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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
Sprechzeiten:

Lehrveranstaltungen

Sommersemester 2025

• Mathematische Software

Wintersemester 2024/25

• Mathematische Software
• Oberseminar Topologie
• Seminar Elemente der Mathematik (BEU)
• Topologie

Sommersemester 2024

• Elemente der Linearen Algebra (BEU)
• Lineare Algebra und analytische Geometrie II
• Mathematische Software
• Oberseminar Topologie

Daten ändern

Research Areas:

• Algebraic geometry 14-XX

• K-theory 19-XX

• Algebraic topology 55-XX

Education and employment

Publications

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. Röndigs, 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; K-Theory—Proceedings of the International Colloquium, Mumbai, 2016, 35–40, Hindustan Book Agency, New Delhi, 2018.
23. O. Röndigs, M. Spitzweck, P. A. Ostvaer: The first stable homotopy groups of motivic spheres; Ann. of Math. (2) 189 (2019), no. 1, 1–74. .
24. O. Röndigs, M. Spitzweck, P. A. Ostvaer: The motivic Hopf map solves the homotopy limit problem for K-theory; Doc. Math. 23 (2018), 1405–1424.
25. M. Spitzweck: A commutative ℙ¹-spectrum representing motivic cohomology over Dedekind domains; Mém. Soc. Math. Fr. (N.S.) No. 157 (2018), 110 pp.
26. M. Spitzweck:  Algebraic Cobordism in mixed characteristic; arXiv:1404.2542, to appear in HHA.

Submitted articles

1. J. Gutiérrez, O. Röndigs, M. Spitzweck, P. A. Ostvaer: On functorial (co)localization of algebras and modules over operads s; arXiv:1812.01715.
2. E. Elmanto, M. Levine, M. Spitzweck, P. A. Ostvaer: Algebraic Cobordism and Étale Cohomology, arXiv:1711.06258.

Preprints

1. H. Heine, M. Spitzweck, P. Verdugo: Real K-theory for Waldhausen infinity categories with genuine duality; arXiv: 1911.11682.
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. M. Spitzweck: Sheaves with transfers, model structures and spaces; 2000.
8. M. Spitzweck: Some Constructions for Voevodsky's Categories of Motives; 2000.

Grants

• DFG-Sachbeihilfe "Applying motivic filtrations" (mit Marc Levine und Oliver Röndigs) im DFG Schwerpunktprogramm 1786
• DFG-Sachbeihilfe "Operads in algebraic geometry and their realizations" (mit Jens Hornbostel,
  Oliver Röndigs und Manfred Stelzer) im DFG Schwerpunktprogramm 1786
• DFG Sachbeihilfe ``Operad structures in motivic homotopy theory'' im DFG Schwerpunktprogramm 1786 ``Homotopy theory and algebraic geometry'' (mit Oliver Röndigs)
• DFG Sachbeihilfe ``Motivic filtrations over Dedekind domains'' im DFG Schwerpunktprogramm 1786 ``Homotopy theory and algebraic geometry'' (mit Marc Levine und Oliver Röndigs)
• DFG Graduiertenkolleg 1916 ``Combinatorial structures in geometry''

Supervision

PhD

• 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, Titel: Restricted L_∞-algebra

Master

• Alexander Poddubny, Masterarbeit über ``Ring spectra and cohomology operations''
• Johannes Bensmann, Masterarbeit über ``Vergleich zweier Modelkategorien von Spektren über einen topologischen Raum''

current:

• Maximilian Koall

Bachelor

• Carl Wanninger, Thema: Das Barr-Beck-Theorem in der Kategorientheorie
• Lukas Freudenberg, Thema: The inverse Galois-Problem - discussing different partial solutions
• Jan-Luca Spellmann, Thema: Lokale Klassenkörpertheorie und der Satz von Kronecker-Weber

Talks:

• 06.07.2001: Kolloquium Osnabrück, ``E<sub>∞</sub>-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<sub>∞</sub>-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<sub>∞</sub>-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
• 29.05.2018: Vortrag: ``Motivic Landweber exact theories and etale cohomology'', Topology Meeting at the University of Oslo
• 29.06.2018: Vortrag ``Hermitian K-theory for infinity categories with genuine duality'', Homotopy Theory Summer Berlin 2018
• 06.07.2018: Vortrag ``Hermitian K-theory for Waldhausen infinity categories with genuine duality'', Isaac Newton Institute Cambridge
• 26.07.2018: Vortrag ``Landweber Exact Theories and Etale Cohomology'', Workshop Motives and Algebraic Cycles, FRIAS Freiburg