Stefan Schwede

Professor
Mathematisches Institut
Universität Bonn
Endenicher Allee 60
53115 Bonn, Germany

Email: schwede@math.uni-bonn.de
Office: Endenicher Allee 60, Room 4.008
Phone: +49-228-73-3158
Secretary: H. Bacher, Ext. -7780, Room 2.002

© VL

Curriculum Vitae
Google Scholar Profile
MathSciNet Profile
articles on arXiv
Mathematics Genealogy Profile

Publications

Universal symmetries: Global equivariant homotopy theory
Expository article, to appear in the proceedings of the 9th ECM, Seville.
21 pp., last updated October 30, 2025
DOI: 10.4171/9ECM/32 PDF-File
Representation-graded Bredon homology of elementary abelian 2-groups
Algebraic & Geometric Topology 25 (2025), 4321-4340
with M. Hausmann
DOI: 10.2140/agt.2025.25.4321 PDF-File
Chern classes in equivariant bordism
Forum of Mathematics, Sigma (2024), Vol. 12:e7 1-11
DOI: 10.1017/fms.2023.124 PDF-File MR 4685685 Video
Proper equivariant stable homotopy theory
Memoirs of the American Mathematical Society 288 (2023), No. 1432, vi+142 pp.
with D. Degrijse, M. Hausmann, W. Lück and I. Patchkoria
DOI: 10.1090/memo/1432 PDF-File MR 4627088
Splittings of global Mackey functors and regularity of equivariant Euler classes
Proceedings of the London Mathematical Society (3) 125 (2022), 258-276
DOI: 10.1112/plms.12446 PDF-File MR 4466235 Video
Global stable splittings of Stiefel manifolds
Documenta Mathematica 27 (2022), 789-845
DOI: 10.25537/dm.2022v27.789-845 PDF-File MR 4452225 Video
Global algebraic K-theory
Journal of Topology 15 (2022), 1325-1454
DOI: 10.1112/topo.12241 PDF-File MR 4461851 Correction
Homotopy invariance of convolution products
International Mathematics Research Notices (2021) No. 8, 6246-6292
with S. Sagave,
DOI: 10.1093/imrn/rnz334 PDF-File MR 4251277
Orbispaces, orthogonal spaces, and the universal compact Lie group
Mathematische Zeitschrift 294 (2020), 71-107
DOI: 10.1007/s00209-019-02265-1 PDF-File MR 4050064
Categories and orbispaces
Algebraic & Geometric Topology 19 (2019), 3171-3215
DOI: 10.2140/agt.2019.19.3171 PDF-File MR 4023338 Correction
Global homotopy theory
New Mathematical Monographs 34.
Cambridge University Press, Cambridge, 2018. xviii+828 pp.
DOI: 10.1017/9781108349161 PDF-File MR 3838307 Errata
Equivariant properties of symmetric products
Journal of the American Mathematical Society 30 (2017), 673-711
DOI: 10.1090/jams/879 PDF-File MR 3630085 Video
The n-order of algebraic triangulated categories
Journal of Topology 6 (2013), 857-867
DOI: 10.1112/jtopol/jtt014 PDF-File MR 3145142
The p-order of topological triangulated categories
Journal of Topology 6 (2013), 868-914
DOI: 10.1112/jtopol/jtt018 PDF-File MR 3145143 Correction
Algebraic versus topological triangulated categories
in Triangulated categories, 389-407, London Mathematical Society Lecture Notes 375,
Cambridge Univ. Press, Cambridge, 2010.
DOI: 10.1017/CBO9781139107075.010 PDF-File MR 2681714
On the homotopy groups of symmetric spectra
Geometry & Topology 12 (2008), 1313-1344
DOI: 10.2140/gt.2008.12.1313 PDF-File MR 2421129
The stable homotopy category is rigid
Annals of Mathematics 166 (2007), 837-863
DOI: 10.4007/annals.2007.166.837 PDF-File MR 2373374
Triangulated categories without models
Inventiones Mathematicae 170 (2007), 231-241
with F. Muro and N. Strickland
DOI: 10.1007/s00222-007-0061-2 PDF-File MR 2342636
Introduction to realizability of modules over Tate cohomology
in Representations of algebras and related topics, Fields Institute Communications Vol. 45 (2005), 81-97
with D. Benson and H. Krause
DOI: 10.1090/fic/045/06 PDF-File MR 2146241
Morita theory in abelian, derived and stable model categories
in Structured Ring Spectra, 33-86, London Mathematical Society Lecture Notes 315,
Cambridge Univ. Press, Cambridge, 2004.
DOI: 10.1017/CBO9780511529955.005 DVI-File MR 2122154
Formal groups and stable homotopy of commutative rings
Geometry & Topology 8 (2004), 335-412
DOI: 10.2140/gt.2004.8.335 PDF-File MR 2033483
Realizability of modules over Tate cohomology
Transactions of the American Mathematical Society 356 (2004), no. 9, 3621-3668
with D. Benson and H. Krause
DOI: 10.1090/S0002-9947-03-03373-7 PDF-File MR 2055748
Stable model categories are categories of modules
Topology 42 (2003), 103-153
with B. Shipley
DOI: 10.1016/S0040-9383(02)00006-X PDF-File MR 1928647
Equivalences of monoidal model categories
Algebraic & Geometric Topology 3 (2003), 287-334
with B. Shipley
DOI: 10.2140/agt.2003.3.287 PDF-File MR 1997322
A uniqueness theorem for stable homotopy theory
Mathematische Zeitschrift 239 (2002), 803-828
with B. Shipley
DOI: 10.1007/s002090100347 PDF-File MR 1902062
The stable homotopy category has a unique model at the prime 2
Advances in Mathematics 164 (2001), 24-40
DOI: 10.1006/aima.2001.2009 PDF-File MR 1870511
Simplicial structures on model categories and functors
American Journal of Mathematics 123 (2001), 551-575
with C. Rezk and B. Shipley
DOI: 10.1353/ajm.2001.0019 PDF-File MR 1833153 Correction
Model categories of diagram spectra
Proceedings of the London Mathematical Society (3) 82 (2001), 441-512
with M. Mandell, J. P. May and B. Shipley
DOI: 10.1112/S0024611501012692 PDF-File MR 1806878
Stable homotopy of algebraic theories
Topology 40 (2001), 1-41
DOI: 10.1016/S0040-9383(99)00046-4 PDF-File MR 1791267
S-modules and symmetric spectra
Mathematische Annalen 319 (2001), 517-532
DOI: 10.1007/PL00004446 PDF-File MR 1819881
Algebras and modules in monoidal model categories
Proceedings of the London Mathematical Society (3) 80 (2000), 491-511
with B. Shipley
DOI: 10.1112/S002461150001220X PDF-File MR 1734325
Stable homotopical algebra and Γ-spaces
Mathematical Proceedings of the Cambridge Philosophical Society 126 (1999), 329-356
DOI: 10.1017/S0305004198003272 PDF-File MR 1670249
An exact sequence interpretation of the Lie bracket in Hochschild cohomology
Journal für die reine und angewandte Mathematik 498 (1998), 153-172
DOI: 10.1515/crll.1998.048 PDF-File MR 1629858
Spectra in model categories and applications to the algebraic cotangent complex
Journal of Pure and Applied Algebra 120 (1997), 77-104
DOI: 10.1016/S0022-4049(96)00058-8 PDF-File MR 1466099

