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<!DOCTYPE html>
<html lang="en">
<head>
<title>Tobias Lenz · Universität Bonn</title>
<link rel="stylesheet" href="mystyle.css"/>
</head>
<body>
<div class="header">
<div style="display:table-row">
<a href="#publications" class="cell"> Publications </a>
<a href="#teaching" class="cell"> Teaching </a>
<a href="https://www.math.uni-bonn.de/ag/topo/" class="cell"> Topology group </a>
</div>
</div>
<div class="body">
<div>
<div class="top-container">
<div>
<div>
<h1> Tobias Lenz </h1>
<table class="addr">
<tr>
<th scope="row">Address</th>
<td><address>
Mathematisches Institut, Universität Bonn<br/>
Endenicher Allee 60<br/>
53115 Bonn<br/>
Germany <br/>
</address></td>
</tr>
<tr>
<th scope="row">Office</th>
<td class="addr">4.009</td>
</tr>
<tr>
<th scope="row">E-mail</th>
<td>lenz (at) math (dot) uni-bonn (dot) de</td>
<tr>
</table>
</div>
<p class="intro" style="margin-bottom:0px;">I’m a postdoc (<i>Akademischer Rat auf Zeit</i>) in the <a href="https://www.math.uni-bonn.de/ag/topo/">topology group</a>
at the University of Bonn. Before that I was a postdoc at the <a href="https://utrechtgeometrycentre.nl/our-algebraic-topology-group/">University of Utrecht</a> (2022–2024) and
at the University of Bonn (2021–2022), where I also obtained my PhD under the supervision of
<a href="https://www.math.uni-bonn.de/people/schwede">Stefan Schwede</a> in 2021.
</p>
</div>
<div class="pic"></div>
</div>
<p class="intro" style="margin-top:8px;">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 <i>K</i>-theory, and the interactions between these subjects.
</p>
<h2 id="publications"> Publications and preprints </h2>
<ol reversed="reversed">
<li><p>
<b>Revisiting (∞, <span class="lining">2</span>)-naturality of the Yoneda embedding</b><br/>
<span class="journal"><i>Bull. Lond. Math. Soc.</i> (to appear in print), 6 pages</span><br/>
<a href="https://doi.org/10.1112/blms.70254">published version</a> <img src="open.svg" style="height:.85em;"></a> 
<a href="https://arxiv.org/abs/2508.11526">arXiv:2508.11526</a>
</p></li>
<li><p>
<b>Mackey functors and classical equivariant <i>K</i>-theory</b><br/>
<span class="journal">preprint, 27 pages</span><br/>
<a href="http://arxiv.org/abs/2508.11525">arXiv:2508.11525</a>
</p></li>
<li><p>
<b>Universality of span <span class="lining">2</span>-categories and the construction of <span class="lining">6</span>-functor formalisms</b><br/>
joint with <a class="sc" href="https://sites.google.com/view/bastiaan-cnossen">Bastiaan Cnossen</a> and <a class="sc" href="https://sites.google.com/view/sil-linskens/">Sil Linskens</a><br/>
<span class="journal">preprint, 57 pages</span><br/>
<a href="https://arxiv.org/abs/2505.19192">arXiv:2505.19192</a>
</p></li>
<li><p>
<b>Norms in equivariant homotopy theory</b><br/>
joint with <a class="sc" href="https://sites.google.com/view/sil-linskens/">Sil Linskens</a> and <a class="sc" href="https://philpuetzstueck.gitlab.io/home/">Phil Pützstück</a><br/>
<span class="journal">preprint, 105 pages</span><br/>
<a href="https://arxiv.org/abs/2503.02839">arXiv:2503.02839</a>
</p></li>
<li><p>
<b>Universality of Barwick’s unfurling construction</b><br/>
joint with <a class="sc" href="https://sites.google.com/view/bastiaan-cnossen">Bastiaan Cnossen</a> and <a class="sc" href="https://sites.google.com/view/maxime-ramzi-en">Maxime Ramzi</a><br/>
