About me

I am universitair hoofddocent (associate professor) in the Department of Mathematics at Radboud University Nijmegen. Here is a short CV.

My primary area of research is algebraic topology, or more specifically homotopy theory. I am also interested in questions about algebraic K-theory, higher category theory, derived algebraic geometry, and homological algebra.


email address
Phone: +31 24 365 2296

HG03.735, Huygensgebouw, Heyendaalseweg 135, 6525 AJ Nijmegen

Postal address
Steffen Sagave, Radboud Universiteit, IMAPP - Mathematics, PO Box 9010, 6500 GL Nijmegen, The Netherlands

Algebraic Topology group

The Algebraic Topology group at Radboud University currently consists of Magdalena Kędziorek and me as permanent staff, Ahina Nandy as postdoctoral researcher, and Miguel Barrero (since 02/2021), Grégoire Marc (since 04/2022), Giorgi Tigilauri (since 03/2023), and Maxime Wybouw (since 09/2022) as PhD candidates. We are part of the Algebraic Geometry and Algebraic Topology group within the Research group Pure Mathematics at Radboud University, have close ties to the Algebraic Topology group at Utrecht University, and are members of the Dutch cluster on Geometry and Quantum Theory (GQT).


Past activities


Spring semester 2023/24
Teaching in previous terms

Publications and preprints

My preprints can be found on the arxiv or in my google scholar profile. Below is a list of my publications and accepted papers in reverse chronological order of acceptance. They are (or eventually get) indexed by mathscinet (subscription required) and zbMATH.

  1. Homotopical and operator algebraic twisted K-theory
    (joint with Fabian Hebestreit)
    Mathematische Annalen, 378 (2020), no. 3–4, 1021–1059
    arXiv:1904.01872, pdf-file, published article (open access)
  2. A strictly commutative model for the cochain algebra of a space
    (joint with Birgit Richter)
    Compositio Mathematica, 156 (2020), no. 8, 1718–1743
    arXiv:1801.01060, pdf-file, published article (open access)
  3. Multiplicative parametrized homotopy theory via symmetric spectra in retractive spaces
    (joint with Fabian Hebestreit and Christian Schlichtkrull)
    Forum of Mathematics, Sigma, 8 (2020), e16, 84 pages
    arXiv:1904.01824, pdf-file, published article (open access)
  4. Homotopy invariance of convolution products
    (joint with Stefan Schwede)
    International Mathematics Research Notices, 2021, no. 8, 6246–6292
    arXiv:1907.05188, pdf-file, published article (open access)
  5. Comparing cyclotomic structures on different models for topological Hochschild homology
    (joint with Emanuele Dotto, Cary Malkiewich, Irakli Patchkoria and Calvin Woo)
    Journal of Topology, 12 (2019), no. 4, 1146–1173
    arXiv:1707.07862, pdf-file, published article (open access)
  6. Virtual vector bundles and graded Thom spectra
    (joint with Christian Schlichtkrull)
    Mathematische Zeitschrift, 292 (2019), no. 3–4, 975–1016
    arXiv:1410.4492, pdf-file, published article
  7. Generalized Thom spectra and their topological Hochschild homology
    (joint with Samik Basu and Christian Schlichtkrull)
    Journal of the Institute of Mathematics of Jussieu, 19 (2020), no. 1, 21-64
    arXiv:1608.08388, pdf-file, published article
  8. Presentably symmetric monoidal infinity-categories are represented by symmetric monoidal model categories
    (joint with Thomas Nikolaus)
    Algebraic & Geometric Topology, 17 (2017), 3189–3212
    arXiv:1506.01475, pdf-file, published article
  9. Logarithmic topological Hochschild homology of topological K-theory spectra
    (joint with John Rognes and Christian Schlichtkrull)
    Journal of the European Mathematical Society (JEMS), 20 (2018), no. 2, 489–527
    arXiv:1410.2170, pdf-file, published article
  10. Topological Hochschild homology and the cyclic bar construction in symmetric spectra
    (joint with Irakli Patchkoria)
    Proceedings of the American Mathematical Society, 144 (2016), no. 9, 4099–4106
    arXiv:1508.03129, pdf-file, published article
  11. Spectra of units for periodic ring spectra and group completion of graded E-infinity spaces
    Algebraic & Geometric Topology, 16 (2016), 1203–1251
    arXiv:1111.6731, pdf-file, published article
  12. Localization sequences for logarithmic topological Hochschild homology
    (joint with John Rognes and Christian Schlichtkrull)
    Mathematische Annalen, 363 (2015), no. 3, 1349–1398
    arXiv:1402.1317, pdf-file, published article
  13. Strictly commutative models for E-infinity quasi-categories
    (joint with Dimitar Kodjabachev)
    Homology, Homotopy and Applications, 17 (2015), no. 1, 121–128
    arXiv:1408.0116, pdf-file, published article
  14. Derived logarithmic geometry I
    (joint with Timo Schürg and Gabriele Vezzosi)
    Journal of the Institute of Mathematics of Jussieu, 15 (2016), no. 2, 367–405
    arXiv:1307.4246, pdf-file, published article
  15. Logarithmic structures on topological K-theory spectra
    Geometry & Topology, 18 (2014), 447–490
    arXiv:1204.0699, pdf-file, published article
  16. Group completion and units in I-spaces
    (joint with Christian Schlichtkrull)
    Algebraic & Geometric Topology, 13 (2013), 625–686
    arXiv:1111.6413, pdf-file, published article
  17. Diagram spaces and symmetric spectra
    (joint with Christian Schlichtkrull)
    Advances in Mathematics, 231 (2012), 2116–2193
    arXiv:1103.2764, pdf-file, published article, corrections
  18. DG-algebras and derived A-infinity algebras
    Journal für die reine und angewandte Mathematik (Crelle's Journal), 639 (2010), 73–105
    arXiv:0711.4499, pdf-file, published article
  19. Universal Toda brackets of ring spectra
    Transactions of the American Mathematical Society, 360 (2008), no. 5, 2767–2808
    arXiv:math/0611808, pdf-file, published article
  20. On the algebraic K-theory of model categories
    Journal of Pure and Applied Algebra, 190 (2004), no. 1–3, 329–340
    pdf-file, published article

Notes from talks

Usually, I give blackboard talks. Presentations from occasions where I used a projector can be found below. Moreover, this list contains a few extended abstracts and a link to a video of a talk.

© 2024 Steffen Sagave
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