About me
I am a PhD student at the University of Münster under the supervision of Thomas Nikolaus, since October 2025. My interests lie in algebraic topology, homotopy theory, (higher) category theory and (higher) topos theory. In particular, I am interested in the interaction between \((\infty,\infty)\)-category theory and geometric topology, e.g. through bordism categories. I also love anything to do with manifolds and bundles.
Previously, I completed my bachelor's and master's degrees at Goethe University Frankfurt, supervised by Matthias Kreck, Jakob Stix and Thomas Nikolaus.
Papers
(The pdf version is more recent, if applicable.)
- The Oriented Freudenthal Suspension Theorem, October 2026 (pdf, arXiv)
- Cocompactness and Presentability, joint with Phil Pützstück and Maxime Ramzi, September 2026 (arXiv)
- Factorization Systems on \(\infty\)-Categories: Un/Straightening and Monadicity, August 2026 (pdf, arXiv)
- On Cofiltered Limits of \(\infty\)-Categories and Adjunctions, August 2026 (pdf, arXiv)
MSc Thesis
- Bordism-type Theories and \((\infty,\infty)\)-categories, MSc Thesis, Goethe-Universität Frankfurt, April 2025 (pdf)
Notes
- A Note on the Functoriality of the Shape of \(\infty\)-Topoi (pdf). This note discusses how to construct the shape of \(\infty\)-topoi as a (\(2\)-)functor \(\Pi_{\infty}\colon\mathrm{RTop}\rightarrow\mathrm{Pro}(\mathrm{An})\), and why multiple such constructions are equivalent. This clarifies a point in the author's previous work.
- An Example in Higher Topos Theory (pdf). We give examples of \(\infty\)-topoi that are not Postnikov-complete, yet in which every Postnikov tower converges. This settles a minor open question in the literature.
- Fun with Topological \(K\)-Theory Spectra (pdf). This note is about computations involving the topological \(K\)-theory spectra \(\mathrm{ku}\) and \(\mathrm{ko}\), taking only their basic properties as input. More precisely, we give a proof of Wood's theorem and compute their \(\mathbb{F}_2\)-homology and Tate \(L\)-theory spectra.
- Higher Presentable Categories as Categories (pdf). We make precise the relationship between \(\kappa\)-compactly generated \((\infty,n)\)-categories in the sense of Stefanich and Aoki and (plain) \((\infty,n)\)-categories. In particular, we exhibit the opposite of Gestalten as a (non-full) subcategory of categorical spectra.
- Notes on Sites and Sheaves (pdf). These are expository notes on the theory of sites and sheaves in the setting of \(\infty\)-categories. They also collect some folklore results.
- Light Condensed Anima and Étale Sheaves (pdf). These are the notes for a talk I gave in the Kleine Topologie Seminar at University of Münster in the Winter of 2025, following Clausen.
Talks
- The Oriented Freudenthal Suspension Theorem, Abstract Homotopy Theory Seminar, MPIM Bonn, October 2026
- The Tate-Frobenius L-groups of the integers (after Land--Nikolaus--Pedersen), European Talbot Workshop on Algebraic & Geometric Surgery, Kolding, Denmark, June 2026
- Bordism-type Theories and Higher Categories, Oberseminar Topologie, Universität Münster, May 2025
- Eine Einführung in topologische Feldtheorien nach Atiyah, Segal und Witten, Gingko-Seminar, Goethe-Universität Frankfurt, July 2024
- An Introduction to Knots, GAUS Junior AG "Knots and Primes", December 2023
Events
- (Upcoming) Functional Analysis, Higher Categories and Quantum Field Theories, ESI Vienna, 11.01.-15.01.27
- (Upcoming) Arithmetic Geometry and Higher Algebra, University of Copenhagen, 09.11.-13.11.26
- (Upcoming) 38th NRW Topology Meeting, Ruhr University Bochum, 05.11.-06.11.26
- Kleine AT III — Embedding Calculus, Bielefeld University, 09.10.26
- Opening Conference: 2nd Funding Period of Mathematics Münster, University of Münster, 16.09.-18.09.26
- Interactions between operator algebras, \(K\)-theory and homotopy theory, University of Münster, 07.09.-11.09.26
- European Talbot Workshop on Algebraic & Geometric Surgery, Kolding, Denmark, 22.06.-25.06.26
- 37th NRW Topology Meeting, University of Münster, 11.06.-12.06.26
- Interactions between higher algebra, manifolds and functor calculus, MPIM Bonn, 18.05.-22.05.26
- 36th NRW Topology Meeting, University of Bonn, 06.11.-07.11.2025
- GAUS Junior AG "Knots and Primes", Heidelberg University, 05.12.23
Contact
You can reach me via e-mail: tgeiss at uni-muenster dot de. You can address me as "Thorger" (he/him).