Steffen Sagave

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.

Contact

Phone: +31 24 365 2296

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

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

News

We were recently advertising two fully-funded PhD positions in Algebraic Topology in our group. One of these positions is under my primary supervision. The application deadline was 10 March 2025, and it is no longer possible to apply.

Algebraic Topology group

The Algebraic Topology group at Radboud University currently consists of Magdalena Kędziorek and me as permanent staff, Ahina Nandy and Niall Taggart as postdoctoral researchers, and Grégoire Marc (since 04/2022), Julius Groenjes (since 09/2024), 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).

Activities

• Together with Gijs Heuts, Lennart Meier and Ieke Moerdijk, I am organizing an European Autumn School in Topology that will take place in September 2025.

• Gijs Heuts (U Utrecht), Renee Hoekzema (VU Amsterdam), Magdalena Kędziorek (RU Nijmegen), Inbar Klang (VU Amsterdam), Lennart Meier (U Utrecht) and I have a joint research grant Symmetry on the interface of topology and higher algebra that will fund several positions and scientific activities between 2025 and 2031. One of the joint activities of the algebraic topologists from Radboud University, University of Utrecht and the VU Amsterdam is the Topology intercity Seminar (see here for an archive of past talks).

• I maintain a YouTube channel with math talks, currently featuring videos from the workshop Motivic and non-commutative aspects of enumerative geometry (playlist) and the conference Homotopy theory, K-theory, and trace methods (playlist), both held in Nijmegen in July 2023.

Past activities

Teaching

Spring semester 2024/25

I am not teaching any courses this semester

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.

20. 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)
19. 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)
18. 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)
17. 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)
16. 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)
15. 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
14. 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
13. 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
12. 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
11. 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
10. 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
9. 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
8. 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
7. 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
6. Logarithmic structures on topological K-theory spectra
   Geometry & Topology, 18 (2014), 447–490
   arXiv:1204.0699, pdf-file, published article
5. 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
4. Diagram spaces and symmetric spectra
   (joint with Christian Schlichtkrull)
   Advances in Mathematics, 231 (2012), 2116–2193
   arXiv:1103.2764, pdf-file, published article, corrections
3. 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
2. 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
1. 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 and recordings from talks

Most of the time, I give blackboard talks. Here are some presentations from occasions where I used a projector, extended abstracts, and video recordings from talks I gave.

• Logarithmic topological cyclic homology
  Seminar talk during the program Equivariant homotopy theory in context at the Isaac Newton Institute for Mathematical Sciences, Cambridge, March 2025
  Video, Abstract
• Logarithmic topological Hochschild homology
  Talk at the Alpine Algebraic and Applied Topology Conference in Saas, August 2016
  Presentation: pdf-file for screen, pdf-file for printing
• Rigidification of homotopy coherent commutative multiplications
  Talk at the Banff workshop Operations in Highly Structured Homology Theories, May 2016
  Video
• Rigidification of homotopy coherent commutative multiplications
  Talk at the workshop Higher Geometric Structures along the Lower Rhine VI, September 2015
  Presentation: pdf-file for screen, pdf-file for printing
• Graded units of ring spectra and R-module Thom spectra
  Talk at the Oberwolfach Workshop Homotopy Theory, March 2015
  Extended abstract: pdf-file (Part of the full Oberwolfach report for this workshop.)
• Logarithmic structures on K-theory spectra
  Talk at the Fourth Arolla Conference on Algebraic Topology, August 2012
  Presentation: pdf-file for screen, pdf-file for printing
• Spectra of units for periodic ring spectra
  Talk at the Oberwolfach Workshop Homotopy Theory, September 2011
  Extended abstract: pdf-file (Part of the full Oberwolfach report for this workshop.)
• Logarithmic structures in homotopy theory
  Talk at the Conference on Current trends in logarithmic geometry, Bordeaux, June 2010
  Presentation: pdf-file for screen, pdf-file for printing
• Graded log symmetric ring spectra
  Talk at the Conference on p-Adic Geometry and Homotopy Theory, Loen, August 2009
  Presentation: pdf-file for screen, pdf-file for printing
• DG-algebras and derived A-infinity algebras
  Talk at the Banff workshop New Topological Contexts for Galois Theory and Algebraic Geometry, March 2008
  Presentation: pdf-file for screen, pdf-file for printing
• DG-algebras and derived A-infinity algebras
  Talk at the Algebra Seminar at the Institut Henri Poincaré, Paris, January 2008
  Slides: pdf-file