Research


Research Interests: Harmonic analysis (especially on fractals), geometric measure theory, metric Diophantine approximation, analytic number theory, algorithms for Diophantine equations


Papers

Published or Accepted

(10) K. Hambrook, “Explicit Salem sets and applications to metrical Diophantine approximation,” Transactions of the American Mathematical Society, accepted with minor revision. pdf
(9) K. Hambrook, “Explicit Salem sets in R^2,” Advances in Mathematics 311 (2017), 634-648 pdf
(8) K. Hambrook, I. Laba “Sharpness of the Mockenhaupt-Mitsis-Bak-Seeger Restriction Theorem in Higher Dimensions,” Bulletin of the London Mathematical Society 48 (2016), 757-770. pdf
(7) A. Akbary, K. Hambrook, “A variant of the Bombieri-Vinogradov theorem with explicit constants and applications,” Mathematics of Computation 84 (2015), 1901-1932 pdf
(6) K. Hambrook, I. Laba, “On the sharpness of Mockenhaupt’s restriction theorem,” Geometric and Functional Analysis 23 (2013), no. 4, 1262-1277. pdf
(5) K. Hambrook, S. L. Wismath, “Minimal characteristic algebras for rectangular k-normal identities,” Algebra Colloquium 18 (2011), no. 4, 611-628. pdf
(4) A. Predoi-Cross, K. Hambrook, R. Keller, D. Hurtmans, C. Povey, H. Over, G. Mellau, “Spectroscopic lineshape study of the self-perturbed oxygen A-Band,” Journal of Molecular Spectroscopy, 248 (2008) 85-110. pdf
(3) A. Predoi-Cross, K. Hambrook, S. Brawley-Tremblay, J.-P. Bouanich, V.M. Devi, M.A.H. Smith, “Room-temperature broadening and pressure-shift coefficients in the 2 band of CH3D-O2: measurements and semi-classical calculations,” Journal of Molecular Spectroscopy 236 (2006) 75-90. pdf
(2) A. Predoi-Cross, K. Hambrook, M. Brawley-Tremblay, J.-P. Bouanich, M.A.H. Smith, “Measurements and theoretical calculations of N2-broadening and N2-shift coefficients in the 2 band of CH3D,” Journal of Molecular Spectroscopy 235 (2006) 35-53. pdf
(1) A. Predoi-Cross, K. Hambrook, M. Brawley-Tremblay, J-P Bouanich, V.M. Devi, D.C. Benner, L.R. Brown, “Measurements and theoretical calculations of self-broadening and self-shift coefficients in the 2 band of CH3D,” Journal of Molecular Spectroscopy 234 (2005) 53-74. pdf

Submitted

(2) R. Fraser, K. Hambrook, “Explicit Salem sets, Fourier restriction, and metric Diophantine approximation in the p-adic numbers,” submitted to Proceedings of the Royal Society of Edinburgh, Section A: Mathematics. pdf
(1) K. Hambrook, A. Iosevich, A. Rice, “Group actions and a multi-parameter Falconer distance problem,” submitted to Bulletin of the London Mathematical Society. pdf

In Preparation

(5) K. Hambrook, H. Yu, “Fourier decay and restriction for fractal measure on curves,” in preparation.
(4) K. Hambrook, “An optimal multi-fractal Fourier restriction theorem,” in preparation.
(3) K. Hambrook, K. Taylor “Dimension and measure of fractal packings,” in preparation.
(2) K. Hambrook, “B. Murphy, “Sharpness of L^2 restriction theorems in intermediate dimensions,” in preparation.
(1) K. Hambrook, “The logical equivalence of l’Hospital’s rule and the least upper bound property,” in preparation.



PhD Thesis

Title: Restriction theorems and Salem sets
Institution: University of British Columbia
Supervisor: Izabella Laba
Link to PDF


Masters Thesis

Title: Implementation of a Thue-Mahler Equation Solver
Institution: University of British Columbia
Supervisor: Michael Bennett
Link to PDF
Updated PDF
Email me if you would like the most up-to-date Magma code for the Thue-Mahler solver.