Tobias Lenz

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 for one year, where I also obtained my PhD under the supervision of Stefan Schwede in 2021.

My research concerns equivariant and global homotopy theory, with a particular focus on equivariant infinite loop space theory and surrounding topics like (global) equivariant algebraic K-theory and parameterized semiadditivity. 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. Global Model Categories and Topological André-Quillen Cohomology.
   joint with Michael Stahlhauer
   preprint, 71 pages
   arXiv:2302.06207

2. Parameterized Stability and the Universal Property of Global Spectra.
   joint with Bastiaan Cnossen & Sil Linskens
   preprint, 103 pages
   arXiv:2301.08240

3. Genuine vs. Naïve Symmetric Monoidal G-Categories.
   preprint, 56 pages
   arXiv:2203.02277

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

5. Categorical Models of Unstable G-Global Homotopy Theory.
   preprint, 27 pages
   arXiv:2109.02067

6. G-Global Homotopy Theory and Algebraic K-Theory.
   to appear in Mem. Amer. Math. Soc., v + 246 pages
   arXiv:2012.12676

7. On the Global Homotopy Theory of Symmetric Monoidal Categories.
   preprint, 44 pages
   arXiv:2009.07004

8. Parsummable Categories as a Strictification of Symmetric Monoidal Categories.
   Theory Appl. Categ. 37 No. 17 (2021), pp. 482–529
   journal link (open access)  arXiv version (arXiv:2006.15068)

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

Teaching

University of Utrecht

Winter 2022/23
Summer 2023

I’m not teaching this term.

University of Bonn

Summer 2022

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

• Hauptseminar Topologische Anwendungen algebraischer K-Theorie
  with Stefan Schwede

Winter 2021/22

• Together with Stefan Schwede I offer two topics for bachelor theses in the upcoming summer term. You can find more information about them in these slides. Both of these topics have been taken now.

• Graduate Seminar Lie Groups and Their Representations
  joint with Stefan Schwede

• Assistant for the lecture Topology I
  taught by Daniel Kasprowski