#
Publications & Preprints

The logarithmic Sarnak conjecture for ergodic weights
(with B. Host)

*Annals of Mathematics*, **187**, no. 3, (2018), 869-931.
Ergodicity of the Liouville system implies the Chowla conjecture

*Discrete Analysis*, 2017:19, 41pp.
An averaged Chowla and Elliott conjecture along independent polynomials

To appear in the *International Mathematics Research Notices*.
Weighted multiple ergodic averages and correlation sequences (with B. Host)

*Ergodic Theory & Dynamical Systems*, **38**, no. 1, (2018), 81-142.
Under recurrence in the Khintchine recurrence theorem (with M. Boshernitzan and M. Wierdl)

*Israel Journal of Mathematics*, **222**, no. 10, (2017), 815-840.
Multiple ergodic theorems for arithmetic sets (with B. Host)

*Transactions of the American Mathematical Society*, **369**, no. 10, (2017), 7085-7105.
Higher order Fourier analysis of multiplicative functions and applications (with B. Host)
Replaces this article

*Journal of the American Mathematical Society*,
**30**, no. 1, (2017), 67-157.
Some open problems on multiple ergodic averages
Updates this article

*Bulletin of the Hellenic Mathematical Society,*
**60**, (2016), 41-90.
Asymptotics for multilinear averages of multiplicative functions (with B. Host)

*Mathematical Proceedings of the Cambridge Philosophical Society*, **161**, no. 1, (2016), 87-101.
Random differences in Szemeredi's theorem and related results (with E. Lesigne and M. Wierdl)

*Journal d'Analyse Mathematique*, ** 130**, no. 1, (2016), 91-133.
Multiple correlation sequences and nilsequences

*Inventiones Mathematicae*,
**202**, no. 2, (2015), 875-892.
Multiple recurrence for non-commuting transformations along rationally independent polynomials
(with
P. Zorin-Kranich)

*Ergodic Theory & Dynamical Systems*, ** 35**, no. 2, (2015), 403-411.
A multidimensional Szemeredi theorem for Hardy sequences of polynomial growth

*Transactions of the American Mathematical Society*, ** 367**, no. 8, (2015), 5653-5692.
The polynomial multidimensional Szemeredi theorem along
shifted primes
(with B. Host and
B. Kra)

*Israel Journal of Mathematics*,
** 194**, no. 1, (2013), 331-348.
Random sequences and pointwise convergence of multiple ergodic averages
(with E. Lesigne and M. Wierdl)

*Indiana University Mathematics Journal*,
** 61**, (2012), 585-617.
Pointwise convergence for cubic and polynomial ergodic averages of
non-commuting transformations
(with Q. Chu)

*Ergodic Theory & Dynamical Systems*, ** 32**, no. 3, (2012), 877-897.
Ergodic averages of
commuting transformations with distinct degree polynomial iterates
(with Q. Chu and B. Host)

*Proceedings of the London Mathematical Society* (3),
**102**, (2011),
801-842.
Powers of sequences and convergence of ergodic averages
(with M. Johnson, E. Lesigne, and M. Wierdl)

*Ergodic Theory & Dynamical Systems*, **30**, (2010), no. 5, 1431-1456.
Multiple recurrence and convergence for Hardy field sequences
of polynomial growth

*Journal d'Analyse Mathematique*, **112**, (2010), 79-135.
Equidistribution of sparse sequences on nilmanifolds

*Journal d'Analyse Mathematique*, **109**, (2009), 353-395.
A Hardy field extension of Szemeredi's theorem
(with M. Wierdl)

* Advances in Mathematics*, **222**, (2009), 1-43.
Powers of sequences and recurrence
(with E. Lesigne and M. Wierdl)

*Proceedings of the London Mathematical Society* (3), **98**, (2009),
no. 2,
504-530.
Ergodic Theory: Recurrence
(with R. McCutcheon)

*Encyclopedia of Complexity and System Science*, Springer, (2009), Part 5, 3083-3095.
Multiple ergodic averages for three polynomials and applications

*Transactions of the American Mathematical Society*, **360**, (2008), no. 10,
5435-5475.
Multiple recurrence and convergence for sequences related
to the prime numbers
(with B. Host and
B. Kra)

*J. Reine Angew. Math.*, **611**, (2007), 131-144.
Uniformity in the polynomial Wiener-Wintner theorem

*
Ergodic Theory & Dynamical Systems*, **26**, (2006), no. 4, 1061-1071.
Ergodic averages for independent polynomials and applications
(with
B. Kra)

*Journal of the London Mathematical Society*, **74**, (2006), no. 1, 131-142.
On the degree of regularity of generalised van der Waerden triples
(with
B. Landman and
A. Robertson)

*Advances in Applied Mathematics*, **37**, (2006), no. 1, 124-128.
Sets of k-recurrence but not (k+1)-recurrence
(with
E. Lesigne, M. Wierdl)

*Annales de
l'Institut Fourier*, **56**, (2006), no. 4, 839-849.
Convergence of multiple ergodic averages for some commuting transformations
(with
B. Kra)

*Ergodic
Theory &
Dynamical Systems*, **25**, (2005), no. 3, 799-809.
Polynomial averages converge to the product of integrals
(with
B. Kra)

*Israel Journal of Mathematics*, **148**, (2005), 267-276.
The structure of strongly stationary systems

*Journal d'Analyse Mathematique*, **93**, (2004), 359-388.
Additive functions modulo a countable subgroup of the reals

*Colloquium Mathematicum*, **95**, (2003), no. 1, 117-122.