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Matheus Fellype Ferraz, M. Sc.
Institut für Mathematik Albrechtstraße 28a 49076 Osnabrück |
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Raum: | 50/603 |
Telefon: | +49 541 969-2476 |
Fax: | +49 541 969-2799 |
E-Mail: | matheus.ferraz@uni-osnabrueck.de |
Homepage: | |
Sprechzeiten: | n.V. |
Lehrveranstaltungen
Wintersemester 2024/25
Sommersemester 2024
Research Areas:
Algebraic geometry 14-XX
K-theory 19-XX
Algebraic topology 55-XX
Education and employment
Feb. 1999 | Diplom in Mathematics, Universität Bonn |
March 1999 - Sept. 1999 | Research position in Cambridge/GB |
Oct. 1999 - Nov. 1999 | Research position at IAS Princeton |
Jan. 2000 - Dec. 2001 | Assistent position Universität Bonn |
Jan. 2002 - Dec. 2002 | Scholarship holder at MPIM Bonn |
Aug. 2003 | Ph.D. in Mathematics, Universität Bonn (Advisor: Prof. Dr. Günter Harder) |
Oct. 2003 - Sept. 2007 | Assistent position Universität Göttingen |
Oct. 2007 - Sept. 2009 | DFG-position Universität Regensburg with Prof. Ulrich Bunke |
Oct. 2009 - March 2011 | Post-Doc position University Oslo |
Apr. 2011 -- Aug. 2011 | W3-Substitute Professor Universität Regensburg |
Sept. 2011 - Sept. 2012 | Assistent position Universität Regensburg |
Since Oct. 2012 | Juniorprofessor at the Universität Osnabrück |
Sept. 2015 | positively evaluated after 3 years of Juniorprofessorship |
Since Oct. 2018 | Professor at the University of Osnabrück |
Publications
- M. Spitzweck: Motivic approach to limit sheaves; Geometric Methods in Algebra and Number Theory, Band 235 von Progr. Math., Birkhäuser, Boston, MA, 2005.
- M. Spitzweck: S-modules; Rep. No. 46/2005 für Arbeitsgemeinschaft mit aktuellem Thema: Modern Foundations for Stable Homotopy Theory.
- M. Spitzweck: The FHT-Theorem I; Rep. No. 46/2006 für Arbeitsgemeinschaft mit aktuellem Thema: Twisted K-Theory.
- 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.
- U. Bunke, T. Schick and M. Spitzweck: Sheaf theory for stacks in manifolds and twisted cohomology for S1-gerbes; Alg. Geom. Topol., 7, 2007.
- N. Hoffmann and M. Spitzweck: Homological algebra with locally compact abelian groups; Adv. Math., 212(2), 2007.
- U. Bunke, T. Schick and M. Spitzweck: Inertia and delocalized twisted cohomology; Homology, Homotopy Appl., 10(1), 2008.
- 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.
- U. Bunke, M. Spitzweck, T. Schick: Periodic twisted cohomology and T-dualit}; Astérisque 337, 2011.
- M. Spitzweck, P.A. Ostvaer: The Bott inverted infinite projective space is homotopy algebraic K-theory; Bull. Lond. Math. Soc., 41(2), 2009.
- M. Spitzweck, P.A. Ostvaer: A Bott inverted model for equivariant unitary topological K-theory; Math. Scand. 106(2), 2010.
- M. Spitzweck: Homotopy limits of model categories over inverse index categories, J. Pure Appl. Algebra 214 (2010), no. 6, 769--777.
- N. Naumann, M. Spitzweck, P.A. Ostvaer: Motivic Landweber Exactness; Doc. Math. 14 (2009), 551--593.
- O. Röndigs, M: Spitzweck, P.A. Ostvaer: Motivic strict ring models for K-theory; Proc. Amer. Math. Soc. 138 (2010).
- M. Spitzweck: Slices of motivic Landweber spectra; Journal of K-theory, February 2012 - Volume 9, Issue 01, pp 103-117.
- M. Spitzweck: Relations between slices and quotients of the algebraic cobordism spectrum; Homology, Homotopy Appl. 12(2), 2010.
- M. Spitzweck, Ostvaer: Universality of mod-p cohomology; Topology Appl. 157(18), 2010.
- N. Naumann, M. Spitzweck: Brown representability in A1-homotopy theory; J. K-Theory 7(3), 2011.
- M. Spitzweck, P.A. Ostvaer: Motivic twisted K-theory; Algebraic & Geometric Topology 12 (2012) 565-599.
- J. Gutiérrez, O. Röndigs, M. Spitzweck, P. A. Ostvaer: Motivic slices and coloured operads; J. Topology, 5(3):727-755, 2012.
- 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.
- 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.
- 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. .
- 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.
- M. Spitzweck: A commutative ℙ1-spectrum representing motivic cohomology over Dedekind domains; Mém. Soc. Math. Fr. (N.S.) No. 157 (2018), 110 pp.
- M. Spitzweck: Algebraic Cobordism in mixed characteristic; arXiv:1404.2542, to appear in HHA.
Submitted articles
- J. Gutiérrez, O. Röndigs, M. Spitzweck, P. A. Ostvaer: On functorial (co)localization of algebras and modules over operads s; arXiv:1812.01715.
- E. Elmanto, M. Levine, M. Spitzweck, P. A. Ostvaer: Algebraic Cobordism and Étale Cohomology, arXiv:1711.06258.
Preprints
- H. Heine, M. Spitzweck, P. Verdugo: Real K-theory for Waldhausen infinity categories with genuine duality; arXiv: 1911.11682.
- M. Spitzweck: A Grothendieck-Witt space for stable infinity categories with duality; arXiv:1610.10044.
- H. Heine, A. Lopez-Avila, M. Spitzweck: Infinity categories with duality and hermitian multiplicative infinite loop space machines; arXiv:1610.10043.
- M. Spitzweck: Derived Fundamental Groups for Tate Motives; arXiv:1005.2670.
- M. Spitzweck: Periodizable motivic ring spectra; arXiv:0907.1510.
- M. Spitzweck: Another viewpoint on J-spaces; arXiv:1012.1264.
- M. Spitzweck: Sheaves with transfers, model structures and spaces; 2000.
- 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∞-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