# 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.

## Research

- 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.

## Publications

*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 Kyoto University.- Please note that the contents of this research report are superseded by the next item.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*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).