<span class="journal"><i>Int. Math. Res. Not.</i> <b>2025</b> No. 18, ID rnaf280, 15 pages</span><br/>
<a href="https://doi.org/10.1093/imrn/rnaf280">published version</a> <span class="closed"></span> <a href="https://arxiv.org/abs/2502.18278">arXiv version (arXiv:2502.18278)</a>
</p></li>
<li><p>
<b>Normed equivariant ring spectra and higher Tambara functors</b><br/>
joint with <a class="sc" href="https://sites.google.com/view/bastiaan-cnossen">Bastiaan Cnossen</a>, <a class="sc" href="https://folk.ntnu.no/runegha/">Rune Haugseng</a>, and <a class="sc" href="https://sites.google.com/view/sil-linskens/">Sil Linskens</a><br/>
<span class="journal">preprint, 64 pages</span><br/>
<a href="https://arxiv.org/abs/2407.08399">arXiv:2407.08399</a>
</p></li>
<li><p>
<b>Parametrized (higher) semiadditivity and the universality of spans</b><br/>
joint with <a class="sc" href="https://sites.google.com/view/bastiaan-cnossen">Bastiaan Cnossen</a> and <a class="sc" href="https://sites.google.com/view/sil-linskens/">Sil Linskens</a><br/>
<span class="journal">preprint, 77 pages</span><br/>
<a href="https://arxiv.org/abs/2403.07676">arXiv:2403.07676</a>
</p></li>
<li><p>
<b>Homotopical commutative rings and bispans</b><br/>
joint with <a class="sc" href="https://sites.google.com/view/bastiaan-cnossen">Bastiaan Cnossen</a>, <a class="sc" href="https://folk.ntnu.no/runegha/">Rune Haugseng</a>, and <a class="sc" href="https://sites.google.com/view/sil-linskens/">Sil Linskens</a><br/>
<span class="journal"><i>J. Lond. Math. Soc.</i> <b>111</b> No. 6 (2025), ID e70200, 33 pages</span><br/>
<a href="https://dx.doi.org/10.1112/jlms.70200">published version <img src="open.svg" style="height:.85em;"></a> 
<a href="https://arxiv.org/abs/2403.06911">arXiv version (arXiv:2403.06911)</a>
</p></li>
<li><p>
<b>The Adams isomorphism revisited</b><br/>
joint with <a class="sc" href="https://sites.google.com/view/bastiaan-cnossen">Bastiaan Cnossen</a> and <a class="sc" href="https://sites.google.com/view/sil-linskens/">Sil Linskens</a><br/>
<span class="journal"><i>Math. Z.</i> <b>308</b> No. 2 (2024), Paper No. 33, 32 pages</span><br/>
<a href="https://doi.org/10.1007/s00209-024-03582-w">published version <img src="open.svg" style="height:.85em;"></a> 
<a href="https://arxiv.org/abs/2311.04884">arXiv version (arXiv:2311.04884)</a>
</p></li>
<li><p>
<b> Simplicial <span style="position:relative;top:.4ex">*</span>-modules and mild actions</b><br/>
joint with <span class="sc">Anna Marie Schröter</span><br/>
<span class="journal"><i>Homology Homotopy Appl.</i> <b>26</b> No. 2 (2024), pp. 229–258</span><br/>
<a href="https://dx.doi.org/10.4310/HHA.2024.v26.n2.a12">published version <img src="open.svg" style="height:.85em;"></a> 
<a href="https://arxiv.org/abs/2307.11002">arXiv version (arXiv:2307.11002)</a>
</p></li>
<li><p>
<b>Partial parametrized presentability and the universal property of equivariant spectra</b><br/>
joint with <a class="sc" href="https://sites.google.com/view/bastiaan-cnossen">Bastiaan Cnossen</a> and <a class="sc" href="https://sites.google.com/view/sil-linskens/">Sil Linskens</a><br/>
<span class="journal"><i>Trans. Amer. Math. Soc.</i> <b>378</b> No. 10 (2025), pp. 6913–6974</span><br/>
