Publications
Peer-Reviewed Publications
- Mildness and the density of rational points on certain transcendental curves
(with D. J. Miller and G. O. Jones) Notre Dame Journal of Formal Logic, 52 (1), 67-74 (2011) - An o-minimal structure without mild parameterization
Annals of Pure and Applied Logic, 162 (6), 409-418 (2011) - The density of algebraic points on certain Pfaffian surfaces
(with G. O. Jones) Quarterly Journal of Mathematics, 63 (3), 637-651 (2012) - Convergence results for functions spaces over o-minimal structures
Journal of Logic and Analysis, 4:1, 1-14 (2012) - Integer-valued definable functions
(with G. O. Jones and A. J. Wilkie) Bulletin of the London Mathematical Society, 44, 1285–1291 (2012) - Rational values of Weierstrass zeta functions
(with G. O. Jones) Proceedings of the Edinburgh Mathematical Society (2), 59 (4), 945-958 (2016) - Ramsey growth in some NIP structures
(with A. Chernikov and S. Starchenko) Journal of the Institute of Mathematics of Jussieu, 20 (1) 1-29 (2021) - Effective Pila–Wilkie bounds for unrestricted Pfaffian surfaces
(with G. O. Jones) Mathematische Annalen, 381, 729–767 (2021) - Directed sets and topological spaces definable in o-minimal structures
(with P. Andújar Guerrero and E. Walsberg) Journal of the London Mathematical Society (2), 104, 989–1010 (2021) - An Effective Pila-Wilkie Theorem for Sets Definable using Pfaffian Functions, with Some Diophantine Applications
(with G. Binyamini, G. O. Jones, H. Schmidt) Journal of the European Mathematical Society (appeared online April 2026)
Submitted
- One-dimensional definable topological spaces in o-minimal structures
(with P. Andújar Guerrero) arXiv, 75pp.
Doctoral Thesis
- Convergence and Parameterization in O-Minimal Structures
D.Phil. Thesis of the University of Oxford (2009).
Further Publications
- Effective Pila–Wilkie Bounds for Restricted Pfaffian Surfaces
(with G. O. Jones) in T. Kaiser, J. Pila, P. Speissegger, A. J. Wilkie (eds.), O-Minimality and its Applications to Number Theory and Analysis. Oberwolfach Rep. 22 (2017). - Smooth Parameterization in O-Minimal Structures
in F. Delon, M. Dickmann, D. Gondard, T. Servi (eds.), Séminaire de Structures Algébriques Ordonnées, 2015-16 (2017).
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