Publications

Universal quadratic forms and Northcott property of infinite number fields

Nicolas Daans, Vı́tězslav Kala, and Siu Hang Man. “Universal quadratic forms and Northcott property of infinite number fields”. In: Journal of the London Mathematical Society 110.5 (2024), e70022. https://doi.org/10.1112/jlms.70022
published version arXiv

Linkage of Pfister forms over semi-global fields

Nicolas Daans. “Linkage of Pfister forms over semi-global fields”. In: Mathematische Zeitschrift 308 (2024), 41. https://doi.org/10.1007/s00209-024-03598-2
published version, arXiv

Universally defining $\mathbb{Z}$ in $\mathbb{Q}$ with $10$ quantifiers

Nicolas Daans. “Universally defining $\mathbb{Z}$ in $\mathbb{Q}$ with $10$ quantifiers”. In: Journal of the London Mathematical Society 109.2 (2024), e12864. https://doi.org/10.1112/jlms.12864
published version, arXiv

Universally defining finitely generated subrings of global fields

Nicolas Daans. “Universally defining finitely generated subrings of global fields”. In: Documenta Mathematica 26 (2021), pp. 1851-1869. https://doi.org/10.4171/dm/858
published version, arXiv

Preprints

Most totally real fields do not have universal forms or Northcott property

Nicolas Daans, Vı́tězslav Kala, Siu Hang Man, Martin Widmer, Pavlo Yatsyna. “Most totally real fields do not have universal forms or Northcott property”. Available as arXiv:2409.11082. Sep. 2024.
arXiv

Failures of integral Springer’s Theorem

Nicolas Daans, Vı́tězslav Kala, Jakub Krásenský, and Pavlo Yatsyna. “Failures of integral Springer’s Theorem”. Available as arXiv:2404.12844. Apr. 2024.
arXiv

Universally defining subrings in function fields

Nicolas Daans and Philip Dittmann. “Universally defining subrings in function fields”. Available as arXiv:2404.02749. Apr. 2024.
arXiv

Uniform existential definitions of valuations in function fields in one variable

Karim Johannes Becher, Nicolas Daans, and Philip Dittmann. “Uniform existential definitions of valuations in function fields in one variable”. Available as arXiv:2311.06044. Nov. 2023.
arXiv

The Pythagoras number of a rational function field in two variables

Karim Johannes Becher, Nicolas Daans, David Grimm, Gonzalo Manzano-Flores, and Marco Zaninelli. “The Pythagoras number of a rational function field in two variables”. Available as arXiv:2302.11425. Feb. 2023.
arXiv

Existential rank and essential dimension of diophantine sets

Nicolas Daans, Philip Dittmann, and Arno Fehm. “Existential rank and essential dimension of diophantine sets”. Available as arXiv:2102.06941. Oct. 2021.
arXiv

Theses

PhD thesis: Existential first-order definitions and quadratic forms

Nicolas Daans. “Existential first-order definitions and quadratic forms”. PhD thesis. University of Antwerp, 2022.
Under the supervision of Karim Johannes Becher and Philip Dittmann. University of Antwerp repository

Master thesis: Diophantine definability in number fields and their rings of integers

Nicolas Daans. “Diophantine definability in number fields and their rings of integers”. Master thesis. University of Antwerp, 2018.
Under the supervision of Karim Johannes Becher. pdf

Bachelor thesis: Het pythagorasgetal van enkele commutatieve ringen

Nicolas Daans. “Het pythagorasgetal van enkele commutatieve ringen [The Pythagoras number of certain commutative rings]”. Bachelor thesis. University of Antwerp, 2016.
Under the supervision of Karim Johannes Becher. Scriptiebank

Bachelor thesis: Iteratieve methoden voor de golfvergelijking

Nicolas Daans. “Iteratieve methoden voor de golfvergelijking [Iterative methods for the wave equation]”. Bachelor thesis. University of Antwerp, 2016.
Under the supervision of Wim Vanroose and Siegfried Cools. pdf