Lior Fishman | Department of Mathematics

COVID-19 updates—In an effort to keep everyone healthy, UNT's on-campus operations are closed until further notice. We're serving students remotely. Please stay connected. Stay up to date on UNT’s response to COVID-19 (Coronavirus).

Have you registered for fall classes yet? While COVID-19 has created some uncertainty for us all, UNT is committed to helping the Mean Green family turn dreams into reality. Let's get through this together!

Register for classes on my.unt.edu
Not a UNT student yet? Apply to UNT
Having trouble registering? Get help from an advisor

Lior Fishman

Research

Published and accepted:

  1. 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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

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

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

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

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

  15. Variations on Dirichlet's theorem
    With: D. Simmons
    J. Number Theory, 162 (2016), 11-22
  16. 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

  17. 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
  18. Extrinsic Diophantine approximation on manifolds and fractals
    With: D. Simmons
    J. Math. Pures Appl. (9) 104 (2015), no. 1, 83-101
  19. Determinacy and indeterminacy of games played on complete metric spaces
    With: T. Ly and D. Simmons
    Bull. Aust. Math. Soc. 90 (2014), 339-351
  20. Diophantine approximation in Banach spaces
    With: D. Simmons and M. Urbanski
    J. Theor. Nombres Bordeaux 26 (2014), no. 2, 363-384
  21. 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
  22. Diophantine properties of measures invariant with respect to the Gauss map
    With: D. Simmons and M. Urbanski
    J. Anal. Math. 122 (2014), 289-315
  23. 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
  24. 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
  25. 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
  26. 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
  27. 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
  28. Diophantine approximations on fractals
    With: M. Einsiedler and U. Shapira
    Geom. Funct. Anal., 21 (2011), no. 1,14-35
  29. Schmidt's game, Badly Approximable Matrices and Fractals
    J. Number Theory, 129 (2009), no. 9, 2133-2153
  30. Schmidt's Game on Fractals
    Israel J. Math., 171 (2009), 77-92
  31. 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. Intrinsic Diophantine approximation on quadric hypersurfaces
    With: D. Kleinbock, K. Merrill and D. Simmons
  4. Determinacy of Schmidt's game and other intersection games
    With: L. Crone and S. Jackson

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

  6. Equivalence Relations and Determinacy
    With: L. Crone and S. Jackson

  7. Hausdorff Dimension Regularity Properties and Games
    With: L. Crone and S. Jackson

Thinking about UNT?

It's easy to apply online. Join us and discover why we're the choice of over 38,000 students.

Apply now