FB 6 Mathematik/Informatik/Physik

Institut für Mathematik

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Geometric Deep Learning




Fundamentals of geometric aspects in machine learning (e.g. invariance, equivariance, multi-scale structure). Overview over representational options (e.g. point clouds, grids, meshes, implicits, parametrics) and corresponding challenges together with advanced technical approaches to learning over and learning of geometric data, in particular 3D objects and scenes. Basic concepts involved in this context include artificial neural networks, convolution, pooling, diffusion, continuous convolution, random walks, transformers, generative approaches. Case studies include shape classification, shape segmentation, shape correspondence, shape generation.

Weitere Angaben

Ort: 32/109
Zeiten: Di. 16:00 - 18:00 (wöchentlich) - Vorlesung, Mi. 14:00 - 16:00 (wöchentlich) - Vorlesung/Übung
Erster Termin: Dienstag, 02.04.2024 16:00 - 18:00, Ort: 32/109
Veranstaltungsart: Vorlesung und Seminar (Offizielle Lehrveranstaltungen)


  • Informatik > Master of Science in Informatik
  • Informatik > Vorlesungen
  • Mathematics/Computer Science

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. 2015

positively evaluated after 3 years of Juniorprofessorship

Since Oct. 2018Professor at the University of Osnabrück


  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 1-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.


  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.


  • 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''



  • 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


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


    • Maximilian Koall


    • 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


    • 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
    • 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