# 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**

**(11)** R. Fraser, K. Hambrook, “Explicit Salem sets, Fourier restriction, and metric Diophantine approximation in the p-adic numbers,” Proceedings of the Royal Society of Edinburgh, Section A: Mathematics, to appear. pdf

**(10)** K. Hambrook, “Explicit Salem sets and applications to metrical Diophantine approximation,” Transactions of the American Mathematical Society, to appear. 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**

**(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

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