Lior Fishman

Previous Scheduled Teaching

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.

Contracts, Grants and 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).