<a href="https://doi.org/10.1090/tran/9497">published version</a> <span class="closed"></span> <a href="https://arxiv.org/abs/2307.11001">arXiv version (arXiv:2307.11001)</a>
</p></li>
<li><p>
<b> Global model categories and topological André-Quillen cohomology</b><br/>
joint with <span class="sc">Michael Stahlhauer</span><br/>
<span class="journal"><i>Trans. Amer. Math. Soc.</i> (to appear in print), 86 pages</span><br/>
<a href="https://www.ams.org/journals/tran/0000-000-00/S0002-9947-2025-09322-X">published version</a> <span class="closed"></span> <a href="https://arxiv.org/abs/2302.06207">arXiv:2302.06207</a>
</p></li>
<li><p>
<b>Parametrized stability and the universal property of global spectra</b><br/>
joint with <a class="sc" href="https://sites.google.com/view/bastiaan-cnossen">Bastiaan Cnossen</a> and <a class="sc" href="https://sites.google.com/view/sil-linskens/">Sil Linskens</a><br/>
<span class="journal"><i>J. Topol.</i> <b>18</b> No. 4 (2025), ID e70044, 119 pages</span><br/>
<a href="https://doi.org/10.1112/topo.70044">published version <img src="open.svg" style="height:.85em;"></a> 
<a href="https://arxiv.org/abs/2301.08240">arXiv:2301.08240</a>
</p></li>
<li><p>
<b>Genuine versus naïve symmetric monoidal <i>G</i>-categories</b><br/>
<span class="journal"><i>Doc. Math.</i> <b>28</b> No. 5 (2023), pp. 1079–1161</span><br/>
<a href="https://doi.org/10.4171/dm/933">published version <img src="open.svg" style="height:.85em;"></a> 
<a href="https://arxiv.org/abs/2203.02277">arXiv version (arXiv:2203.02277)</a>
</p></li>
<li><p>
<b>Global homotopy theory via spectral Mackey functors</b><br/>
<span class="journal">preprint, 28 pages</span><br/>
<a href="https://arxiv.org/abs/2202.07272">arXiv:2202.07272</a>
</p></li>
<li><p>
<b> Categorical models of unstable <i>G</i>-global homotopy theory</b><br/>
<span class="journal"><i>Cah. Topol. Géom. Différ. Catég.</i> <b>64</b> No. 4 (2023), pp. 439–481</span><br/>
<a href="http://cahierstgdc.com/index.php/volume-lxiv-2023/#4">published version <img src="open.svg" style="height:.85em;"></a> 
<a href="https://arxiv.org/abs/2109.02067">arXiv version (arXiv:2109.02067)</a>
</p></li>
<li><p>
<b> <i>G</i>-global homotopy theory and algebraic <i>K</i>-theory</b><br/>
<span class="journal"><i>Mem. Amer. Math. Soc.</i> <b>306</b> No. 1545 (2025), v + 246 pp.<br/></span>
<a href="https://doi.org/10.1090/memo/1545">published version</a> <span class="closed"></span> <a href="https://arxiv.org/abs/2012.12676">arXiv version (arXiv:2012.12676)</a>
</p></li>
<li><p>
<b> On the global homotopy theory of symmetric monoidal categories</b><br/>
<span class="journal"><i>New York J. Math.</i> <b>29</b> (2023), pp. 635–686</span><br/>
<a href="https://nyjm.albany.edu/j/2023/29-26.html">published version <img src="open.svg" style="height:.85em;"></a> 
<a href="https://arxiv.org/abs/2009.07004">arXiv version (arXiv:2009.07004)</a>
</p></li>
<li><p>
<b> Parsummable categories as a strictification of symmetric monoidal categories</b><br/>
<span class="journal"><i>Theory Appl. Categ.</i> <b>37</b> (2021), Paper No. 17, pp. 482–529<br/></span>
<a href="http://www.tac.mta.ca/tac/volumes/37/17/37-17abs.html">published version <img src="open.svg" style="height:.85em;"></a> 
<a href="https://arxiv.org/abs/2006.15068">arXiv version (arXiv:2006.15068)</a>
