# Papers

**
Exponential sums and polynomial congruences in two
variables: the quasi-homogeneous case
Elementary inequalities involving the roots of a polynomial
with applications in harmonic analysis and number theory
(with Michael W. Kowalski).
Weak-type (1,1) bounds for oscillatory singular
integrals with rational phases
(with Magali Folch-Gabayet).
On polynomial congruences
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),
Józef Marcinkiewicz Centenary Volume, Banach Center
Publications, 95 (2011), 235-250.
A variation norm Carleson theorem
(with Richard Oberlin, Andreas Seeger, Terence Tao
and Christoph Thiele),
J. European Math. Soc. 14 (2012), 421-464.
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.
**