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
    • 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
    • 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 

    • Beta Cantor series expansion and admissible sequences (with S. Demegillo), Acta Polytechnica vol. 60, no. 3 (2020) 214 – 224. pdf

    • 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

    • Corona Limit of Tilings: Periodic Case (with S. Akiyama, K. Imai, H. Kaneko), Discrete Comput. Geom. 61 (2019) 626-652. pdf
    • On the Lie algebra associated to \(S\)-unitary matrices (with C. Canlubo, and Y. Tanaka), Linear Algebra Appl. 553 (2018), 167–181. pdf
    • Invariant measure of rotational beta expansion and Tarski’s plank problem (with S. Akiyama), Discrete Comput. Geom. 57 (2017), no. 2, 357–370. pdf
    • Rotational beta expansion: Ergodicity and Soficness (with Akiyama), J. Math Soc. Japan 69 (2017), no. 1, 395–413. pdf