</p></li>
<li><p>
<b> Homotopy (pre)derivators of cofibration categories and quasicategories</b><br/>
<span class="journal"><i> Algebr. Geom. Topol. </i><b>18</b> No. 6 (2018), pp. 3601–3646<br/></span>
<a href="https://dx.doi.org/10.2140/agt.2018.18.3601">published version</a> <span class="closed"></span> <a href="https://arxiv.org/abs/1712.07845">arXiv version (arXiv:1712.07845)</a>
</p></li>
</ol>
<h2 id="teaching"> Teaching </h2>
<h4>Winter 2025/26</h4>
<ul>
<li><p>
Graduate seminar <a href="seminar-HA-25.pdf">Higher Algebra</a><br/>
with <a href="https://www.math.uni-bonn.de/people/schwede">Stefan Schwede</a>
</p></li>
<li><p>
Assistant for lecture <a href="https://www.math.uni-bonn.de/people/schwede/at1-ws2526">Algebraic Topology I</a> (lecturer: <a href="https://www.math.uni-bonn.de/people/schwede">Stefan Schwede</a>)
</p></li>
</ul>
<h4>Summer 2025</h4>
<ul>
<li><p>
Graduate seminar <a href="seminar-lie-groups-25.pdf">Lie Groups and Their Representations</a><br/>
with <a href="https://www.jmdavies.org/">Jack Davies</a>
</p></li>
<li><p>
Assistant for lecture <a href="https://www.math.uni-bonn.de/people/schwede/topo2-ss25.html">Topology II</a> (lecturer: <a href="https://www.math.uni-bonn.de/people/schwede">Stefan Schwede</a>)
</p></li>
<li><p>
<a href="https://www.math.uni-bonn.de/ag/topo/BA_thesis_seminar_SS25">Bachelor thesis seminar</a><br/>
joint with the rest of the topology group
</p></li>
</ul>
<details>
<summary>Teaching in previous terms</summary>
<div>
<h4>Winter 2024/25</h4>
<ul>
<li><p>
Assistant for lecture <a href="https://www.math.uni-bonn.de/people/schwede/topo1-ws2425.html">Topology I</a> (lecturer: <a href="https://www.math.uni-bonn.de/people/schwede">Stefan Schwede</a>)
</li></p>
<li><p>
Assistant for lecture Einführung in die Algebra (lecturer: <a href="https://www.math.uni-bonn.de/people/gmartin/">Gebhard Martin</a>)
</li></p>
</ul>
<h4> Fall 2023 (Utrecht)</h4>
<ul>
<li><p>
Lecture course <span lang="nl">Bewijzen in de Wiskunde</span> (Proofs in Mathematics)<br/>
with <a href="https://math.commelin.net/"> Johan Commelin</a>, <a href="https://www.uu.nl/staff/MMartineziSellares">Mireia Martínez i Sellarès</a>, <a href="https://webspace.science.uu.nl/~meier007/">Lennart Meier</a>, <a href="https://www.uu.nl/staff/GMTerraBleeker">Guido Terra-Bleeker</a>, and <a href="https://www.uu.nl/staff/MvanderWegen">Marieke van der Wegen</a>
</p></li>
</ul>
<h4>Summer 2022 (Bonn)</h4>
<ul>
<li><p>
Lecture course Selected Topics in Topology: Homotopy Coherent Algebraic Structures
</li></p>
<li><p>
Seminar Topologische Anwendungen algebraischer <i>K</i>-Theorie (Applications of Algebraic <i>K</i>-Theory in Topology)<br/> with <a href="https://www.math.uni-bonn.de/people/schwede">Stefan Schwede</a>
</li></p>
</ul>
<h4>Winter 2021/22 (Bonn)</h4>
<ul>
<li><p>
Graduate seminar Lie Groups and Their Representations<br/> with <a href="https://www.math.uni-bonn.de/people/schwede">Stefan Schwede</a>
</li></p>
<li><p>
Assistant for the lecture <a href="https://www.math.uni-bonn.de/people/daniel/2021/topo1/">Topology I</a> (lecturer: <a href="https://www.math.uni-bonn.de/people/daniel/">Daniel Kasprowski</a>)
</li></p>
</ul>
</div>
</details>
</div>
<div class="footer">
last updated: December 20, 2025
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