Home / Faculty / Caalim, Jonathan

Caalim, Jonathan

Associate Professor
Email Addressjcaalim@math.upd.edu.ph
RoomMath Building 247
Research Interests
Number theory. Numeration systems. Mathematical tilings.
Academic Groups
  • Education
    • Doctor of Philosophy in Mathematics
      University of Tsukuba

      Dissertation: Rotational beta expansion

    • Master's in Mathematics
      University of the Philippines Diliman

      Thesis: On \(\theta\)-congruent numbers, elliptic curves and quadratic fields

    • Bachelors of Science in Mathematics, cum laude
      University of the Philippines Diliman
  • Publications
    1. Periodic quaternion expansion in Pisot bases (with N. Nollen), Osaka Journal of Mathematics vol 63 no. 1 (2026) 123 – 140. pdf
    2. Rotational beta expansions and Schmidt games (with H. Knaeko, N. Nollen), Acta Mathematica Hungarica vol 176 (2025) 400 – 436. pdf
    3. Lexicographically Minimal Extension of a Finite Binomid Index (with Y. Tanaka), Integers: Electronic Journal of Combinatorial Number Theory vol 24 (2024). pdf
    4. Real dimension of the Lie algebra of S-skew Hermitian matrices (with Y. Tanaka), Electronic Journal of Linear Algebra vol 38 (2022) 49 – 62.  pdf
    5. 2n-by-2n symplectic completions of matrices of order 2n−1 (with R. J. de la Cruz), Asian-European Journal of Mathematics vol. 14 no. 4 (2021). pdf 
    6. Beta Cantor series expansion and admissible sequences (with S. Demegillo), Acta Polytechnica vol. 60, no. 3 (2020) 214 – 224. pdf
    7. Isometric and selfadjoint operators on a vector space with nondegenerate diagonalizable form (with V. Futorny, V. Sergeichuk, and Y. Tanaka), Linear Algebra Appl. 587 (2020) 92-110. arXiv
    8. Corona Limit of Tilings: Periodic Case (with S. Akiyama, K. Imai, H. Kaneko), Discrete Comput. Geom. 61 (2019) 626-652. pdf
    9. On the Lie algebra associated to \(S\)-unitary matrices (with C. Canlubo, and Y. Tanaka), Linear Algebra Appl. 553 (2018), 167–181. pdf
    10. Invariant measure of rotational beta expansion and Tarski’s plank problem (with S. Akiyama), Discrete Comput. Geom. 57 (2017), no. 2, 357–370. pdf
    11. Rotational beta expansion: Ergodicity and Soficness (with Akiyama), J. Math Soc. Japan 69 (2017), no. 1, 395–413. pdf