Publications & Preprints

  • The logarithmic Sarnak conjecture for ergodic weights (with B. Host)
        Preprint.
  • Ergodicity of the Liouville system implies the Chowla conjecture
        Preprint.
  • An averaged Chowla and Elliott conjecture along independent polynomials
        To appear in the International Mathematics Research Notices.
  • Under recurrence in the Khintchine recurrence theorem (with M. Boshernitzan and M. Wierdl)
        To appear in the Israel Journal of Mathematics.
  • Weighted multiple ergodic averages and correlation sequences (with B. Host)
        To appear in Ergodic Theory & Dynamical Systems.
  • 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.