Department of Mathematics
231 West 18th Avenue
Ohio State University
(614)292-1180
Some publications:
Ergodic Ramsey Theory -- an update,
Ergodic Theory ofZ^{d}-actions
(edited by M. Pollicott and K. Schmidt),
London Math. Soc. Lecture Note Series
228 (1996), 1-61.
pdf
Polynomial extensions
of van der Waerden's and Szemerédi's theorems
(jointly with A. Leibman),
Journal of AMS9 (1996), no.3, 725-753.
pdf
A Roth theorem for amenable groups
(jointly with R. McCutcheon and Q. Zhang),
Amercan Journal of Mathematics119 (1997), 1173-1211.
pdf
Recurrence for semigroup actions and a non-commutative Schur theorem
(jointly with R. McCutcheon),
Topological dynamics and applications, 205-222,
Contemporary Mathematics, 215 (1998), Amer. Math. Soc., Providence, RI.
pdf
Set-polynomials
and polynomial extension of the Hales-Jewett theorem
(jointly with A. Leibman),
Annals of Mathematics150 (1999), 33-75.
pdf
The multifarious Poincare recurrence theorem,
Descriptive set theory and dynamical systems
(edited by M. Foreman, A. Kechris, A. Louveau, B. Weiss),
London Math. Soc. Lecture Note Series
277 (2000), 31-57.
pdf
Ergodic theory and diophantine problems,
Topics in symbolic dynamics and applications
(edited by F. Blanchard, A. Maass and A. Nogueira),
London Math. Soc. Lecture Note Series
279 (2000), 167-205.
pdf
An ergodic IP polynomial Szeméredi theorem
(jointly with R. McCutcheon),
Memoirs of the AMS146 (2000), viii+106pp.
pdf
Krengel-type theorems for nilpotent groups
(jointly with A. Leibman, I. Kornfeld and B. Mityagin),
Ergodic Theory and Dynamical Systems21 (2001), 1359-1369.
pdf
A nilpotent Roth theorem
(jointly with A. Leibman),
Inventiones Mathematicae147 (2002), 429-470.
pdf
Squarefree numbers, IP sets and ergodic theory
(jointly with I. Ruzsa),
"Paul Erdős and his Mathematics I", Bolyai Society Mathematical Studies 11,
Budapest (2002), 147-160.
pdf
Topological multiple recurrence
for polynomial configurations in nilpotent groups
(jointly with A. Leibman),
Advances in Mathematics175 (2003), no. 2, 271-296.
pdf
Minimal idempotents and ergodic Ramsey theory,
Topics in Dynamics and Ergodic Theory
8-39,
London Math. Soc. Lecture Note Series 310,
Cambridge Univ. Press, Cambridge, 2003.
pdf
Failure of Roth theorem for solvable groups of exponential growth
(jointly with A. Leibman),
Ergodic Theory and Dynamical Systems24 (2004), no. 1, 45-53.
pdf
Weakly mixing group actions: a brief survey and an example
(jointly with A. Gorodnik),
Modern dynamical systems and applications
3-25, Cambridge Univ. Press, Cambridge, 2004.
(Revised and updated version.)
pdf
Some historical comments and modern questions
around the Ergodic Theorem,
Dynamics of Complex Systems
1-11, Research Institute for Math. Sciences, Kyoto, 2004.
pdf
Polynomial Szemerédi theorem
for countable modules over integral domains and finite fields
(jointly with A. Leibman and R. McCutcheon),
Journal d'Analyse Mathematique95 (2005), 243-296.
pdf
Simultaneous Diophantine approximations and VIP systems
(jointly with I. Haaland and R. McCutcheon),
Acta Arithmetica
116 (2005), no. 1, 13-23.
pdf
Multiple recurrence and nilsequences
(jointly with B. Host and B. Kra,
with an appendix by I. Ruzsa),
Inventiones Mathematicae160 (2005), no. 2, 261-303.
pdf
Multiplicatively large sets and ergodic Ramsey theory,
Israel Journal of Mathematics148 (2005), 23-40.
pdf
Combinatorial and Diophantine Applications of Ergodic Theory
(with appendices by A. Leibman and by A. Quas and M. Wierdl),
Handbook of Dynamical Systems,
vol. 1B, B. Hasselblatt and A. Katok, eds., Elsevier, 2006, 745-841.
pdf
Piecewise-Bohr sets of integers and combinatorial number theory
(jointly with H. Furstenberg and B. Weiss),
Topics in Discrete Mathematics
(Dedicated to Jarik Nesetril on the occasion of his 60th birthday)
Springer, 2006, 13-37.
pdf
Ergodic Ramsey Theory: a dynamical approach to static theorems,
Proceedings of the International Congress of Mathematicians
Vol. II, 1655-1678, European Math. Society, Zurich, 2006.
pdf
Affine actions of a free semigroup on the real line
(jointly with M. Misiurewicz and S. Senti),
Ergodic Theory and Dynamamical Systems26 (2006), 1285-1305.
