Dr. John Vincent S. Morales
Associate Professor
Educational Background
PhD in Information Science,
Tohoku University, Japan
MS in Mathematics,
De La Salle University
Bachelor of Secondary Education major in Mathematics,
De La Salle University
I am mostly interested in algebraic combinatorics and representation theory. I look into objects such as graphs or association schemes and study them using tools available from linear and abstract algebras. I analyze association schemes based on their related algebras (e.g., Bose–Mesner algebra, Terwilliger algebra, and quantum adjacency algebra). I am interested on determining whether or not a certain Terwilliger algebra, for example, supports a structure of some classical or non-classical Lie algebra. If a Lie algebra can be embedded in a graph’s Terwilliger algebra, the information can be applied to codes and designs.
I finished Ph.D. in Information Science at Tohoku University in Sendai, Japan. My dissertation is on extensions of commutative association schemes. I finished Master of Science in Mathematics at De La Salle University. I finished Bachelor of Secondary Education major in Mathematics at De La Salle University and I also graduated cum laude.
For my research works, I focus on Terwilliger algebras of some graphs or association schemes and explore whether a classical or non-classical Lie algebra can be embedded on that Terwilliger algebra. Recently, I devote my time to exploring the special orthogonal Lie algebra so(4) and the tetrahedron algebra and their q-analogs.
For my personal interests, I play video games or volleyball during my free time.
My research involves the formulation of game models and the analyses of these using various approaches.
Research Interest
- Algebraic Combinations
- Representation Theory
- Matrix Analysis
Selected Publications
- Morales, J.V.S., Linking the special orthogonal algebra so(4) and the tetrahedron algebra, Linear Algebra and its Applications, 673 (2022) 212—239. Available at doi.org/10.1016/j.laa.2021.12.009.
- Morales, J.V.S. & Palma, T.M., On quantum adjacency algebra of Doob graphs and their irreducible modules, Journal of Algebraic Combinatorics, 54 (2021) 979—998. Available at doi.org/10.1007/s10801- 021-01034-w.
- Morales, J.V.S., Obata, N., & Tanaka, H., Asymptotic joint spectra of Cartesian powers of strongly regular graphs and bivariate Charlier— Hermite polynomials, Colloquium Mathematics (2020). Available at DOI: 10.4064/cm7724-7-2019.
- Morales, J.V.S. & Tanaka, H., Assmus—Mattson theorem for codes over commutative association schemes, Designs, Codes, and Cryptography, 86 (2018) 1039—1062. Available at doi.org/10.1007/s10623-017-0376-y.
- Morales, J.V.S., On Lee association schemes over Z4 and their Terwilliger algebra, Linear Algebra and its Applications 510 (2016) 311—328. Available at doi.org/10.1016/j.laa.2016.08.033.
- Morales, J.V.S. & Pascasio, A.A., An action of the tetrahedron algebra on the standard module for the Hamming graphs and Doob graphs, Graphs and Combinatorics 30 (2014) 1513—1527. Available at doi.org/10.1007/s00373-013-1366-0.
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2401 Taft Avenue, Malate 1004, Manila, Philippines
Tel. Nos.: (632) 8536-0270 (direct line)
(632) 8524-4611 local 420 (trunk line)
