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Caalim, Jonathan

Associate Professor

jcaalim@math.upd.edu.ph

Math Building 247

Research Interests
Number theory. Numeration systems. Mathematical tilings.

Academic Groups

Discrete Geometry and Combinatorics (member)
Coding and Number Theory (affiliate)

Education
- Doctor of Philosophy in Mathematics
  University of Tsukuba
  Dissertation: Rotational beta expansion
- Master's in Mathematics
  University of the Philippines Diliman
  Thesis: On $θ$ -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- symplectic completions of matrices of order
- 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