Publications & Preprints
Partition regularity of generalized Pythagorean pairs
(with O. Klurman and J. Moreira)
Preprint.
Bohr recurrence and density of non-lacunary semigroups of ℕ
(with B. Host and B. Kra)
To appear in Proceedings of the American Mathematical Society .
Partition regularity of Pythagorean pairs
(with O. Klurman and J. Moreira)
To appear in Forum of Mathematics, Pi .
Furstenberg systems of pretentious and MRT multiplicative functions
(with M. Lemanczyk and T. de la Rue)
Preprint.
Degree lowering for ergodic averages along arithmetic progressions
(with B. Kuca)
To appear in Journal d'Analyse Mathematique .
Seminorm control for ergodic averages with commuting transformations along pairwise dependent polynomials
(with B. Kuca)
Ergodic Theory & Dynamical Systems , 43 , (2023), 4074-4137.
Joint ergodicity for commuting transformations and applications to polynomial sequences
(with B. Kuca)
Preprint.
Multiple recurrence and convergence without commutativity
(with B. Host)
Journal of the London Mathematical Society , 107 , no. 5, (2023), 1635-1659.
Joint ergodicity of fractional powers of primes
Forum of Mathematics, Sigma, 10 , (2022), e30.
Joint ergodicity of sequences
Advances in Mathematics , 417 , 108918 (2023), (63pp).
Here is an exposition that appeared in D. Gatzouras memorial volume, Univ. of Athens, 2022
Furstenberg systems of Hardy field sequences and applications
Journal d'Analyse Mathematique , 147 , (2022), 333-372.
Correlations of multiplicative functions along deterministic and independent sequences
Transactions of the American Mathematical Society,
373 , no. 9, (2020), 6595-6620.
Good weights for the Erdős discrepancy problem
Discrete Analysis , 2020:8, 23 pp.
Furstenberg systems of bounded multiplicative functions and applications
(with B. Host)
International Mathematics Research Notices , 2021 , no. 8, (2021), 6077-6107.
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. (Updated version 2019)
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.