math [at] cidrb . me

# Cid Reyes Bustos

Mathematician

## About me

I am currently a Research Associate in the NTT Institute for Fundamental Mathematics at the NTT Corporation. I also have a position of Visiting Assistant Professor at the School of Computing at Tokyo Institute of Technology.

My CV can be downloaded here. Last updated November 2023.

## Research interests

- Representation theory and orthogonal polynomials.
- Number theory, zeta functions and continued fractions.
- Graph theory, generalizations of Cayley graphs and harmonic analysis of graphs.
- Spectral analysis of quantum Rabi model and non-commutative harmonic oscillator.

I am a member of the Crypto-Math CREST project in the group lead by Masato Wakayama. I was awarded the "AIP Challenge Program" grant of JST for support of independent research for the periods 22-23 and 23-24.

## Upcoming talks

No talks announced at this moment.

## News

**2023/11**The preprint*Wolstenholme primes and group determinants of cyclic groups*was uploaded to arXiv.**2023/10**The preprint*Spacing distribution for quantum Rabi models*was uploaded to arXiv.**2023/09**The paper*The heat kernel of the asymmetric quantum Rabi model*was published in J. Phys. A: Math. Theor.**2023/08**The paper*Covering models of the asymmetric quantum Rabi model: η-shifted non-commutative harmonic oscillators*was published in Communications in Mathematical Physics. See here for a only-read version.**2023/06**I was awarded a the "AIP Challenge Program 2023" grant of AIP Network Laboratories of JST.

## Main Publications and preprints

Visit the publications page for the complete list of publications.

**2023.***Wolstenholme primes and group determinants of cyclic groups*with**Naoya Yamaguchi and Yuka Yamaguchi**. Preprint**2023**. arXiv:2311.00010**2023.***Spacing distribution for quantum Rabi models*with**Daniel Braak, Linh Thi Hoai Nguyen and Masato Wakayama**. Preprint**2023**. arXiv:2310.09811.**2023.***The heat kernel of the asymmetric quantum Rabi model*. J. Phys. A: Math. Theor.**56**425302, 2023. doi:10.1088/1751-8121/acfbc8. Preprint version arxiv:2012.13595.**2023**.*Covering models of the asymmetric quantum Rabi model: η-shifted non-commutative harmonic oscillators*with**Masato Wakayama**. Comm. Math. Phys. 2023. Published Online 25 August 2023. doi:10.1007/s00220-023-04825-3. SharedIt link (read-only version here)**2023.***Zeta limits for the spectrum of quantum Rabi models*with**Masato Wakayama**. Preprint 2023. arXiv:2304.08943.**2022**.*Heat kernel for the quantum Rabi model*with**Masato Wakayama**. Adv. Theor. Math. Phys.**26**(5), 2022. doi:https:10.4310/ATMP.2022.v26.n5.a8**2022**.*Degeneracy and symmetry hidden for the asymmetric quantum Rabi model with integral bias*with**Masato Wakayama**Commun. Number Theory Phys.**17**(3) 615-672, 2022. doi:10.4310/CNTP.2022.v16.n3.a4.**2021.***Remarks on the hidden symmetry of the asymmetric quantum Rabi model*with**Daniel Braak**and**Masato Wakayama**. J. Phys. A: Math. Theor.**54**285202, 2021. doi:10.1088/1751-8121/ac0508.**2021.***Heat kernel for the quantum Rabi model II: propagators and spectral determinants*with**Masato Wakayama**. Phys. A: Math. Theor.**54**115202, 2021. doi:10.1088/1751-8121/abdca7.**2020.***Extended divisibility relations for constraint polynomials of the asymmetric quantum Rabi model*in "International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC 2019)" eds. T. Takagi et al. doi:10.1007/978-981-15-5191-8_{13}**2020.***Determinant expressions of constraint polynomials and the spectrum of the asymmetric quantum Rabi model*with**Masato Wakayama**and**Kazufumi Kimoto**. International Mathematics Research Notices, Volume 2021, Issue**12**(2021), 9458–9544.**2017**.*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. doi: 10.1007/978-981-10-5065-7 7**2016.***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

## Activities

- Member of the Mathematical Society of Japan (since 2017).
- Member of Sociedad Matemática Mexicana (since 2019).
- I write reviews for Mathematical Reviews (MathSciNet) of the American Mathematical Society (My Profile) and zbMATH Open (My Profile).