Publications Teaching Topology group

Tobias Lenz

Address
Mathematisches Institut, Universität Bonn
Endenicher Allee 60
53115 Bonn
Germany
Office 4.006
E-mail lenz (at) math (dot) uni-bonn (dot) de

I’m a postdoc (Akademischer Rat auf Zeit) in the topology group at the University of Bonn. Before that I was a postdoc at the University of Utrecht (2022–2024) and at the University of Bonn (2021–2022), 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 (parametrized) higher category theory, (global) equivariant homotopy theory, algebraic K-theory, and the interactions between these subjects.

Publications and preprints

  1. Norms in Equivariant Homotopy Theory
    joint with Sil Linskens and Phil Pützstück
    preprint, 105 pages
    arXiv:2503.02839

  2. Universality of Barwick’s Unfurling Construction
    joint with Bastiaan Cnossen and Maxime Ramzi
    preprint, 15 pages
    arXiv:2502.18278

  3. Normed Equivariant Ring Spectra and Higher Tambara Functors
    joint with Bastiaan Cnossen, Rune Haugseng, and Sil Linskens
    preprint, 64 pages
    arXiv:2407.08399

  4. Parametrized (Higher) Semiadditivity and the Universality of Spans
    joint with Bastiaan Cnossen and Sil Linskens
    preprint, 75 pages
    arXiv:2403.07676

  5. Homotopical Commutative Rings and Bispans
    joint with Bastiaan Cnossen, Rune Haugseng, and Sil Linskens
    preprint, 34 pages
    arXiv:2403.06911

  6. The Adams Isomorphism Revisited
    joint with Bastiaan Cnossen and Sil Linskens
    Math. Z. 308 No. 2 (2024), Paper No. 33, 32 pp.
    published version arXiv:2311.04884

  7. Simplicial *-Modules and Mild Actions
    joint with Anna Marie Schröter
    Homology Homotopy Appl. 26 No. 2 (2024), pp. 229–258
    published version arXiv version (arXiv:2307.11002)

  8. Partial Parametrized Presentability and the Universal Property of Equivariant Spectra
    joint with Bastiaan Cnossen and Sil Linskens
    preprint, 56 pages
    arXiv:2307.11001

  9. Global Model Categories and Topological André-Quillen Cohomology
    joint with Michael Stahlhauer
    to appear in Trans. Amer. Math. Soc., 79 pages
    arXiv:2302.06207

  10. Parametrized Stability and the Universal Property of Global Spectra
    joint with Bastiaan Cnossen and Sil Linskens
    preprint, 110 pages
    arXiv:2301.08240

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

  12. Global Algebraic K-Theory is Swan K-Theory
    preprint, 53 pages
    arXiv:2202.07272

  13. 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)

  14. G-Global Homotopy Theory and Algebraic K-Theory
    Mem. Amer. Math. Soc. 306 No. 1545 (2025), v + 246 pp.
    published versionarXiv version (arXiv:2012.12676)

  15. 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)

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

  17. 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)

Teaching

Summer 2025

Winter 2024/25

Teaching in previous terms

Fall 2023 (Utrecht)

Summer 2022 (Bonn)

  • Lecture course Selected Topics in Topology: Homotopy Coherent Algebraic Structures

  • Seminar Topologische Anwendungen algebraischer K-Theorie (Applications of Algebraic K-Theory in Topology)
    with Stefan Schwede

Winter 2021/22 (Bonn)