Papers and Preprints
Problems on infinite sumset configurations in the integers and beyond. pdf
Strong Approximations of Shifts and the Characteristic Measures Problem.
pdf
A proof of Erdős's B+B+t conjecture. pdf
Infinite sumsets in sets with positive density. pdf
Characteristic measures for language stable subshifts. pdf
joint with V. Cyr.
Monatsh. Math. 201 (2023), no. 3, 659-701.
The complexity threshold for the emergence of Kakutani inequivalence. pdf
Boshernitzan's condition, factor complexity, and an application. pdf
joint with V. Cyr.
Proc. Amer. Math. Soc. Ser. B 9 (2022), 95-110.
The stabilized automorphism group of a subshift. pdf
Realizing ergodic properties in zero entropy subshifts. pdf
joint with V. Cyr.
Israel J. Math. 240 (2020), no. 1, 119-148.
A prime system with many self-joinings. pdf
joint with J. Chaika.
J. Mod. Dyn. 17 (2021), 213-265.
Polygonal Z^2-subshifts. pdf
joint with J. Franks.
Proc. Lond. Math. Soc. (3) 121 (2020), no. 2, 252-286.
Equidistribution of dilated curves on nilmanifolds pdf
joint with N. Shah and W. Sun.
J. Lond. Math. Soc. (2) 98 (2018), no.3, 708-732.
The automorphism group of a shift
of slow growth is amenable. pdf
joint with V. Cyr.
Ergodic Theory Dynam. Systems 40 (2020), no. 7, 1788-1804.
Distortion and the automorphism group of a shift. pdf
The spacetime of a shift automorphism. pdf
joint with V. Cyr and J. Franks.
Trans. Amer. Math. Soc. 371 (2019), no 1, 461-488.
Free ergodic Z^2-systems and complexity. pdf
joint with V. Cyr. Proc.
Amer. Math. Soc. 145 (2017), no. 3, 1163-1173.
The automorphism group of a minimal shift of stretched exponential growth.
pdf
joint with V. Cyr. J. Mod. Dyn. 10 (2016) 483-495.
Counting generic measures for a subshift of linear growth. pdf
joint with V. Cyr. J. Eur. Math. Soc. (JEMS) 21 (2019), no 2, 355-380.
The automorphism group of a shift of linear growth: beyond transitivity. pdf
joint with V. Cyr.
Forum Math. Sigma 3 (2015), (27 pages).
Complexity and directional entropy in two dimensions. pdf
joint with R. Broderick and V. Cyr. Israel J. Math. 215 (2016), no. 1, 135-162.
Variations on topological recurrence. pdf
joint with B. Host and A. Maass. Monatsh. Math. 179 (2016), no. 1, 57-89.
The automorphism group of a shift of subquadratic growth. pdf
joint with V. Cyr. Proc. Amer. Math. Soc. 144 (2016), no. 2, 613-621.
Complexity of short rectangles and periodicity. pdf
joint with V. Cyr. European J. Combin. 52 (2016), part A, 146-173.
Rudolph's two step coding
theorem and Alpern's lemma R^d actions. pdf
joint with A. Quas
and A. Şahin.
Trans. Amer. Math. Soc. 367 (2015), no. 6, 4253-4285.
Nonexpansive Z^2-subdynamics
and Nivat's conjecture. pdf
joint with V. Cyr Trans. Amer. Math. Soc. 367 (2015), no. 9, 6487-6537.
Giving a talk. pdf
Notices Amer. Math. Soc. 60 (2013), 242-244.
Complexity of Nilsystems and systems lacking nilfactors. pdf
joint with B. Host and A. Maass. J. Anal. Math. 124 (2014) 261-295.
A point of view on Gowers
uniformity norms. pdf
joint with B. Host. New York J.
Math., 18 (2012), 213-248.
The polynomial multidimensional
Szemeredi theorem along shifted primes. pdf
Poincare recurrence
and number theory: thirty years later. pdf
Bull. Amer. Math. Soc. 48 (2011), 497-501.
Nil-Bohr Sets of Integers. pdf
joint with B. Host. Erg. Th. Dyn. Sys. 31 (2011),
113-142.
Nilsequences and a structure theorem for topological dynamical systems. pdf
joint with B. Host and A. Maass. Adv. in Math. 224 (2010), 103-129.
Uniformity seminorms on
l-infinity and applications. pdf
joint with B. Host. J. Anal. Math. 108 (2009),
219-276.
Analysis of two step
nilsequences. pdf
joint with B. Host. Ann. Inst. Fourier 58 (2008),
1407-1453.
Ergodic methods in additive
combinatorics. pdf
Additive combinatorics, 103, CRM Proc. Lecture Notes, 43, Amer. Math. Soc., Providence, RI, 2007.
Multiple
recurrence and convergence for sequences related to the prime
numbers. pdf
Parallelepipeds, nilpotent
groups, and Gowers norms. pdf
joint with B. Host. Bull. Soc. Math. France 136 (2008), 405-437
From combinatorics to
ergodic theory and back again. pdf
Proceedings of International Congress of
Mathematicians, Madrid 2006, volume III, 57-76.
Ergodic averages for
independent polynomials and applications. pdf
The Green-Tao Theorem on
arithmetic progressions in the primes: an ergodic point of view.
pdf
Bull. Amer. Math. Soc., 43
(2006), 3-23.
This is a revised version
of the write up for the
Special Session on current events at the annual meeting of the AMS
Multiple recurrence and nilsequences. pdf
joint with V. Bergelson
and B. Host, with an appendix by I. Rusza.
Inventiones Math., 160, 2, (2005) 261-303.
The original publication is
available
here
Convergence
of
multiple
ergodic averages for some commuting transformations.
pdf
Polynomial
averages converge to the product of integrals.
pdf
Convergence
of Polynomial ergodic averages. pdf
joint with B.
Host. Israel J. Math., 149 (2005) 1-19.
Nonconventional
ergodic averages and nilmanifolds.
pdf
joint with B.
Host. Annals of Math. 161, 1 (2005) 397-488.
Averaging
along cubes. pdf
joint with B.
Host. In Modern Dynamical Systems and Applications, Cambridge
University Press, 2004.
An
Odd Furstenberg-Szemeredi Theorem
and quasi-affine systems. pdf
joint with B.
Host. J. D'Analyse., 86 (2002), 183-220.
Diophantine numbers,
dimension
and
Denjoy maps. pdf
joint
with J. Schmeling. Acta Arith., 105 (2002), 323-340.
Convergence of Conze-Lesigne
Averages. pdf
joint with B.
Host. Erg. Th. & Dyn.
Sys., 21 (2001), 493-509.
A Generalization of
Furstenberg's Diophantine
result. pdf
Proc.
Amer. Math. Soc., 127, 7 (1999) 1951-1956.
The conjugating map for
commutative
groups of circle diffeomorphisms.
pdf
Israel
J. Math., 93 (1996) 303-316. erratum
Iterated Spectra of Numbers
- Elementary,
Dynamical, and Algebraic Approaches. pdf
Nilpotent Structures in Ergodic Theory
Bernard Host and Bryna Kra, Mathematical Surveys and Monographs, Volume 235, American Mathematical Society, 2018