Lior Fishman | Department of Mathematics
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Lior Fishman

Research

Published and accepted:

  1. Determinacy of Schmidt's game and other intersection games
    With: L. Crone and S. Jackson
    To be published in J. Symb. Log.

  2. Equivalence Relations and Determinacy
    With: L. Crone and S. Jackson
    Tobe published in J. Math. Log.

  3. Hausdorff Dimension Regularity Properties and Games
    With: L. Crone and S. Jackson
    To be published: Israel J. Math

  4. Intrinsic Diophantine approximation on quadric hypersurfaces
    With: D. Kleinbock, K. Merrill and D. Simmons
    To be published: J. Eur. Math. Soc. (JEMS)

  5. Equivalence of the Rothberger and 2-Rothberger games for Hausdorff spaces
    With: L. Crone, N. Hiers and S. Jackson
    Topology Appl., 258, (2019), 172-176

  6. Extremality and dynamically defined measures, part II: Measures from conformal dynamical systems
    With: T. Das, D. Simmons and M. Urbanski
    To be published: Ergodic Theory Dynam. Systems

  7. Badly approximable points on self-affine sponges and the lower Assouad dimension
    With: T. Das, D. Simmons and M. Urbanski
    Ergodic Theory Dynam. Systems, 39, Issue 3, (2019), 638-657

  8. Quantative results using variants of Schmidt's game: dimension bounds, arithmetic progressions and more
    With: R. Broderick and D. Simmons
    Acta. Arith. 188 (2019) , 289-316

  9. Hausdorff dimensions of very well intrinsically approximable subsets of quadratic hypersurfaces
    With: K. Merrill and D. Simmons
    Sel. Math. Volume 24, Issue 5, (2018), 3875-3888

  10. 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), 835-846

  11. Extremality and dynamically defined measures, part I: Diophantine properties of quasi-decaying measures
    With: T. Das, D. Simmons and M. Urbanski
    Sel. Math. New Ser., 24, (2018) 2165-2206

  12. Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces
    With: D. Simmons and M. Urbanski
    Mem. Amer. Math. Soc., vol. 254, no 1215 (2018), 137 pg

  13. Badly approximable vectors and fractals defined by conformal dynamical systems
    With: T. Das, D. Simmons and M. Urbanski
    Math. Res. Lett., 25, No. 2 (2018), 437-467

  14. Intrinsic Diophantine approximation on manifolds: general theory
    With: D. Kleinbock, K. Merrill and D. Simmons
    Trans. Amer. Math. Soc., 370, No. 1 (2018), 577-599

  15. Uniformly de Bruijn sequences and symbolic Diophantine approximation on fractals
    With: K. Merrill and D. Simmons
    ​Ann. Comb., 22 (2018), no. 2, 271-293

  16. Decaying and non-decaying badly approximable numbers
    With: R. Broderick and D. Simmons
    Acta. Arith., 3513 (2017), 143-152

  17. Unconventional height functions in simultaneous Diophantine approximation
    With: D. Simmons
    Monatsh. Math., 182 (2017), no. 3, 587-618

  18. The Banach Mazur Schmidt game and the Banach Mazur McMullen game
    With: V. Reams and D. Simmons
    J. Number Theory, 167 (2016), 169-179

  19. Variations on Dirichlet's theorem
    With: D. Simmons
    J. Number Theory, 162 (2016), 11-22

  20. 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, 205-213

  21. Rigidity of limit sets for nonplanar geometrically finite Kleinian groups of the second kind
    With: D. Simmons and M. Urbanski
    Geom. Dedicata 178, (2015), 95-101
  22. Extrinsic Diophantine approximation on manifolds and fractals
    With: D. Simmons
    J. Math. Pures Appl. (9) 104 (2015), no. 1, 83-101
  23. Determinacy and indeterminacy of games played on complete metric spaces
    With: T. Ly and D. Simmons
    Bull. Aust. Math. Soc. 90 (2014), 339-351
  24. Diophantine approximation in Banach spaces
    With: D. Simmons and M. Urbanski
    J. Theor. Nombres Bordeaux 26 (2014), no. 2, 363-384
  25. 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, 189-212
  26. Diophantine properties of measures invariant with respect to the Gauss map
    With: D. Simmons and M. Urbanski
    J. Anal. Math. 122 (2014), 289-315
  27. Badly Approximable Systems of Affine Forms and Incompressibility on Fractals
    With: R. Broderick and D. Simmons
    J. Number Theory 133 (2013), no. 7, 2186-2205
  28. 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, 319-339
  29. Intrinsic Approximation on Cantor-like Sets, a Problem of Mahler
    With: R. Broderick and A. Reich
    Mosc. J. Comb. Number Theory, 1 (2011) no.4, 3-12
  30. Schmidt's game, fractals, and orbits of toral endomorphisms
    With: R. Broderick and D. Kleinbock
    Ergodic Theory Dynam. Systems, 31 (2011), no 4, 1095-1107
  31. 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, 307-321
  32. Diophantine approximations on fractals
    With: M. Einsiedler and U. Shapira
    Geom. Funct. Anal., 21 (2011), no. 1,14-35
  33. Schmidt's game, Badly Approximable Matrices and Fractals
    J. Number Theory, 129 (2009), no. 9, 2133-2153
  34. Schmidt's Game on Fractals
    Israel J. Math., 171 (2009), 77-92
  35. Very Small Sets
    With: H. Judah and I. Reclaw
    Colloq. Math., 72 (1998), no. 2, 207-213

Submitted:

  1. A Variational principle in the parametric geometry of numbers
    With: T. Das, D. Simmons and M. Urbanski

  2. Hausdorff dimensions of perturbations of a conformal iterated function system via thermodynamic formalism
    With: T. Das, D. Simmons and M. Urbanski

  3. The Measure game
    With: L. Crone and S. Jackson