Dr. Lior Fishman
University of North Texas
Mathematics
(940) 369-8145
Email:

Education

PhD, Ben Gurion University, 2009.
Major: 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 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, 8 courses.
MATH 3400, Number Theory, 3 courses.
MATH 3510, Abstract Algebra I, 3 courses.
MATH 3996, Honors College Mentored Research Experience, 1 course.
MATH 4060, Foundations of Geometry, 1 course.
MATH 4500, Introduction to Topology, 4 courses.
MATH 4520, Introduction to Functions of a Complex Variable, 2 courses.
MATH 4900, Special Problems, 14 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, 4 courses.
MATH 5610, Topology., 2 courses.
MATH 5620, Topology, 2 courses.
MATH 5900, Special Problems, 17 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, 10 courses.
MATH 6950, Doctoral Dissertation, 21 courses.

Non-Credit Instruction

Other, 7. (May 2018 – Present).

Directed Student Learning

Dissertation Committee Chair,"TBA," Mathematics. (May 2022 – Present).

Dissertation Committee Co-Chair,"TBA," Mathematics. (May 2022 – Present).

Dissertation Committee Chair,"Waldschmidt's Conjecture," Mathematics. (May 2, 2018 – Present).

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., 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 and Sponsored Research

Grant - Research
Fishman, L. (Principal), "Diophantine Approximation," Sponsored by Simons Foundation, Private, $35000 Funded. (2012 – 2017).
Grant - Teaching
Fishman, L., "The Incubator project," Sponsored by UNT, University of North Texas, $20000 Funded. (2020 – 2020).

Service

University Service

Member, Undergraduate committee. (2021 – Present).

Other, 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, 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).