stable homotopy groups of motivic spheres; arXiv:1604.00365.
  2. O. Röndigs, M. Spitzweck, P. A. Ostvaer: The motivic Hopf map solves the homotopy limit problem for K-theory; arXiv:1701.06144.
  3. M. Spitzweck: A commutative 1-spectrum representing motivic cohomology over Dedekind domains; arXiv:1207.4078.


  1. M. Spitzweck:  Algebraic Cobordism in mixed characteristic; arXiv:1404.2542.
  2. M. Spitzweck:  A Grothendieck-Witt space for stable infinity categories with duality;  arXiv:1610.10044.
  3. H. Heine, A. Lopez-Avila, M. Spitzweck: Infinity categories with duality and hermitian multiplicative infinite loop space machines; arXiv:1610.10043.
  4. M. Spitzweck: Derived Fundamental Groups for Tate Motives; arXiv:1005.2670.
  5. M. Spitzweck: Periodizable motivic ring spectra; arXiv:0907.1510.
  6. M. Spitzweck: Another viewpoint on J-spaces; arXiv:1012.1264.
  7. J. Gutiérrez, O. Röndigs, M. Spitzweck, P. A. Ostvaer: Colocalization of algebras; 2010.
  8. M. Spitzweck: Sheaves with transfers, model structures and spaces; 2000.
  9. M. Spitzweck: Some Constructions for Voevodsky's Categories of Motives; 2000.


  • DFG graduate school ``Combinatorial structures in geometry''  (together with seven colleagues from Osnabr\ück, 2 postdocs and 8 Ph.D.  positions for 4.5 - 9 years)
  • Grants for 2 projects within the DFG-Priority Program 1786 ``Homotopy Theory and Algebraic Geometry'' (one with Prof. Marc Levine and Prof. Oliver Röndigs, one with Prof. Oliver Röndigs); the grants include two Post-Doc positions and one PhD position



  • Peter Arndt, Titel: Abstract motivic homotopy theory
  • Hongyi Chu, Titel: Enriched Infinity Operads
  • Alejo Lopez, Titel: E-ring structures in motivic hermitian K-theory


  • Hadrian Heine, Arbeitsgebiet: unendlichkategorielle Versionen von Liealgebren und deren Bedeutung für die Beschreibung von Homotopietypen und Deformationstheorie
  • Paula Verdugo: Arbeitsgebiet: Hermitesche K-Theorie für Unendlichkategorien


    • Alexander Poddubny, Masterarbeit über ``Ring spectra and cohomology operations''


    • Johannes Bensmann, Thema: Das Cup-Produkt mithilfe des Eilenberg-Zilber Theorems
    • Carl Wanninger, Thema: Das Barr-Beck-Theorem in der Kategorientheorie


