Recent
Papers
Averages along polynomial
sequences in discrete nilpotent groups: Singular Radon transforms
(with A. Ionescu, S. Wainger, Analysis and Applications, Conf. Proc.
in honor of E. M. Stein, to appear)
On the distribution of solutions to
diophantine equations (in Panorama of Discrepancy Theory,
Springer-Verlag, to appear)
Constellations in P^d (with
B. Cook, I.M.R.N., v 12 pp. 2794-2816, 2012)
On restricted arithmetic progressions over
finite fields (with B. Cook, O.J.M, v 7, pp. 1-10, 2012)
Optimal polynomial recurrence
(with N. Lyall, Canad. J. Math. 65(2013), 171-194,)
Simultaneous polynomial recurrence
(with N. Lyall, Bull. London Math. Soc.,v43/4, pp. 765-785, 2011)
k-point configurations in sets
of positive density of Z^n (Duke Math. J., v 146/1, pp. 1-34,
2009)
Polynomial configurations in
difference sets (with N. Lyall, J. Num. Theory, v. 129/2,
pp.439-450, 2009)
On distance sets of large sets of
integer points (Israel J. Math., v 164/1, pp. 251-263, 2008)
These are two papers discussing discrete maximal functions, singular
Radon transforms and ergodic theorems related to nilpotent groups.
(in joint work with A. Ionescu, E. M. Stein and S. Wainger):
Maximal
operators
associated
to discrete subgroups of nilpotent Lie groups ( J. d'Analyse
Math., v. 101, pp. 257-313, 2007)
Discrete
Radon
transforms and applications to ergodic theory ( Acta Math., v.
198, No 2, pp. 231-298, 2007)
Here is a paper on the uniformity of distribution of integer points
on certain polynomial surfaces:
On
the distribution of lattice points on spheres and on level
surfaces of polynomials (J. Num. Theory, v.122/1 pp. 69-83,
2007)
This preprint deals with the restriction of the Fourier transform to
two-dimensional analytic surfaces in R^3:
On
Fourier restriction and the Newton polygon. (Proc. Amer. Math.
Soc., v 137/2, pp. 615-625, 2009)
Here is a survey article which appeared in a book called "Fourier
analysis and Convexity" (ANHA, Birkahauser '04)
Discrete
maximal
functions and ergodic theorems related to polynomials.
The details of the proofs can be found in these two earlier papers:
"Diophantine
equations
and ergodic theorems" (Amer J. Math., v.124, p.921-953) and
"Discrete
analogues
in harmonic analysis: spherical averages" (Annals of
Math., v.155, p.189-208)
Here one can find some expository notes (jointly with Neil Lyall)
and some links on Ramsey
Theory.