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Dr. Lior Fishman

Associate Professor

University of North Texas

Department of Mathematics

(940) 369-8145

Email: Lior.Fishman@unt.edu

Education

  • PhD, Ben-Gurion University of The Negev, 2009
    Major: Mathematics
    Specialization: Schmidt's game and fractals
  • MS, Bar Ilan University, 1995
    Major: Very small sets
  • BS, Bar Ilan University, 1993
    Major: Mathematics

Teaching

Teaching Experience

    University of North Texas

  • MATH 1650 - Pre Calculus, 1 course.
  • MATH 1710 - Calculus I, 3 courses.
  • MATH 1720 - Calculus II, 4 courses.
  • MATH 1780 - Probability Models, 1 course.
  • MATH 2000 - Discrete Mathematics, 2 courses.
  • MATH 2700 - Linear Algebra and Vector Geometry, 3 courses.
  • MATH 2730 - Multivariable Calculus, 1 course.
  • MATH 3000 - Real Analysis I, 9 courses.
  • MATH 3400 - Number Theory, 4 courses.
  • MATH 3410 - Differential Equations I, 2 courses.
  • MATH 3510 - Abstract Algebra I, 3 courses.
  • MATH 3996 - Honors College Mentored Research Experience, 2 courses.
  • MATH 4060 - Foundations of Geometry, 2 courses.
  • MATH 4500 - Introduction to Topology, 5 courses.
  • MATH 4520 - Introduction to Functions of a Complex Variable, 2 courses.
  • MATH 4900 - Special Problems, 15 courses.
  • MATH 4910 - Special Problems, 1 course.
  • MATH 4951 - Honors College Capstone Thesis, 2 courses.
  • MATH 5400 - Introduction to Functions of a Complex Variable, 2 courses.
  • MATH 5410 - Functions of a Complex Variable, 1 course.
  • MATH 5420 - COMPLEX VARIABLE, 1 course.
  • MATH 5600 - Introduction to Topology, 5 courses.
  • MATH 5610 - Topology., 2 courses.
  • MATH 5620 - Topology, 2 courses.
  • MATH 5900 - Special Problems, 19 courses.
  • MATH 5910 - Special Problems, 3 courses.
  • MATH 6110 - Topics in Analysis, 3 courses.
  • MATH 6220 - Logic and Dynamics Seminar, 7 courses.
  • MATH 6610 - Topics in Topology and Geometry, 1 course.
  • MATH 6900 - Special Problems, 12 courses.
  • MATH 6950 - Doctoral Dissertation, 24 courses.

Non-Credit Instruction

  • Other (Study and Research group), 7 participants. (May 2018).

Directed Student Learning

  • Postdoctoral Research Supervision, Mathematics. (August 2023).
  • Master's Thesis Committee Chair, Mathematics. (2023).
  • Dissertation Committee Chair, "TBA," Mathematics. (May 2022).
  • Dissertation Committee Co-Chair, "TBA," Mathematics. (May 2022).
  • Dissertation Committee Chair, "Waldschmidt's Conjecture," Mathematics. (May 2, 2018).
  • Undergraduate Honors Thesis, "Determinacy of the Banach Mazur game," Mathematics. (May 2021 - 2022).
  • Master's Thesis Committee Chair, "Conway’s External Steiner-Lehmus Bisector Theorem," Mathematics. (March 2021 - October 2022).
  • Master's Thesis Committee Chair, "The Banach Tarski paradox," Mathematics. (2021 - May 2022).
  • Master's Thesis Committee Chair, "Ulam's proof for non measurable sets," Mathematics. (2020 - May 2021).
  • Dissertation Committee Member, "Games and labeled tree homomorphisms," Mathematics. (2020).
  • Master's Thesis Committee Chair, "A topological proof of the Fundamental Theorem of Algebra," Mathematics. (2019 - 2020).
  • Undergraduate Honors Thesis, "The Urinal Problem," Mathematics. (2019 - 2020).
  • Dissertation Committee Co-Chair, "Determinacy of Schmidt's game and other intersection games," Mathematics. (May 2, 2016 - 2020).
  • Dissertation Committee Chair, "Winning sets and the Banach - Mazur - McMullen game," Mathematics. (May 2, 2017 - May 2020).
  • Dissertation Committee Co-Chair, "EQUIVALENCE OF THE ROTHBERGER AND 2-ROTHBERGER GAMES FOR HAUSDORFF SPACES," Mathematics. (May 2, 2016 - 2019).
  • Master's Thesis Committee Chair, "Determinacy and indeterminacy of certain games," Mathematics. (June 2, 2016 - May 2, 2017).
  • Master's Thesis Committee Chair, "The Banach Mazur Schmidt game and the Banach Mazur McMullen game," Mathematics. (June 2, 2015 - May 2, 2016).

