Prof. Dr. Jens Hornbostel

Fakultät für Mathematik und Naturwissenschaften
Fachgruppe Mathematik und Informatik
Bergische Universität Wuppertal
Gaußstraße 20
42119 Wuppertal
Raum: G.15.12
Telefon: ++ (49)(202) 439-2672
Fax: ++ (49)(202) 439-3135
e-mail: hornbostel (at) math.uni-wuppertal.de

Sprechstunde: Donnerstag 11 bis 12 Uhr (in der Vorlesungszeit) und nach Vereinbarung per Email

Lehre im Sommersemester 2024: Topologie 2 (Vertiefung Topologie): Mo 12-14 in G.13.18 und Mi 12-14 Uhr in G.15.25.

Lehre im Wintersemester 2024/25: Einführung in die Topologie, Mi 10-12 Uhr in G.15.34 und Do 12-14 Uhr in K.12.16, Übungsgruppe Mo 12-14 Uhr in G.14.34.

Archiv und Ausblick Lehre

Oberseminar Algebra und Topologie am Mittwoch um 16:30 Uhr, Raum I.13.71.

Arbeitsgruppe Topologie

33rd NRW Topology Meeting, 26./27. April 2024

Summer school on derived and triangulated categories, Wuppertal, 13.-17. September 2021

Gauss-Vorlesung der DMV in Wuppertal am 21. November 2019

New trends in K-theory and homotopy theory - A conference in honor of Max Karoubi's 80th birthday, IHP Paris, 15./16. November 2018

Postdocs: Tommy Lundemo, Doosung Park

Doktoranden: Andrea Lachmann, Pengcheng Zhang

Ehemalige

Sonstiges

Publications and Preprints:

• Sur la K-théorie des catégories additives et exactes hermitiennes, C. R. Acad. Sci. Paris, t.329 (1999), 469-474.
• Constructions and Dévissage in Hermitian K-theory, K-theory 26 (2002), 139-170.
• Localization in Hermitian K-theory of rings (joint with M. Schlichting), Journal of the LMS 70 (2004), 77-124.
• A¹-representability of hermitian K-theory and Witt groups, Topology 44 (2005), 661-687.
• A Zero Theorem for the Transfer of Coherent Witt Groups (joint with S. Gille), Math. Nachrichten 278 (2005), 815-823.
• Motives and étale motives with finite coefficients (joint with C. Häsemeyer), K-theory 34 (2005), 195-207.
• Localizations in motivic homotopy theory, Math. Proc. of the Cambridge Phil. Soc. 140 (2006), 95-114.
• On non-commutative twisting in étale and motivic cohomology (joint with G. Kings), Annales de l'Institut Fourier 56 (2006), 1257-1279.
• Rigidity for Henselian local rings and A¹-representable theories (joint with S. Yagunov), Math. Zeitschrift 225 (2007), 437-449.
• Witt motives, transfers and reductive groups (joint with B. Calmès), preprint 2004. Available as preprint no. 143 of the Linear Algebraic Groups and Related Structures Preprint Server .
• Witt motives, transfers and dévissage (joint with B. Calmès), preprint 2006 (extending parts of the previous item). Available as preprint no. 786 of the K-theory preprint archives .
• Beta-elements and divided congruences (joint with N. Naumann), American Journal of Mathematics 129 (2007), 1377-1402.
• Oriented Chow groups, hermitian K-theory and the Gersten conjecture, Manuscripta Math. 125 (2008), 273-284.
• Tensor-triangulated categories and dualities (joint with B. Calmès), Theory and Appl. of Categories 22 (2009), 136-198.
• Push-forwards for Witt groups of schemes (joint with B. Calmès), Comment. Math. Helv. 86 (2011), 437-468.
• Schubert calculus for algebraic cobordism (joint with V. Kiritchenko), J. Reine Angew. Math. (Crelle) 656 (2011), 59-86.
• Preorientations of the derived motivic multiplicative group, Alg. Geom. Topology 13 (2013), 2667-2712. Erratum ibid. 18 (2018), 1257-1258.
• Equivariant semi-topological K-homology and a theorem of Thomason (joint with J. Heller), Journal of K-theory 12 (2013), 493-549.
• Infinite CW-complexes, Brauer groups and phantom cohomology (joint with S. Schröer), Israel J. Math. 207 (2015), 77-101.
• Semistable symmetric spectra in A1-homotopy theory (joint with S. Hähne), New York J. Math. (2015), 1-56.
• Some comments on motivic nilpotence (with an appendix by M. Zibrowius), Transactions of the AMS 370 (2018), 3001-3015.
• Smooth Schubert varieties and generalized Schubert polynomials in algebraic cobordism of Grassmannians (joint with N. Perrin), Pacific J. Math. 294 (2018), 401-422.
• Chow-Witt rings of classifying spaces for symplectic and special linear groups (joint with M. Wendt), J. of Topology 12 (2019), 915-965.
• Chow-Witt rings of split quadrics (joint with H. Xie and M. Zibrowius), in "Motivic homotopy theory and refined enumerative geometry", Contemp. Math. vol. 745 (2020), 123-161.
• The real cycle class map (joint with M. Wendt, H. Xie and M. Zibrowius), Ann. K-Theory 6 (2021), 239-317.
• Formal ternary laws and Buchstaber's 2-groups (joint with D. Coulette, F. Déglise, J. Fasel), Manuscripta Mathematica 174 (2024), 453-490.
• Real topological Hochschild homology of schemes (joint with D. Park), J. Inst. Math. Jussieu 23 (2024), 1461-1518, Addendum ibid. 1519-1520.
• Atiyah-Segal completion for the Hermitian K-theory of Symplectic Groups (joint with H. Rohrbach and M. Zibrowius), Preprint 2023, available on the arxiv.
• Real Topological Hochschild Homology of Perfectoid Rings (joint with D. Park), Preprint 2023, available on the arxiv.
• A few computations about the real cycle class map in low dimensions, Preprint 2024, available on the arxiv, to appear in Quartely J. Math..