I am a mathematician and computer scientist currently working as a proof theorist in the department of computer science at the University of the Bundeswehr Munich under the supervision of Prof. Dr. Vasco Brattka. You can find me on arXiv or ORCID.
Previously, I worked in the department of mathematical logic at the University of Würzburg led by Prof. Dr. Anton Freund, under whose supervision I also obtained my PhD (Dr. rer. nat.). Before that, I worked in the department of mathematical logic at the Technical University of Darmstadt, where I began my PhD before our group moved to Würzburg.
In proof theory / logic, I am mostly interested in reverse mathematics and well order principles involving recursion, dilators, and maximal order types. I also like functional interpretations and their interplay with linear logic. I have also done some Weihrauch reducibility.
In computer science, I am interested in proof assistants, program reduction and weak memory models.
Email: patrick dot uftring at unibw dot de
Education and Degrees
October 2021 - March 2025: PhD candidate under the supervision of Prof. Dr. Anton Freund at TU Darmstadt (until March 2023) and the University of Würzburg (since April 2023)
January 2021: M.Sc. in computer science (with honors) under the supervision of Prof. Dr.-Ing. Heiko Mantel at TU Darmstadt
An Example-driven Investigation of Effects and Consequences of Weak Memory Behavior on DependenciesDecember 2018: M.Sc. in mathematics (with honors) under the supervision of Prof. Dr. Ulrich Kohlenbach at TU Darmstadt
Proof-theoretic characterization of Weihrauch reducibility
Work
Preprints
The uniform Kruskal theorem over RCA0 (submitted, arXiv)
More conservativity for weak Kőnig's lemma (jww Anton Freund, submitted, arXiv)
On inverse Goodstein sequences (submitted, arXiv)
Published
Weihrauch degrees without roots (arXiv)
Computability Pre-press (https://doi.org/10.3233/COM-230471)The uniform Kruskal theorem: between finite combinatorics and strong set existence (jww Anton Freund, arXiv)
Philosophical Transactions of the Royal Society A 381 (2248) (2023), 20220016 (https://doi.org/10.1098/rsta.2022.0016)Weak and Strong Versions of Effective Transfinite Recursion (arXiv)
Annals of Pure and Applied Logic 174 (4) (2023), 103232 (https://doi.org/10.1016/j.apal.2022.103232)The characterization of Weihrauch reducibility in systems containing E-PAω + QF-AC0,0 (arXiv)
The Journal of Symbolic Logic 86 (1) (2021), pp. 224 - 261 (https://doi.org/10.1017/jsl.2020.53)
Conferences and Talks
Leeds Computability Days, July 2024, Leeds, UK
Invited Talk: Weihrauch degrees without rootsLogic Colloquium, June 2024, Gothenburg, Sweden
Talk: Sequences with gap condition and binary trees with ascending labelsTrends in Proof Theory 2024, February 2024, Vienna, Austria
Talk: Gap sequences and ascending treesAutumn school "Proof and Computation", September 2023, Herrsching, Germany
Summer School and Workshop on Proof Theory and its Applications, July 2023, Barcelona, Spain
Logic Colloquium, June 2023, Milan, Italy
Talk: On inverse Goodstein sequencesTrends in Proof Theory, January 2023, Ghent, Belgium
Talk: On inverse Goodstein sequencesAutumn school "Proof and Computation", September 2022, Fischbachau, Germany
Logic Colloquium, June 2022, Reykjavik, Iceland
Talk: Weak and Strong Versions of Effective Transfinite RecursionLeeds-Ghent Virtual Logic Seminar, March 2022, Online
Invited Talk: Weak and Strong Versions of Effective Transfinite Recursion"Computability Theory and Applications" Online Seminar, September 2020, Online
Invited Talk: The characterization of Weihrauch reducibility in systems containing E-PAω + QF-AC0,0Measuring the Complexity of Computational Content, September 2018, Dagstuhl, Germany
Talk: Proof-theoretic characterization of Weihrauch reducibility