Research

Published Intellectual Contributions

    Journal Article

  • Fishman, L., Urbanski, M., Das, T., Simmons, D. (2024). A variational principle in the parametric geometry of numbers. Advances in Mathematics. 437
  • Fishman, L., Das, T., Urbanski, M., Simmons, D. (2023). Hausdorff dimensions of perturbations of a conformal iterated function system via thermodynamic formalism. Selecta Mathematica. 29 (19) 56.
  • Fishman, L., Jackson, S.C., Crone, L. (2022). Equivalence Relations and Determinacy. Journal of Mathematical Logic. 22 (1) 19.
  • Fishman, L., Crone, L., Jackson, S.C. (2022). DETERMINACY OF SCHMIDT’S GAME AND OTHER INTERSECTION GAMES. The Journal of Symbolic Logic.
  • Fishman, L., Jackson, S.C., Crone, L. (2022). Hausdorff Dimension Regularity Properties and Games. Israel Journal of Mathematics. 248 (481–500)
  • Fishman, L., Kleinbock, D., Merrill, K., Simmons, D. (2021). Intrinsic Diophantine approximation on quadric hypersurfaces. Journal of the European Mathematical Society. 24 (3) 1045–1101.
  • Urbanski, M., Das, T., Fishman, L., Simmons, D. (2021). Extremality and Dynamically Defined Measures, Part II. Ergodic Theory and Dynamical Systems. 41 2311-2348.
  • Fishman, L., Crone, L., Hiers, N., Jackson, S.C. (2019). EQUIVALENCE OF THE ROTHBERGER AND 2-ROTHBERGER GAMES FOR HAUSDORFF SPACES. Topology and its Applications. 258 172-176.
  • Fishman, L., Broderick, R., Simmons, D. (2019). QUANTITATIVE RESULTS USING VARIANTS OF SCHMIDT’S GAME: DIMENSION BOUNDS, ARITHMETIC PROGRESSIONS, AND MORE. Acta Arithmetica. 188 289-316.
  • Urbanski, M., Das, T., Fishman, L., Simmons, D. (2019). Badly approximable points on self-affine sponges and the lower Assouad dimension. Ergodic Theory and Dynamical Systems. (39) 638-657.
  • Fishman, L., Merrill, K., Simmons, D. (2018). Hausdorff dimensions of very well intrinsically approximable subsets of quadratic hypersurfaces. Selecta Mathematica, New Series. 24 (5) 3875-3888.
  • Fishman, L., Merrill, K., Simmons, D. (2018). Intrinsic Diophantine approximation on manifolds: general theory. Transactions of the American Mathematical Society. 370 (1) 577-599.
  • Fishman, L., Merrill, K., Simmons, D. (2018). Uniformly de Bruijn sequences and symbolic Diophantine approximation on fractals. Annals of Combinatorics. 22 (2) 271-293.
  • Urbanski, M., Das, T., Fishman, L., Simmons, D. (2018). Badly approximable vectors and fractals defined by conformal dynamical systems. Mathematical Research Letters. 25 437--467.
  • Urbanski, M., Das, T., Fishman, L., Simmons, D. (2018). Extremality and Dynamically Defined Measures, Part I. Selecta Mathematica. 24 2165-2206.
  • Fishman, L., Urbanski, M., Das, T., Simmons, D. (2017). A variational principle in the parametric geometry of numbers, with applications to metric Diophantine approximation. Comptes Rendus Mathématique. 355 (8) 835-846.
  • Fishman, L., Broderick, R., Simmons, D. (2017). Decaying and non-decaying badly approximable numbers. Acta Arithmetica. 3513 143-152.
  • Fishman, L., Simmons, D. (2017). Unconventional height functions in simultaneous Diophantine approximation. Monatshefte für Mathematik. 182 (3) 587-618.
  • Fishman, L., Reams, V., Simmons, D. (2016). The Banach Mazur Schmidt game and the Banach Mazur McMullen game. Journal of Number Theory. 167 169-179.
  • Fishman, L., Simmons, D. (2016). Variations on Dirichlet's theorem. Journal of Number Theory. 162 11-22.

    • Monograph

  • Urbanski, M., Fishman, L., Simmons, D. (2018). Diophantine Approximation and the Geometry of Limit Sets in Gromov Hyperbolic Metric Spaces. Memoirs of the American Mathematical Society. 254 (Issue: 1215) 1-137. Memoirs of American Mathematical Society.

Presentations Given

    Invited Talk

  • Fishman, L. (Presenter), University of Houston - Colloquium talk., Intrinsic Approximation on Smooth Surfaces, University of Houston, Houston, United States of America. (2016 - 2016).
  • Fishman, L. (Presenter), University of Houston - Undergraduate colloquium talk., Mathematical Games, University of Houston, Houston, United States of America. (2016 - 2016).

Contracts, Grants, Sponsored Research

    Grant - Research

  • Fishman, L. (Principal), "Diophantine Approximation," sponsored by Simons Foundation, Private, $35000 Funded. (2012 - 2017).
  • Fishman, L. (Principal), "Diophantine Approximation," sponsored by Simons Foundation, Private, Funded. (2012 - 2017).
  • Fishman, L. (Principal), Gao, S. (Principal), "Diophantine Approximation on Fractals," sponsored by Simons Foundation, FOND, Funded. (2012 - 2017).

    • Grant - Teaching

  • Fishman, L., "The Incubator project," sponsored by UNT, University of North Texas, $20000 Funded. (2020 - 2020).

Service

University Service

  • Chairperson, Library liaison. (2023 - Present).
  • Committee Member, Ricco Ethics committee. (2023 - Present).
  • Committee Member, Search Committee. (2023 - Present).
  • Member, Undergraduate committee. (2021 - Present).
  • Other (Initiator and organizer (with Dr. Kawamura)), STaRS seminar. (2020 - Present).
  • Member, Real Analysis Qualification Exam. (2018 - Present).
  • Chairperson, Post Doc Hiring. (November 2021 - January 2022).
  • Chairperson, Faculty Search Committee. (November 2020 - January 2021).
  • Other (Organizer), Millican. (2019 - 2020).
  • Member, Executive Committee. (2018 - 2019).
  • Member, Graduate Affairs committee. (2018 - 2019).
  • Member, Search committee joint CS. (2018 - 2018).
  • Member, Search committee Logic and Set Theory. (2018 - 2018).
  • Member, Strategic Planning. (2018 - 2018).
  • Member, Topology Qualification. (2016 - 2018).

Professional Service

  • Committee Member, Conference in honor of Prof. Urbanski's 60th birthday. Warsaw, (April 2019 - April 2019).