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| 1996 | Dr. math., University of Bielefeld | | 1996 | Postdoc, University of Chicago, IL, USA | | 1997 - 1998 | Postdoc, Massachusetts Institute of Technology, Cambridge, MA, USA | | 1998 - 2001 | Assistant Professor (C1), University of Bielefeld | | 2001 | Habilitation, University of Bielefeld | | 2002 - 2003 | Head of Junior Research Group, DFG Collaborative Research Center SFB 478 “Geometric structures in mathematics”, University of Münster | | Since 2003 | Professor (C4), University of Bonn |
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My main area of expertise is algebraic topology, specifically stable homotopy theory. I contributed to the foundations of stable homotopy theory (comparison of models for the stable homotopy category, rigidity theorem for the stable homotopy category, foundations of the theory of symmetric spectra). Further research concerned basic questions about triangulated categories, in particular the existence and uniqueness of models for triangulated categories, the distinction of algebraic and topological triangulated categories and examples of exotic triangulated categories.
Much of my current and future research is in equivariant stable homotopy theory, in particular ''global'' phenomena, i.e., spaces or spectra with simultaneous and compatible actions of all compact Lie groups, up to deformations that preserve all symmetries. I introduced a framework for global equivariant homotopy theory based on orthogonal spectra which opens the door for a rigorous study of global stable homotopy types. The global perspective reveals systematic patterns and facilitates equivariant calculations, for example in the rank filtrations of equivariant infinite symmetric products or global equivariant K-theory.
Future goals include a better understanding of the universal properties of global K-theory (both algebraic and topological) and global equivariant bordism. Alongside, we want to further exploit naturally occuring global structures for new computations.
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DFG Research Training Group GRK 1150 “Homotopy and Cohomology”
Scientific Member
DFG Priority Program SPP 1786 “Homotopy Theory and Algebraic Geometry”
Initiator
Series of Oberwolfach Workshops on “Homotopy theory” (2007, 2011, 2015)
Organizer
Abel Symposion, 2007
Organizer
HIM-Trimester, 2015
Organizer
Semester program “Homotopy Harnessing Higher Structures” at Isaac Newton Institute, 2018
Organizer
“Bonn International Graduate School of Mathematics”
Director, 2013 - 2017
DFG Cluster of Excellence “Hausdorff Center for Mathematics”
Vice-Coordinator (2017 - 2019) and Principal Investigator
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[ 1] Stefan Schwede
Equivariant properties of symmetric products
J. Amer. Math. Soc. , 30: (3): 673--711
2017
DOI: 10.1090/jams/879[ 2] Stefan Schwede
The n-order of algebraic triangulated categories
J. Topol. , 6: (4): 857--867
2013
DOI: 10.1112/jtopol/jtt014[ 3] Stefan Schwede
The p-order of topological triangulated categories
J. Topol. , 6: (4): 868--914
2013
DOI: 10.1112/jtopol/jtt018[ 4] Stefan Schwede
On the homotopy groups of symmetric spectra
Geom. Topol. , 12: (3): 1313--1344
2008
DOI: 10.2140/gt.2008.12.1313[ 6] Fernando Muro, Stefan Schwede, Neil Strickland
Triangulated categories without models
Invent. Math. , 170: (2): 231--241
2007
DOI: 10.1007/s00222-007-0061-2[ 7] M. A. Mandell, J. P. May, S. Schwede, B. Shipley
Model categories of diagram spectra
Proc. London Math. Soc. (3) , 82: (2): 441--512
2001
DOI: 10.1112/S0024611501012692[ 8] Stefan Schwede, Brooke E. Shipley
Algebras and modules in monoidal model categories
Proc. London Math. Soc. (3) , 80: (2): 491--511
2000
DOI: 10.1112/S002461150001220X[ 9] Stefan Schwede, Brooke Shipley
Stable model categories are categories of modules
Topology , 42: (1): 103--153
2003
DOI: 10.1016/S0040-9383(02)00006-X[ 10] Stefan Schwede
An exact sequence interpretation of the Lie bracket in Hochschild cohomology
J. Reine Angew. Math. , 498: : 153--172
1998
DOI: 10.1515/crll.1998.048[ 11] Sagave Steffen, Stefan Schwede
Homotopy invariance of convolution products
2020
DOI: 10.1093/imrn/rnz334 |
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• Documenta Mathematica (2003 - 2016)
• Mathematische Zeitschrift (2006 - 2012)
• Geometry & Topology (since 2016)
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| 2019 | Fellow of the American Mathematical Society |
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| 2007 | Plenary talk, Joint International Meeting UMI - DMV, Perugia, Italy | | 2008 | Plenary talk, European Mathematical Society -- Joint Mathematical Weekend, Copenhagen, Denmark |
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Christian Ausoni (2008), now Professor, University of Paris 13, France
Gerald Gaudens (2010)
Steffen Sagave (2013), now Assistant Professor, Radboud University Nijmegen, Netherlands
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Steffen Sagave (2006): “Universal Toda Brackets of Ring Spectra”,
now Assistant Professor, Radboud University Nijmegen, Netherlands
Constanze Roitzheim (2007): “Rigidity and Exotic Models for the K-local Stable Homotopy Category”,
now Senior Lecturer, University of Kent, England, UK
Morith Rahn (née Groth) (2011): "On the theory of derivators",
now Akademischer Rat, University of Mainz
Lennart Meier (2012): “United elliptic homology”,
now Assistant Professor, Utrecht University, Netherlands
Irakli Patchkoria (2013): “Rigidity in equivariant stable homotopy theory”,
now Lecturer, University of Aberdeen
Karol Szumilo (2014): “Two models for the homotopy theory of cocomplete homotopy theories”,
now Postdoc, University of Leeds
Markus Hausmann (2016): “Symmetric products, subgroup lattices and filtrations of global K-theory”,
now Postdoc, University of Bonn
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- Master theses: 19, currently 1
- Diplom theses: 15
- PhD theses: 14, currently 2
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