Research output per year
Research output per year
Personal profile
Overview
I am interested in various problems related to field theory, with motivation and techniques coming from number theory, model theory, and algebraic geometry. In particular this includes definability questions over global fields and finitely generated fields, with a view towards variants of Hilbert's Tenth Problem.
I am looking to take on a PhD student starting September 2025. Topics are likely to involve the model theory of valued fields or variants of Hilbert's 10th Problem. Informal expressions of interest are very welcome, although admissions decisions are ultimately made after an application through the usual university route.
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Research output
- 12 Article
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Axiomatizing the existential theory of Fq((t))
Anscombe, S., Dittmann, P. & Fehm, A., 3 Oct 2023, In: Algebra & Number Theory. 17, 11, p. 2013–2032Research output: Contribution to journal › Article › peer-review
Open Access -
Characterizing finitely generated fields by a single field axiom
Dittmann, P. & Pop, F., 1 Nov 2023, In: Annals of Mathematics. 198, 3, p. 1203-1227Research output: Contribution to journal › Article › peer-review
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Definable valuations on ordered fields
Dittmann, P., Jahnke, F., Krapp, L. S. & Kuhlmann, S., 26 Jun 2023, In: Model Theory. 2, 1, p. 101–120Research output: Contribution to journal › Article › peer-review
Open Access -
Two examples concerning existential undecidability in fields
Dittmann, P., 23 Nov 2023, In: The Journal of Symbolic Logic.Research output: Contribution to journal › Article › peer-review
Open Access -
Odoni’s conjecture on arboreal Galois representations is false
Dittmann, P. & Kadets, B., 1 Apr 2022, In: Proceedings of the American Mathematical Society.Research output: Contribution to journal › Article › peer-review