Publications TopICS Teaching Algebraic topology group

Tobias Lenz

Mathematical Institute, University of Utrecht
Budapestlaan 6
3584 CD Utrecht
The Netherlands
Office 704
E-mail t.lenz (at) uu (dot) nl

I’m a postdoc (onderzoeker) in the algebraic topology group at the University of Utrecht, where my mentor is Ieke Moerdijk. Before that I was a postdoc at the University of Bonn, where I also obtained my PhD under the supervision of Stefan Schwede in 2021.

My research concerns various aspects of homotopy theory, and I am particularly interested in questions relating to (global) equivariant homotopy theory, algebraic K-theory, (parametrized) higher category theory, and the interactions between these subjects. You can find an overview about some of the work I did before 2021 in this video I contributed to the Junior Mathematician Research Archive.

Publications and preprints

  1. The Adams Isomorphism Revisited.
    joint with Bastiaan Cnossen and Sil Linskens
    preprint, 29 pages

  2. Simplicial *-Modules and Mild Actions.
    joint with Anna Marie Schröter
    to appear in Homology Homotopy Appl., 27 pages

  3. Partial Parametrized Presentability and the Universal Property of Equivariant Spectra.
    joint with Bastiaan Cnossen and Sil Linskens
    preprint, 56 pages

  4. Global Model Categories and Topological André-Quillen Cohomology.
    joint with Michael Stahlhauer
    preprint, 71 pages

  5. Parametrized Stability and the Universal Property of Global Spectra.
    joint with Bastiaan Cnossen and Sil Linskens
    preprint, 110 pages

  6. Genuine Versus Naïve Symmetric Monoidal G-Categories.
    Doc. Math. 28 No. 5 (2023), pp. 1079–1161
    published version arXiv version (arXiv:2203.02277)

  7. Global Algebraic K-Theory is Swan K-Theory.
    preprint, 53 pages

  8. Categorical Models of Unstable G-Global Homotopy Theory.
    Cah. Topol. Géom. Différ. Catég. 64 No. 4 (2023), pp. 439–481
    published version arXiv version (arXiv:2109.02067)

  9. G-Global Homotopy Theory and Algebraic K-Theory.
    to appear in Mem. Amer. Math. Soc., v + 246 pages

  10. On the Global Homotopy Theory of Symmetric Monoidal Categories.
    New York J. Math. 29 (2023), pp. 635–686
    published version arXiv version (arXiv:2009.07004)

  11. Parsummable Categories as a Strictification of Symmetric Monoidal Categories.
    Theory Appl. Categ. 37 No. 17 (2021), pp. 482–529
    published version arXiv version (arXiv:2006.15068)

  12. Homotopy (Pre)Derivators of Cofibration Categories and Quasicategories.
    Algebr. Geom. Topol. 18 No. 6 (2018), pp. 3601–3646
    published version (doi:10.2140/agt.2018.18.3601) arXiv version (arXiv:1712.07845)

Seminar organization

Together with Christian Carrick and the colleagues from Amsterdam and Nijmegen I’m organizing the current iteration of the Topology Intercity Seminar (TopICS).


University of Utrecht

Fall 2023

University of Bonn

Summer 2022

Winter 2021/22