Matthias Wendt

Fakultät für Mathematik und Naturwissenschaften
Fachgruppe Mathematik und Informatik
Bergische Universität Wuppertal
Gaußstraße 20
42119 Wuppertal
Raum: G.15.13
Telefon: ++ (49)(202) 439-2528
Fax: ++ (49)(202) 439-3135
e-mail: last name (paste relevant symbol here) math.uni-wuppertal.de

Sekretariat (bis 13:00 Uhr):
Gabriele Birkenfeld
Raum: G.15.24
Telefon: ++ (49)(202) 439-3553

Sprechstunde: nach Vereinbarung

Lehre

Veranstaltungen im Wintersemester 2024/25

Vorlesung Topologie 1 (Mathematik MSc)
Mittwoch 10-12, Raum I.13.70, und Freitag 10-12, Raum G.15.20
Übungsgruppe Freitag 14-16 Uhr, Raum G.10.05 (Hörsaal 7)
Erste Vorlesung ist am 9. Oktober 2024.
Für die Veranstaltung gibt es einen Moodle-Kurs, bitte tragen Sie sich dort ein. Link zum Moodle-Kurs

Skripte

Topologie I+II (Version vom 16.07.2020)
Analysis auf Mannigfaltigkeiten (Version vom 16.07.2020)
Algebraische Zahlentheorie (WS 2011/12 in Freiburg)

Archiv und Ausblick Lehre der Arbeitsgruppe Topologie

Oberseminar Algebra und Topologie am Mittwoch 16:30-17:30, Raum F.13.11.

Research, publications and preprints:

My research interests include motivic homotopy theory, in particular homotopy of algebraic groups and torsor classification, computations of group homology for linear groups relevant for K-theory (in particular of elliptic curves), and the theory of motives (as applied to number theory or to geometric representation theory). At this point, my favourite questions revolve around the relations between motivic cohomology, group homology and scissors congruences in Hilbert's third problem.

Lately, I've been studying Witt-sheaf cohomology of classifying spaces, its connection with representations and torsor classification.

Lectures on motivic cohomology, group homology and scissors congruences at the Euler Institute, St. Petersburg, September 2018.

I sometimes post questions or answers on MathOverflow, see my profile.

Preprints and notes

4-torsion classes in the integral cohomology of oriented Grassmannians. (with Ákos K. Matszangosz). Preprint, arXiv:2403.06897
Chow--Witt rings and topology of flag varieties. (with Ákos K. Matszangosz and Thomas B. Hudson). Preprint, arXiv:2302.11003
On motivic obstructions to Witt cancellation over schemes. Preprint, arXiv:1810.04228, 28pp., submitted.
Equivariant motives and geometric representation theory. (with Wolfgang Soergel and Rahbar Virk, includes an appendix with Fritz Hörmann) Preprint, arXiv:1809.05480, 198pp., under revision.
On the cohomology of GL₃ of elliptic curves and Quillen's conjecture. Preprint, arXiv:1609.08278v1, 50pp., under revision.
Homology of GL₃ over elliptic curves. Note, arXiv:1501.02613.
Units in Grothendieck-Witt rings and A¹-spherical fibrations. Note, arXiv:1304.5922. (largely superseded by Tom Bachmann's paper Some remarks on units in Grothendieck-Witt rings)
More examples of motivic cell structures. Note, arXiv:1012.0454.

Oriented Grassmannians

The mod 2 cohomology rings of oriented Grassmannians via Koszul complexes (with Ákos Matszangosz). Math. Z. 308, 2 (2024), doi:10.1007/s00209-024-03556-y via Springer Link, arXiv:2310.11129.

Chow--Witt characteristic classes

Chow--Witt rings of Grassmannians. Algebr. Geom. Topol. 24 (1), 2024, pp. 1-48, doi:10.2140/agt.2024.24.1, arxiv:1805.06142
The real cycle class map (with Jens Hornbostel, Heng Xie and Marcus Zibrowius). Ann. K-Theory 6-2, 2021, pp. 239-317, arXiv:1911.04150
Oriented Schubert calculus in Chow--Witt rings of Grassmannians. In: Motivic homotopy theory and refined enumerative geometry. F. Binda, M. Levine, M.T. Nguyen und O. Röndigs, eds., Contemporary Math. 745 (2020), pp. 217-267, arXiv:1808.07296v1.
Chow--Witt rings of classifying spaces of symplectic and special linear groups. (with Jens Hornbostel) J. Topol. 12 (3), 2019, pp. 915--965, arXiv:1703.05362v2.

Geometric representation theory

Perverse motives and graded derived category O. (with Wolfgang Soergel) J. Inst. Math. Jussieu 17 (2), 2018, pp. 347--395, arXiv:1404.6333.