    • Lukas Freudenberg, Thema: Einige Fälle des inversen Galois-Problems


    • 06.07.2001: Kolloquium Osnabrück, ``E-Algebren und Limesmotive''
    • 14.03.2002: Mathematisches Kolloquium der Universität Wien, ``Anwendungen von E-Algebren inder algebraischen Geometrie''
    • 09.04.2002: MPI Bonn, Seminar on Algebra, Geometry and Physics, ``E-algebras in model categories and applications''
    • 18.12.2003: University Miami, Winter School, Vortrag über ein ausgewähltes Thema meiner Doktorarbeit
    • 28.05.2004: Workshop: Motivic Homotopy Theory, Institut Henri Poincaré (Paris) ``The Hodge theoretic realization of certain limit motives''
    • 26.11.2004: Jacobs University Bremen, ``Motives and homotopy theory''
    • 04.10.2005: Arbeitsgemeinschaft Oberwolfach, ``S-modules''
    • 06.09.2006: Topological Algebraic Geometry Workshop Oslo, ``Statements and conjectures in derived Tannakian duality''
    • 13.09.2006: Stockholm, KTH, ``Some special cases of derived Tannakian Duality''
    • 13.10.2006: Arbeitsgemeinschaft Oberwolfach, ``The FHT-THeorem I''
    • 08.11.2006: Topology Seminar Oslo, ``2-periodic cohomology and T-duality''
    • 17.05.2007: Fields Institute Toronto, Workshop on Stacks in Geometry and Topology, ``Integral derived fundamental groups for Tate motives''
    • 15.11.2007: Göttingen, Kolloquium des Graduiertenkollegs Gruppen und Geometrie, ``Das Theorem von Snaith in der stabilen A1-Homotopietheorie''
    • 15.04.2008: München, Oberseminar Geometrie, ``Motivic cohomology theories''
    • 18.04.2008: München, gemeinsames Seminar Seminar München/Regensburg, ``Landweber exact spectra for motivic homotopy''
    • 29.04.2008: Universität Bonn, ``Slices of motivic Landweber spectra''
    • 30.07.2009: Workshop Münster ``Motivic Homotopy Theory'', ``Slices and Landweber spectra''
    • 24.11.2009: Topology Seminar Oslo, ``The motivic slice filtration and Landwweber spectra''
    • 10.01.2010: Copenhagen Topology Conference, ``The rational motivic operad of framed open genus 0 moduli spaces''
    • 27.01.2010: Topology Seminar Oslo, ``The motivic spectra P(n) and applications''
    • 23.02.2010: Workshop in Sion über T-Dualität, ``T-Dualitätstripel aus homologischer Sicht''
    • 17.03.2010: Topology Seminar Oslo, ``Extensions in stable -categories''
    • 24.03.2010: Topology Seminar Oslo, ``T-duality triples from homological algebra''
    • 11.06.2010: Topology Symposium Bergen, ``Derived motivic fundamental groups''
    • 06.07.2010: Universität Barcelona, ``Motivic Twisted K-Theory''
    • 02.12.2010: National Topology Symposium Fredrikstad, ``Motivic Twisted K-Theory''
    • 27.04.2011: Kolloquium Osnabrück, ``E-Structures on Motivic Spectra''
    • 04.05.2011: Münster, ``E-Strukturen auf algebraischer K-Theorie''
    • 16.05.2011: Universität Zürich, ``Strict ring models for hermitian K-theory''
    • 3./4.8.2011: Summer School on Rigidity and the Conjecture of Friedlander and Milnor, Regensburg, ``The unstable connectivity theorem I/II''
    • 02.11.2011: Regensburg, ``On the motivic Eilenberg-MacLane spectrum in mixed characteristic''
    • 15.11.2011: Universität Toulouse, ``On the motivic Eilenberg-MacLane spectrum in mixed characteristic''
    • 25.11.2011: Topology Seminar Oslo, ``On the motivic Eilenberg-MacLane spectrum in mixed characteristic''
    • 16./30.10.2012: Osnabrück, ``A motivic Eilenberg-MacLane Spectrum in the arithmetic case I/II''
    • 19.12.2012: Bielefeld, Oberseminar Geometrie und Topologie, ``From homotopy theory to motives''
    • 19.03.2013: Workshop ``Grothendieck-Teichmüller Groups, Deformation and Operads'', Isaac Newton Institute Cambridge, ``The abelian category of mixed Tate motives with integer coefficients''
    • 02.09.2013: Regensburg Graduiertenkolleg, ``Motives for arbitrary schemes''
    • 06.09.1013: Oslo University, ``Motives for arbitrary schemes''
    • 19.09.2013: Purdue University, ``Motives for arbitrary schemes''
    • 09.10.2013: UCLA, Algebra Seminar, ``Triangulated Categories of Motives over General Base Schemes''
    • 25./26. 11. 2013: International Workshop on motives in Tokyo, 2013, Vorträge ``Triangulated Categories of Motives I/II''
    • 25.03.2014: Workshop ``Étale and motivic homotopy theory'', Heidelberg,``Triangulated categories of motives over general base schemes''
    • 17.04.2014: SFB-Kolloquium Regensburg, ``Motivic cohomology and algebraic cobordism in mixed characteristic''
    • 29.04.2014: Toulouse, ``Motivic cohomology and algebraic cobordism in mixed characteristic''
    • 04.06.2014: Workshop ``Motivic Homotopy Groups of Spheres'', Essen, ``Algebraic cobordism in mixed characteristic''
    • 5.12.2014: Vorstellungsvortrag für eine W3-Stelle in Regensburg,``From étale to motivic cohomology''
    • 25.09.2015: DMV-Jahrestagung in Hamburg, Minisymposium, ``Integral Tate Motives and Fundamental Groups''
    • 04.02.2016: Universität Freiburg, ``Mixed Tate Motives''
    • 18.03.2016: Closing Conference for the Program on Higher Structures in Geometry and Physics, MPIM Bonn, ``Hermitian multiplicative infinite loop space machines''
    • 22.04.2016: 25th NRW Topology Meeting in Essen, ``Direct sum hermitian K-theory of infinity categories with duality''
    • 21.06.2016: Workshop on motivic homotopy groups of spheres II, Essen,``The slice tower of the motivic sphere spectrum''
    • 14.-16.9.2016: 3-teiliger Minikurs über ``Mixed Tate motives and fundamental groups'' auf Workshop ``Interactions between operads and motives'', HIM Bonn
    • 10.11.2016: Vortrag ``A Grothendieck-Witt space for stable infinity categories with duality'' auf Workshop ``Hermitian K-theory and trace methods'', HIM Bonn
    • 5.12.-9.12.2016: 3-teilige Vortragsreihe über ``Hermitian K-theory for infinity categories with duality'', Winter School on Bordism, L-theory, and Real Algebraic K-theory, Kastell Windsor
    • 27.02.2017: Vortrag ``Hermitian K-theory for stable infinity categories with duality'', KTH Stockholm
    • 28.02.2017: Vortrag ``Hermitian K-theory for stable infinity categories with duality'', Mittag-Leffler-Institut Stockholm