pdf
Multiplicative structures in additively large sets
(jointly with M. Beiglbock, N. Hindman and D. Strauss),
Journal of Combinatorial Theory (Ser. A)113 (2006), 1291-1242.
pdf
IP-systems, generalized polynomials and recurrence
(jointly with I.J. Haaland Knutson and R. McCutcheon),
Ergodic Theory and Dynamical Systems26 (2006), 1-21.
pdf
Central sets and a non-commutative Roth theorem
(jointly with R. McCutcheon),
American Journal of Mathematics129 (2007), no. 5, 1251-1275.
pdf
Mixing properties of noncommutative groups of automorphisms of compact groups
(jointly with A. Gorodnik),
Proceedings of London Math. Soc.95 (2007), no. 2, 329-359.
pdf
Distribution of values of bounded generalized polynomials
(jointly with A. Leibman),
Acta Mathematica198 (2007), 155-230.
pdf
Weyl complexity of a system of polynomials
and constructions in combinatorial number theory
(jointly with A. Leibman and E. Lesigne),
Journal D'Analyse Mathematique103 (2007), 47-92.
pdf
Large sets of integers and hierarchy of mixing
properties of measure-preserving systems
(jointly with T. Downarowicz),
Colloquium Mathematicum110 (2008), no. 1, 117-150.
pdf
Some new results in multiplicative and additive Ramsey Theory
(jointly with M. Beiglbock, N. Hindman and D. Strauss),
Transactions of AMS360 (2008) no. 2, 819-847.
pdf
Van der Corput sets in Z^{d}
(jointly with E. Lesigne),
Colloquium Mathematicum110 (2008), no. 1, 1-49.
pdf
Questions on amenability,
L'Enseignement Mathematique54 (2008), no. 2, 28-30.
pdf
Ledrappier's system is almost mixing of all orders
(jointly with L. Arenas and D. Berend),
Ergodic Theory and Dynamical Systems28 (2008), no. 2, 339-365.
pdf
Intersective polynomials and the polynomial Szemerédi theorem
(jointly with A. Leibman and E. Lesigne),
Advances in Mathematics219 (2008), 369-388.
pdf
Sumsets in difference sets
(jointly with I. Ruzsa),
Israel Journal of Mathematics174 (2009), 1-18.
pdf
Weak mixing implies weak mixing of higher orders along tempered functions
(jointly with I.J.H. Knutson),
Ergodic Theory and Dynamical Systems29 (2009), no.5, 1375-1416.
pdf
Solvability of Rado systems in D-sets
(jointly with H. Beiglbock, T. Downarowicz and A. Fish),
Topology and its Applications156 (2009) no.16, 2565-2571.
pdf
WM groups and Ramsey theory
(jointly with H. Furstenberg),
Topology and its Applications156 (2009), no.16, 2572-2580.
pdf
Idempotent ultrafilters, multiple weak mixing
and Szemerédi's theorem for generalized polynomials
(jointly with R. McCutcheon),
Journal D'Analyse Mathematique111 (2010) 77-130.
pdf
Sumset Phenomenon in Countable Amenable Groups
(jointly with M. Beiglbock and A. Fish),
Advances in Mathematics223 (2010), no. 2, 416-432.
pdf
Ultrafilters, IP sets, Dynamics, and Combinatorial Number Theory,
Contemporary Mathematics530 (2010), 23-47.
pdf
An inverse theorem for the uniformity seminorms
associated with the action of F^{ω}
(jointly with T. Tao and T. Ziegler),
GAFA19 (2010), 1539-1596.
pdf
Polynomials at iterated spectra near zero
(jointly with N. Hindman and D. Strauss),
Topology and its Applications158 (2011), 1815-1830.
pdf
The shifted primes and the multidimensional Szemerédi
and polynomial van der Waerden theorems
(jointly with A. Leibman and T. Ziegler),
C. R. Math. Acad. Sci. Paris349 (2011), no. 3-4, 123-125.
Arxiv
From discrete- to continuous-time ergodic theorems
(jointly with A. Leibman and C.G. Moreira),
Ergodic Theory and Dynamical Systems32 (2012), no.2, 383-426.
pdf
Quotient sets and density recurrent sets
(jointly with N. Hindman),
Transactions of AMS364 (2012), no. 9, 4495-4531.
pdf
Strongly central sets and sets of polynomial returns mod 1
(jointly with N. Hindman and D. Strauss),
Proceedings of AMS140 (2012), no. 8, 2671-2686.
pdf
Polynomial extensions of the Milliken-Taylor theorem
(jointly with N. Hindman and K. Williams),
Transactions of AMS366 (2014), no. 11, 5727-5748.
pdf
Rigidity and non-recurrence along sequences
(jointly with A. del Junco, M. Lemańczyk, J. Rosenblatt),
Ergodic Theory and Dynamical Systems34 (2014), no. 5, 1464-1502.
