Publications

41

An application of algebraic number theory to higher dimensional Steinhaus problems (with R. Roeder), preprint

40

Deviations of ergodic averages for linearly repetitive cut and project sets (with A. Julien, H. Koivusalo, J. Walton), preprint

39

Bounded remainder sets for rotations on the Adelic torus (with J. Furno, H. Koivusalo), submitted

38

Higher dimensional Steinhaus and Slater problems via homogeneous dynamics (with J. Marklof), submitted

37

A characterization of linearly repetitive cut and project sets (with H. Koivusalo, J. Walton), Nonlinearity, to appear

36

Statistics of patterns in typical cut and projects sets (with A. Julien, H. Koivusalo, J. Walton), Ergodic Theory Dyn. Syst., to appear

35

A measure theoretic result for approximation by Delone sets (with M. Baake), book chapter, to appear in AMS Contemporary Mathematics

34

Sums of reciprocals of fractional parts and multiplicative Diophantine approximation (with V. Beresnevich, S. Velani), monograph, Mem. Amer. Math. Soc., to appear

33

Averaging almost periodic functions along exponential sequences (with M. Baake, D. Lenz), book chapter, to appear in Aperiodic Order, vol II

32

Perfectly ordered quasicrystals and the Littlewood Conjecture (with H. Koivusalo, J. Walton), Trans. Amer. Math. Soc., to appear

31

A randomized version of the Littlewood conjecture (with H. Koivusalo), J. Number Theory, J. Number Theory 178 (2017), 201-207.

30

Constructing bounded remainder sets and cut-and-project sets which are bounded distance to lattices, II (with M. Kelly, H. Koivusalo), Indag. Math. 28 (2017), 138-144

29

Gaps problems and frequencies of patches in cut and project sets (with H. Koivusalo, L. Sadun, J. Walton), Math. Proc. Cambridge Philos. Soc. 161 (2016), no. 1, 65-85

28

Open problems and conjectures related to the theory of mathematical quasicrystals (with F. Adiceam, D. Damanik, F. Gahler, U. Grimm, A. Julien, A. Navas, L. Sadun, B. Weiss), Arnold Math. J. 2 (2016), no. 4, 579-592

27

Hankel determinants of zeta values (with W. Zudilin), Symmetry, Integrability and Geometry: Methods and Applications 11 (2015)

26

Constructing bounded remainder sets and cut-and-project sets which are bounded distance to lattices (with H. Koivusalo), Israel J. Math. 212 (2016), no. 1, 189-201

25

Equivalence classes of codimension one cut-and-project nets, Ergodic Theory Dynam. Systems 36 (2016), no. 3, 816-831

24

Projective metric number theory (with A. Ghosh), J. Reine Angew. Math. 712 (2016), 39-50

23

Diophantine approximation and coloring (with S. Munday), Amer. Math. Monthly 122 (2015), no. 6, 567-580

22

Equivalence relations on separated nets arising from linear toral flows (with M. Kelly, B. Weiss), Proc. Lond. Math. Soc. (3) 109 (2014), no. 5, 1203-1228

21

Deformation quantization and irrational numbers (with E. Hawkins), J. Symplectic Geom. 12 (2014), no. 1, 1-22

20

Quantitative ergodic theorems for weakly integrable functions, Ergodic Theory Dyn. Syst. 34 (2014), no. 2, 534-542

19

Group automorphisms with prescribed growth of periodic points, and small primes in arithmetic progressions in intervals (with C. White), Adv. Math. 252C (2014), 572-585

18

Metrical musings on Littlewood and friends (with J. L. Jensen, S. Kristensen), Proc. Amer. Math. Soc. 142 (2014), no. 2, 457-466

17

Density of orbits of semigroups of endomorphisms acting on the Adeles (with S. Munday), New York J. Math. 19 (2013), 443-454

16

The mixed Littlewood conjecture for pseudo-absolute values (with S. Harrap), Math. Ann. 357 (2013), no.3, 942-960

15

The Duffin-Schaeffer Conjecture with extra divergence II (with V. Beresnevich, G. Harman, S. Velani), Math Z. 275 (2013), no.1-2, 127-133

14

Multiplicative zero-one laws and metric number theory (with V. Beresnevich, S. Velani), Acta. Arith. 160 (2013), no.2, 101-114

13

Incomplete Kloosterman sums and multiplicative inverses in short intervals (with T. D. Browning), Int. J. Number Theory 9 (2013), no.2, 481-486

12

The Duffin-Schaeffer Conjecture with extra divergence (with A. Pollington, S. Velani), Math. Ann. 353 (2012), no.2, 259-273

11

Inhomogeneous approximation by coprime integers, New York J. Math. 18 (2012) 249-259

10

Metric considerations concerning the mixed Littlewood Conjecture (with Y. Bugeaud, S. Velani), Int. J. Number Theory 7 (2011), no. 3, 593-609

9

A note on Farey fractions with denominators in arithmetic progressions (with D. Badziahin), Acta. Arith. 147 (2011), no.3, 205-215

8

Numerators of differences of nonconsecutive Farey fractions, Int. J. Number Theory 6 (2010), no.3, 1-12

7

The metric theory of p-adic approximation, Int. Math. Res. Not. 2010, no.1, 18-52

6

Intermediate convergents and a metric theorem of Khinchin, Bull. Lond. Math. Soc. 41 (2009), 396-410

5

The group ring of Q/Z and an application of a divisor problem (with K. Homma), Proc. Amer. Math. Soc. 137 (2009), 1285-1293

4

Martingale differences and the metric theory of continued fractions (with J. Vaaler), Illinois J. Math. 52 (2008), no.1, 213-242

3

Tools and techniques in Diophantine approximation, thesis, University of Texas at Austin (2006), 154pp

2

The distribution of special subsets of the Farey sequence, J. Number Theory 107 (2004), no.1, 95-104

1

A note on Farey fractions with odd denominators, J. Number Theory 98 (2003), no.1, 89-104