JOHN VINCENT S. MORALES, PhD

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.

Associate Professor

PhD in Information Science

Algebraic Combinations, Representation Theory, Matrix Analysis

• 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.