Arxiv
Multiple recurrence in quasirandom groups
(jointly with T. Tao),
Geometrical and Functional Analysis24 (2014), no. 1, 1-48.
pdf
Uniform distribution of prime powers and sets of recurrence
and van der Corput sets in Z^{k}
(jointly with G. Kolesnik, M. Madritsch, and Y. Son),
Israel Journal of Mathematics201 (2014), no. 2, 729-760.
pdf
Cubic averages and large intersections
(jointly with A. Leibman),
Recent trends in ergodic theory and dynamical systems, 5-19,
Contemporary Mathematics, 631, Amer. Math. Soc., Providence, RI, 2015.
pdf
Multiple recurrence and convergence results associated to F_{P}^{ω}-actions
(joint with T. Tao and T. Ziegler),
Journal D'Analyse Mathematique127 (2015), 329-378.
pdf
Simultaneous dense and nondense orbits for commuting maps
(jointly with M. Einsiedler and J. Tseng),
Israel Journal of Mathematics210 (2015), no. 1, 23-45.
pdf
A Weyl-type equidistribution theorem in finite characteristic
(jointly with A. Leibman),
Advances in Mathematics289 (2016), 928-950.
pdf
Finite products sets and minimally almost periodic groups
(jointly with J.C. Christopherson, D. Robertson, and P. Zorin-Kranich),
Journal of Functional Analysis270 (2016), no. 6, 2126-2167.
pdf
Van der Corput's difference theorem: some modern developments
(jointly with J. Moreira),
Indagationes Mathematicae (N.S.) 27 (2016), no. 2, 437-479.
pdf
Polynomial multiple recurrence over rings of integers
(jointly with D. Robertson),
Ergodic Theory and Dynamical Systems36 (2016), no. 5, 1354-1378.
pdf
Polynomial recurrence with large intersection over countable fields
(jointly with D. Robertson),
Israel Journal of Mathematics214 (2016), no. 1, 109-120.
pdf
Joint ergodicity along generalized linear functions
(jointly with A. Leibman and Y. Son),
Ergodic Theory and Dynamical Systems36 (2016), no. 7, 2044-2075.
pdf
New polynomial and multidimensional extensions of classical partition results
(jointly with J.H. Johnson and J. Moreira),
Journal of Combinatorial Theory Ser. A147 (2017), 119-154.
pdf
New examples of complete sets, with connections to a Diophantine theorem of Furstenberg
(jointly with D. Simmons),
Acta Arithmetica177 (2017), no. 2, 101-131.
pdf
Triangles in Cartesian squares of quasirandom groups
(jointly with D. Robertson and P. Zorin-Kranich),
Combininatorics, Probabability and Computing26 (2017), no. 2, 161-182.
pdf
Ergodic theorem involving additive and multiplicative groups of a field and {x+y, xy} patterns
(jointly with J. Moreira),
Ergodic Theory and Dynamical Systems37 (2017), no. 3, 673-692.
pdf
On the density of coprime tuples of the form(n,⌊f_{1}(n)⌋,...,⌊f_{k}(n)⌋),
wheref_{1},...,f_{k}are functions from a Hardy field
(jointly with F.K. Richter),
Number theory-Diophantine problems, uniform distribution and applications
109-135, Springer, 2017.
pdf
Sets of large values of correlation functions for polynomial cubic configurations
(jointly with A. Leibman),
Ergodic Theory and Dynamical Systems (published online in April 2016).
pdf
Measure preserving actions of affine semigroups and {x+y, xy} patterns
(jointly with J. Moreira),
Ergodic Theory and Dynamical Systems (published online in July 2016).
pdf
Multiplicative richness of additively large sets in Z^{d}
(jointly with D. Glasscock),
to appear in Journal of Algebra.
pdf
An almost mixing of all orders property of algebraic dynamical systems
(jointly with L. Arenas-Carmona and D. Berend),
Ergodic Theory and Dynamical Systems (published online in 2017).
pdf
Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics
(jointly with J. Kułaga-Przymus, M. Lemańczyk, and F.K. Richter),
Ergodic Theory and Dynamical Systems (published online in 2018).
pdf
Uniform distribution of subpolynomial functions along primes and applications
(jointly with G.Kolesnik and Y. Son),
to appear in Journal d'Analyse Mathematique.
pdf
Interplay between notions of additive and multiplicative largeness
(jointly with D. Glasskock).
Arxiv
IP_{r}^{*} recurrence and nilsystems
(jointly with A. Leibman).
Arxiv
A generalization of Kátai's orthogonality criterion with applications
(jointly with J. Kułaga-Przymus, M. Lemańczyk, and F. K. Richter).
Arxiv
A structure theorem for level sets of multiplicative functions and applications
(jontly with J. Kułaga-Przymus, M. Lemańczyk, and F. K. Richter).
Arxiv