Publications

For this list of publications in Provost-approved format, please click here.

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

• One-dimensional definable topological spaces in o-minimal structures
  (with P. Andújar Guerrero) link , arXiv , 75pp.
• 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.

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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