#
Publications & Preprints

Correlations of multiplicative functions along deterministic and independent sequences

Preprint
Good weights for the Erdös discrepancy problem

Preprint
Furstenberg systems of bounded multiplicative functions and applications
(with B. Host)

To appear in *International Mathematics Research Notices*.
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

*International Mathematics Research Notices*, **2018**, no. 12, (2018), 3721-3743.
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 different 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.