Publications & Preprints

  • A multidimensional Szemeredi theorem for Hardy sequences of polynomial growth., Submitted
  • Some open problems on multiple ergodic averages. Not for publication
  • The polynomial multidimensional Szemeredi theorem along shifted primes. (joint with B. Host and B. Kra), To appear in Israel Journal of Mathematics
  • Random sequences and pointwise convergence of multiple ergodic averages. (joint with E. Lesigne and M. Wierdl), To appear in Indiana University Mathematics Journal
  • Pointwise convergence for cubic and polynomial ergodic averages of non-commuting transformations. (joint with Q. Chu), To appear in Ergodic Theory & Dynamical Systems
  • Ergodic averages of commuting transformations with distinct degree polynomial iterates. (joint 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. (joint 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. (joint with M. Wierdl), Advances in Mathematics, 222, (2009), 1-43
  • Powers of sequences and recurrence. (joint with E. Lesigne and M. Wierdl), Proceedings of the London Mathematical Society (3), 98, (2009), no. 2, 504-530
  • Ergodic Theory: Recurrence. (joint 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. (joint 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. (joint 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. (joint 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. (joint 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. (joint with B. Kra), Ergodic Theory & Dynamical Systems, 25, (2005), no. 3, 799-809
  • Polynomial averages converge to the product of integrals. (joint 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