Steffen Sagave

About me

I am universitair docent (assistant professor) in the Department of Mathematics at Radboud University Nijmegen.

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

Activities

• Together with Gijs Heuts, Lennart Meier and Ieke Moerdijk, I was organizing an European Autumn School in Topology that was scheduled to take place September 2020 and has now been canceled due to the uncertainties and restrictions resulting from the corona pandemic.

• Gijs Heuts, Magdalena Kędziorek, Lennart Meier, Ieke Moerdijk and I run the bi-weekly Topology intercity seminar Utrecht-Nijmegen.

• Together with Ioan Mărcuț, I am organizing the Geometry Seminar at Radboud University.

Past activities

Teaching

Autumn semester 2020/21

• I am not teaching any courses this semester.

Teaching in previous terms

Preprints

20. Homotopical and operator algebraic twisted K-theory
    (joint with Fabian Hebestreit)
    arXiv:1904.01872, pdf-file

Publications and accepted papers

(in reverse chronological order of acceptance)

19. A strictly commutative model for the cochain algebra of a space
    (joint with Birgit Richter)
    Accepted for publication in Compositio Mathematica
    arXiv:1801.01060, pdf-file
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 (2020), doi:10.1093/imrn/rnz334, 1–47
    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 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.

• 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