Since May 2024 I am a PhD student in algebraic topology at the Münster Topology Group under supervision of Thomas Nikolaus. My main interests lie in (stable) homotopy theory, algebraic K-theory and higher category theory / higher algebra.

Previously, I completed my master’s at the University of Bonn under supervision of Stefan Schwede. Even earlier, I obtained Bachelor degrees in Mathematics and Computer Science at RWTH-Aachen University under supervision of Erich Grädel.

Publications & Preprints

  1. Norms in Equivariant Homotopy Theory, joint with Tobias Lenz and Sil Linskens, preprint available on arXiv, to appear in Forum of Mathematics, Sigma

  2. Global Picard Spectra and Borel Parametrized Algebra, preprint available on arXiv or here as pdf

  3. Logics of Dependence and Independence: The Local Variants, joint with Erich Grädel, Journal of Logic and Computation (2021), arXiv

Other writing

On Bipresentability and Posets, joint with Thorger Geiß, pdf
Under mild additional hypotheses, we prove an \(\infty\)-categorical version of the classical theorem that if \(\mathcal{C}\) is a category for which both \(\mathcal{C}\) and \(\mathcal{C}^\textsf{op}\) are presentable, then \(\mathcal{C}\) is a poset.

Exercises on Spectra pdf
An axiomatic and exercise-based introduction to spectra. Work-in-progress. Any feedback is appreciated!

Lecture Notes: Sheaves on Manifolds, joint with Achim Krause and Thomas Nikolaus. Last Update: 07.11.2024 pdf
I helped write these lecture notes for the course “Sheaves on Manifolds” held at the University of Münster in WS23/24 and SS24. Despite the title, the lecture was mostly concerned with the recent theory of compactly assembled categories and continuous K-Theory, as initiated by Sasha Efimov.

Parametrized Higher Algebra and Global Picard Spectra pdf
My master’s thesis. A revised version is available as a preprint, see above.

Decidability and Bisimulation for Logics of Functional Dependence pdf
My bachelor thesis. A condensed and improved version has been published in the Journal of Logic and Computation, see above. I gave a talk on the main results at the Amsterdam Logic and Interactive Rationality Seminar, a recording of which can be found here.

CV and contact

My CV as of 10.08.24: Curriculum Vitae

You can reach me under: philpuetzstueck at gmail dot com