## 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) (appeared online 2019)__Effective Pila–Wilkie bounds for unrestricted Pfaffian surfaces__

(with G. O. Jones) Mathematische Annalen, 381, 729–767 (2021) (appeared online 2020)__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) (appeared online 2021)

### Submitted

__An Effective Pila-Wilkie Theorem for Sets Definable using Pfaffian Functions, with Some Diophantine Applications__

(with G. Binyamini, G. O. Jones, H. Schmidt) arXiv , 43pp.

### Publications In Preparation

__One-dimensional definable topological spaces in o-minimal structures (working title)__

(with P. Andújar Guerrero and E. Walsberg) 70pp.

### 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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