Philip Dittmann
I am a researcher at the Institut für Algebra working in the research group of Prof. Arno Fehm. I am interested in various problems related to field theory and model theory. In particular this includes definability questions over global fields and finitely generated fields, with a view towards variants of Hilbert's Tenth Problem.
Papers and preprints
- Two examples concerning existential undecidability in fields - manuscript
- When is the étale open topology a field topology? (with Erik Walsberg, Jinhe Ye) - to appear in Israel Journal of Mathematics
- Definable valuations on ordered fields (with Franziska Jahnke, Lothar Sebastian Krapp, Salma Kuhlmann) - to appear in Model Theory
- Axiomatizing the existential theory of F_p((t)) (with Sylvy Anscombe, Arno Fehm) - to appear in Algebra & Number Theory
- Appendix to Galois groups of large fields with simple theory by Anand Pillay and Erik Walsberg - to appear in Model Theory
- Existential rank and essential dimension of diophantine sets (with Nicolas Daans, Arno Fehm) - manuscript
- Odoni's conjecture on arboreal Galois representations is false (with Borys Kadets) - Proceedings of the American Mathematical Society 150(8):3335-3343, 2022
- Characterizing finitely generated fields by a single field axiom (with Florian Pop) - manuscript
- Non-definability of rings of integers in most algebraic fields (with Arno Fehm) - Notre Dame Journal of Formal Logic 62(3):589-592, 2021
- A class of fields with a restricted model completeness property (with Dion Leijnse) - Journal of Symbolic Logic 86(2):701-708, 2021
- Denseness results in the theory of algebraic fields (with Sylvy Anscombe, Arno Fehm) - Annals of Pure and Applied Logic 172(8), 2021
- The dimension growth conjecture, polynomial in the degree and without logarithmic factors (with Wouter Castryck, Raf Cluckers, Kien Huu Nguyen) - Algebra & Number Theory 14(4):2261-2294, 2020 (see the addenda file on RC's homepage for minor corrections, affecting none of the main theorems of the paper)
- A p-adic analogue of Siegel's Theorem on sums of squares (with Sylvy Anscombe, Arno Fehm) - Mathematische Nachrichten 293(8):1434-1451, 2020
- Approximation theorems for spaces of localities (with Sylvy Anscombe, Arno Fehm) - Mathematische Zeitschrift 296(3):1471-1499, 2020
- Irreducibility of Polynomials over Global Fields is Diophantine - Compositio Math. 154 (4):761-772, 2018
I wrote my doctoral thesis A Model-Theoretic Approach to the Arithmetic of Global Fields at the University of Oxford under the supervision of Jochen Koenigsmann.
Contact
+49 351 463-33908
Zellescher Weg 12-14
Willersbau Zi. C 114
TU Dresden
Fachrichtung Mathematik
Institut für Algebra
01062 Dresden