The contents and opinions expressed on this web page do not necessarily reflect the views of  nor are they endorsed by the university system of georgia
Last modified 2 October 2010
Preprints and Expository Notes   

Papers and Preprints:

Multilinear maximal operators associated to simplices (with Brian Cook and Akos Magyar)

Weak hypergraph regularity and applications to geometric Ramsey theory (with Akos Magyar)

Distances and trees in dense subsets of Z^d (with Akos Magyar)
          to appear in Israel J. Math.

Distance graphs and sets of positive upper density in R^d (with Akos Magyar)
          Analysis and PDE, Vol. 13 (2020), No. 3, 685-700

Spherical configurations over finite fields (with Akos Magyar and Hans Parshall)
          Amer. J. Math. Volume 142, Number 2, April 2020, 373-404

Product of simplices and sets of positive upper density in R^d (with Akos Magyar)
Math. Proc. Cambridge Philos. Soc. 165 (2018), no. 1, 25-51

Simplices and sets of positive upper density in R^d (with Lauren Huckaba and Akos Magyar)
Proc. Amer. Math. Soc. 145 (2017), no. 6, 2335–2347

Polynomials and primes in generalized arithmetic progressions (with Ernie Croot and Alex Rice)
          Int. Math. Res. Not. (2015), no. 15, 6021-6043

A quantitative result on Diophantine approximation for intersective polynomials (with Alex Rice)
          INTEGERS Volume 15A (2015), Proceedings of Integers 2013: The Erdös Centennial Conference

A purely combinatorial approach to simultaneous polynomial recurrence modulo 1 (with Ernie Croot and Alex Rice)
Proc. Amer. Math. Soc. 143 (2015), no. 8, 3231-3238

Improved bounds on Sarkozy's theorem for quadratic polynomials (with Mariah Hamel and Alex Rice)
Int. Math. Res. Notices (2013), no. 8, 1761-1782

A new proof of Sarkozy's theorem
Proc. Amer. Math. Soc. 141 (2013), 2253-2264

Polynomial differences in the primes (with Alex Rice)
Combinatorial and Additive Number Theory (Proceedings of CANT 2011 and 2012), pp 129-146. Springer Proc. in Math. & Stat., 2014

Optimal polynomial recurrence (with Akos Magyar)
Canad. J. Math. 65 (2013), no. 1, 171-194
      Here is an exposition of the special case of squares: An optimal version of Sarkozy's theorem

Simultaneous polynomial recurrence (with Akos Magyar)
Bull. Lond. Math. Soc. 43 (2011), no. 4, 765-785

Arithmetic structure in sparse difference sets (with Mariah Hamel, Katherine Thompson and Nathan Walters)
J. Number Theory 130 (2010), 1581-1589

Polynomial configurations in difference sets (with Akos Magyar)
J. Number Theory 129 (2009), 439-450

Strongly singular Radon transforms on the Heisenberg group and folding singularities (with Norberto Laghi)
Proc. Amer. Math. Soc. 136 (2008), no. 4, 1261-1272

Strongly singular integrals along curves (with Norberto Laghi)
Pacific J. Math. 233 (2007), no. 2, 403-415

Strongly singular integral operators associated to different quasi-norms on the Heisenberg group (with Norberto Laghi)
Math. Res. Lett. 14 (2007), no. 5, 825-838
      Here is a related determinant calculation

Two-weight estimates for singular and strongly singular integral operators (with V. Kokilashvili and A. Meskhi)
Acta Math. Hungar. 116 (2007), no.1-2, 1-25

A class of strongly singular Radon transforms on the Heisenberg group
Proc. Edinb. Math. Soc. (2) 50 (2007), 429-457

Strongly singular convolution operators on the Heisenberg group
Trans. Amer. Math. Soc. 359 (2007), 4467-4488

Expository Notes:

  • Two theorems of Sarkozy (with Alex Rice) [This note supersedes the first note in the list below and in addition discusses prime minus one differences]

Some Additional Expository Notes (these are very old, but might still be useful to someone):