Research
Published and accepted:

Badly approximable points on selfaffine sponges and the lower Assouad dimension
With: T. Das, D. Simmons and M. Urbanski
To be published in Ergodic Theory Dynam. Systems 
A variational principle in the parametric geometry of numbers, with applications to metric Diophantine approximation
With: T. Das, D. Simmons and M. Urbanski
C. R. Math. Acad. Sci. Paris, 365, Issue 8 (2017), 835846 
Extremality and dynamically defined measures, part I: Diophantine properties of quasidecaying measures
With: T. Das, D. Simmons and M. Urbanski
To be published in Sel. Math. New Ser. 
Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces
With: D. Simmons and M. Urbanski
To be published in Mem. Amer. Math. Soc. 
Badly approximable vectors and fractals defined by conformal dynamical systems
With: T. Das, D. Simmons and M. Urbanski
To be published in Math. Res. Lett. 
Intrinsic Diophantine approximation on manifolds: general theory
With: D. Kleinbock, K. Merrill and D. Simmons
Trans. Amer. Math. Soc., 370, No. 1 (2018), 577599 
Uniformly de Bruijn sequences and symbolic Diophantine approximation on fractals
With: K. Merrill and D. Simmons
To be published in Ann. Comb. 
Decaying and nondecaying badly approximable numbers
With: R. Broderick and D. Simmons
Acta. Arith., 3513 (2017), 143152 
Unconventional height functions in simultaneous Diophantine approximation
With: D. Simmons
Monatsh. Math., 182 (2017), no. 3, 587618 
The Banach Mazur Schmidt game and the Banach Mazur McMullen game
With: V. Reams and D. Simmons
J. Number Theory, 167 (2016), 169179  Variations on Dirichlet's theorem
With: D. Simmons
J. Number Theory, 162 (2016), 1122 
Shrinking targets for nonautonomous dynamical systems corresponding to Cantor series expansions
With: B. Mance, D. Simmons and M. Urbanski
Bull. Aust. Math. Soc., 92 (2015), no. 2, 205213  Rigidity of limit sets for nonplanar geometrically finite Kleinian groups of the second kind
With: D. Simmons and M. Urbanski
Geom. Dedicata 178, (2015), 95101  Extrinsic Diophantine approximation on manifolds and fractals
With: D. Simmons
J. Math. Pures Appl. (9) 104 (2015), no. 1, 83101  Determinacy and indeterminacy of games played on complete metric spaces
With: T. Ly and D. Simmons
Bull. Aust. Math. Soc. 90 (2014), 339351  Diophantine approximation in Banach spaces
With: D. Simmons and M. Urbanski
J. Theor. Nombres Bordeaux 26 (2014), no. 2, 363384  Intrinsic approximation for fractals defined by rational iterated function systems  Mahler's research suggestion
With: D. Simmons
Proc. Lond. Math. Soc. (3) 109 (2014), no. 1, 189212  Diophantine properties of measures invariant with respect to the Gauss map
With: D. Simmons and M. Urbanski
J. Anal. Math. 122 (2014), 289315  Badly Approximable Systems of Affine Forms and Incompressibility on Fractals
With: R. Broderick and D. Simmons
J. Number Theory 133 (2013), no. 7, 21862205  The set of badly approximable vectors is strongly C^1 incompressible
With: R. Broderick, D. Kleinbock, A. Reich and B. Weiss
Math. Proc. Cambridge Philos. Soc., 153 (2012), no 2, 319339  Intrinsic Approximation on Cantorlike Sets, a Problem of Mahler
With: R. Broderick and A. Reich
Mosc. J. Comb. Number Theory, 1 (2011) no.4, 312  Schmidt's game, fractals, and orbits of toral endomorphisms
With: R. Broderick and D. Kleinbock
Ergodic Theory Dynam. Systems, 31 (2011), no 4, 10951107  Schmidt's game, fractals, and numbers normal to no base
With: R. Broderick, Y. Bugeaud, D. Kleinbock and B. Weiss
Math. Res. Lett., 17 (2010), no. 2, 307321  Diophantine approximations on fractals
With: M. Einsiedler and U. Shapira
Geom. Funct. Anal., 21 (2011), no. 1,1435  Schmidt's game, Badly Approximable Matrices and Fractals
J. Number Theory, 129 (2009), no. 9, 21332153  Schmidt's Game on Fractals
Israel J. Math., 171 (2009), 7792  Very Small Sets
With: H. Judah and I. Reclaw
Colloq. Math., 72 (1998), no. 2, 207213
Submitted:
 Extremality and dynamically defined measures, part II: Measures from conformal dynamical systems
With: T. Das, D. Simmons and M. Urbanski 
Equivalence of the Rothberger and 2Rothberger games for Hausdorff spaces
With: L. Crone and S. Jackson  Hausdorff dimensions of very well intrinsically approximable subsets of quadratic hypersurfaces
With: K. Merrill and D. Simmons  Intrinsic Diophantine approximation on quadric hypersurfaces
With: D. Kleinbock, K. Merrill and D. Simmons 
Quantative results using variants of Schmidt's game: dimension bounds, arithmetic progressions and more
With: R. Broderick and D. Simmons 
Determinacy of Schmidt's game and other intersection games
With: L. Crone and S. Jackson