Papers

  • On polynomial congruences
  • An elementary inequality and some applications (with Michael W. Kowalski).
  • From oscillatory integrals to complete exponential sums Mathematical Research Letters 18 (2011), no. 2, 231-250.
  • Problems on averages and lacunary maximal functions (with Andreas Seeger), to appear in the Józef Marcinkiewicz Centenary Volume.
  • A variation norm Carleson theorem (with Richard Oberlin, Andreas Seeger, Terence Tao and Christoph Thiele), to appear in J. European Math. Soc.
  • From oscillatory integrals and sublevel sets to polynomial congruences and character sums J. Geom. Anal. 21 (2011), 224-240. [Minor errors corrected here]
  • An affine invariant inequality for rational functions and applications in harmonic analysis (with Spyros Dendrinos and Magali Folch-Gabayet), Proc. Edin. Math. Soc. 53 (2010), 639–655.
  • Fourier restriction to polynomial curves I: a geometric inequality (with Spyros Dendrinos), Amer. J. Math. 132 (2010), no. 4, 1031-1076.
  • Universal Lp improving for averages along polynomial curves in low dimensions (with Spyros Dendrinos and Norberto Laghi), J. Funct. Anal. 257 (2009), no. 5, 1355-1378.
  • Triple Hilbert transforms along polynomial surfaces in R^4 (with Tony Carbery and Steve Wainger), Rev. Mat. Iber. 25 (2009), no. 2, 471-519.
  • Strong variational and jump inequalities in harmonic analysis (with Roger Jones and Andreas Seeger), Trans. Amer. Math. Soc. 360 (2008), no. 12, 6711-6742.
  • Averages in vector spaces over finite fields (with Tony Carbery and Brendan Stones), Math. Proc. Camb. Phil. Soc. 144 (2008), no. 13, 13-27.
  • Singular integral operators associated to curves with rational components (with Magali Folch-Gabayet), Trans. Amer. Math. Soc. 360 (2008), no. 3, 1661-1679.