Cid Reyes Bustos

About me

I am currently a Ph.D. student of Mathematics at Kyushu University under the supervision of Professor Masato Wakayama. My main research interests are representation theory and number theory.

My e-mail is (first letter of name) dash reyes @ math dot kyushu-u dot ac dot jp.


  • Representation theory, in particular representation of finite groups and group determinant.
  • Number theory, Zeta functions and Ramanujan graphs.
  • Graph theory, generalizations of Cayley graphs and harmonic analysis of graphs. Applications to coding theory and cryptography.
  • Spectral Analysis of quantum Rabi model and Non-commutative Harmonic Oscillator.


  • Group-subgroup pair graphs. RIMS kokyuroku 1925 (2014). New Developments of Representation Theory and Harmonic Analysis. Research Institute for Mathematical Science. Kyoto University.
    • Please note that the contents of this research report are superseded by the next item.
  • Cayley-type graphs for group-subgroup pairs. Linear Algebra and its Appplications. Volume 488 (2016), pages 320-349. doi: 10.1016/j.laa.2015.09.049
    • An accepted manuscript version is available here. The Mathematica source code for the figure files is available here.
  • Spectral degeneracies in the asymmetric quantum Rabi model. With Masato Wakayama. in "Mathematical Modelling for Next- Generation Cryptography" eds. T. Takagi et al., Mathematics for Industry, Springer, 2017 (to appear).