Group homology and K-theory

On Farrell--Tate cohomology of GL₃ over rings of quadratic integers. (with Bui Anh Tuan and Alexander D. Rahm) J. Algebra (Computational Section), 615, 2023, pp. 328-357, arXiv:2001.04277
The Farrell--Tate and Bredon homology for PSL₄(Z) via rigid facets subdivision. (with Bui Anh Tuan and Alexander D. Rahm) J. Pure Appl. Alg. 223 (7), 2019, pp. 2872--2888, arXiv:1611.06099v2.
On Farrell--Tate cohomology of SL₂ over S-integers. (with Alexander D. Rahm) J. Algebra 512, 2018, 427--464, arXiv:1411.3542v2.
Homology of SL₂ over function fields I: parabolic subcomplexes. J. Reine Angew. Math. 739, 2018, pp. 159--205, arXiv:1404.5825v1.
A refinement of a conjecture of Quillen. (with Alexander D. Rahm) C. R. Math. Acad. Sci. Paris 353 (9), 2015, pp. 779--784.
On third homology of SL₂ and weak homotopy invariance. (with Kevin Hutchinson) Trans. Amer. Math. Soc. 367 (10), 2015, pp. 7481--7513, arXiv:1307.3069
On homology of linear groups over k[t]. Math. Res. Lett. 21 (6), 2014, pp. 1483--1500.
On homotopy invariance for homology of rank two groups. J. Pure Appl. Algebra 216 (10), 2012, pp. 2291--2301.

Motivic homotopy theory

A¹-connected components of classifying spaces and purity for torsors. (with Elden Elmanto and Girish Kulkarni). Doc. Math. 27, 2022, pp. 2657-2690, arXiv:2104.06273
Variations in A¹ on a theme of Mohan Kumar. Int. Math. Res. Not. IMRN, 2021, Issue 9, pp. 6621-6655, arXiv:1704.00141.
Affine representability results in A¹-homotopy theory III: finite fields and complements. (with Aravind Asok and Marc Hoyois) Algebr. Geom. 7(5) (2020), 634-644, arXiv:1807.03365v1.
Generically split octonion algebras and A¹-homotopy theory. (with Aravind Asok and Marc Hoyois) Algebra Number Theory 13 (3), 2019, pp. 695--747, arXiv:1704.03657v1.
On stably trivial spin torsors over low-dimensional schemes. Q. J. Math. 69 (4), 2018, pp. 1221--1251, arXiv:1704.07768v1.
Affine representability results in A¹-homotopy theory II: principal bundles and homogeneous spaces. (with Aravind Asok and Marc Hoyois) Geom. Topol. 22 (2), 2018, pp. 1181--1225, arXiv:1507.08020v1.
Affine representability results in A¹-homotopy theory I: vector bundles. (with Aravind Asok and Marc Hoyois) Duke Math. J. 166 (10), 2017, pp. 1923--1953, arXiv:1506.07093v1.
Comparing A¹-h-cobordisms and A¹-weak equivalences. (with Aravind Asok and Stefan Kebekus) Ann. Sc. Norm. Super. Pisa. Cl. Sci. 17 (2), 2017, pp. 531--572, arXiv:1410.3038.
On A¹-fundamental groups of isotropic reductive groups. (with Konrad Voelkel) C. R. Math. Acad. Sci. Paris 354 (5), 2016, pp. 453--458, arXiv:1207.2364.
Fibre sequences and localization of simplicial sheaves. Alg. Geom. Topol. 13 (3), 2013, pp. 1779--1813, arXiv:1011.4784.
Rationally trivial torsors in A¹-homotopy theory. J. K-Theory 7 (3), 2011, pp. 541--572.
Classifying spaces and fibrations of simplicial sheaves. J. Homotopy Relat. Struct. 6 (1), 2011, pp. 1--38, arXiv:1009.2930.
A¹-homotopy of Chevalley groups. J. K-Theory 5 (2), 2010, pp. 245--287.
On the A¹-fundamental groups of smooth toric varieties. Adv. Math. 223 (1), 2010, pp. 352--378.

Logic Programming and Artificial Intelligence

A uniform approach to logic programming semantics. (with Pascal Hitzler) Theory and Practice of Logic Programming 5(1-2): 93--121. Cambridge University Press, 2005.
Formal concept analysis and resolution in algebraic domains. (with Pascal Hitzler) In: A. de Moor and B. Ganter (eds.). Using Conceptual Structures -- Contributions to ICCS 2003: 157--170. Shaker Verlag, Aachen, 2003.
A semi-supervised method for learning the structure of robot-environment interaction. (with Axel Großmann und Jeremy Wyatt) In: F. Pfenning, M.R. Berthold, H.-J. Lenz, E. Bradley, R. Kruse, C. Borgelt (eds.): Advances in Intelligent Data Analysis - Proceedings of the 5th International Symposium on Intelligent Data Analysis. Lecture Notes in Computer Science 2810: 36--47. Springer, 2003.
The well-founded semantics is a stratified Fitting semantics. (with Pascal Hitzler) In: M. Jarke, J. Koehler and G. Lakemeyer. Proceedings of the 25th German Conference on Artificial Intelligence (KI2002), Aachen, September 2002. Lecture Notes in Artificial Intelligence 2479: 205--221. Springer, 2002.
Unfolding the well-founded semantics. Proceedings of the 4th Slovakian Student Conference in Applied Mathematics, Bratislava, April 2002. Journal of Electrical Engineering 53(12/s): 56--59. Slovak Academy of Sciences, 2002.