Preprints and projects

A Real-global equivariant Segal-Becker splitting, explicit Brauer induction, and global Adams operations
70 pp., last updated March 18, 2026; arxiv:2603.17848 PDF-File
Character theory and Euler characteristic for orbispaces and infinite groups
with W. Lück and I. Patchkoria, 50 pp., last updated October 18, 2024; arxiv:2410.14510 PDF-File
The universal property of bordism of commuting involutions
with M. Hausmann, 50 pp., last updated June 1, 2024; arxiv:2406.00404 PDF-File
Lecture notes on equivariant stable homotopy theory
113 pp., last updated February 5, 2023; PDF-File
Symmetric spectra
unfinished book project. DVI-File PDF-File (154 pp., updated July 12, 2007)

Presentations

Universal symmetries: global-equivariant homotopy theory
Talk slides, Invited Lecture at the 9th ECM, Seville, July 18, 2024; PDF-File
Equivariant bordism from the global perspective
Talk slides, December 7, 2015; PDF-File
Equivariant stable homotopy theory
Videos of a lecture series during the Summer School Spectral methods in algebra, geometry, and topology at the Hausdorff Research Institute for Mathematics, September 19-23, 2022
Lecture 1 Lecture 2 Lecture 3
Global localization and equivariant Thom spectra
Video of a talk at the Institut Mittag-Leffler, March 15, 2022
The global stable homotopy category
Video of a talk at BIRS, June 23, 2016
Universal properties of global equivariant Thom spectra
Video of a talk at BIRS, February 15, 2016
Lecture course Global homotopy theory
Video lectures, "Advanced Topics in Topology (V5D1)", summer term 2020
youtube channel

Teaching/Lehre

Theses with the Bonn topology group

SS 2026

Algebraic Topology II (V4D2), Mondays 14:15-16:00 in "Großer Hörsaal" and Wednesdays, 8:15-10:00 in "Kleiner Hörsaal" (Wegeler Str. 10)

Graduate Seminar Advanced Topology (S4D4): Compact transformation groups, Tuesdays, 14:15-15:45 in SR 1.007

Master Thesis Seminar / Research Seminar Homotopy Theory, Wednesdays, 10:15-11:45, SR 0.007

WS 2026/27

Advanced Topics in Topology: Equivariant stable homotopy theory (V5D1), Tuesdays, 10:15-12:00 and Thursdays, 14:15-16:00 in SR 1.008

Hauptseminar Homotopietheorie (S2D4), Tuesdays, 14:15-15:45
Organization meeting and distribution of talks: Tuesday, July 21, at 14:15 in SR 1.007