Steffen Sagave

About me

I am assistant professor in the Department of Mathematics at Radboud University Nijmegen.

My primary area of research is algebraic topology. 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

• Gijs Heuts, Magdalena Kędziorek, Lennart Meier, Ieke Moerdijk and I run the bi-weekly Topology intercity seminar Utrecht-Nijmegen. This term we are covering various basic notions.

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

• Together with Gijs Heuts, Lennart Meier and Ieke Moerdijk, I have organized an European Autumn School in Topology that took place September 2018. There were earlier editions of this event in 2016 and 2017.

• Together with Christian Blohmann, Marius Crainic, Ioan Mărcuț, and Ieke Moerdijk, I am organizing the workshop series "Higher Geometric Structures along the Lower Rhine". The last meeting Higher Geometric Structures along the Lower Rhine XII was in Nijmegen January 31 - February 1, 2019.

Teaching

Spring semester 2018/19
Master Seminar (together with Stefanie Sonner)
Course description, times and brightspace page

Teaching in previous terms

Preprints

19. Homotopical and operator algebraic twisted K-theory
    (joint with Fabian Hebestreit)
    arXiv:1904.01872, pdf-file
18. Multiplicative parametrized homotopy theory via symmetric spectra in retractive spaces
    (joint with Fabian Hebestreit and Christian Schlichtkrull)
    arXiv:1904.01824, pdf-file
17. A strictly commutative model for the cochain algebra of a space
    (joint with Birgit Richter)
    arXiv:1801.01060, pdf-file
16. Comparing cyclotomic structures on different models for topological Hochschild homology
    (joint with Emanuele Dotto, Cary Malkiewich, Irakli Patchkoria and Calvin Woo)
    arXiv:1707.07862, pdf-file

Publications and accepted papers

(in reverse chronological order of acceptance)

15. Virtual vector bundles and graded Thom spectra
    (joint with Christian Schlichtkrull)
    Mathematische Zeitschrift (2018), 1-42, doi:10.1007/s00209-018-2131-0
    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 (2017), 1-44, doi:10.1017/S1474748017000421
    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
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