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レジェス ブストス シッド/ 学術研究員



レジェス  ブストス  シッド/レジェス  ブストス  シッド レジェス ブストス シッド / レジェス ブストス シッド(学術研究員) My main area of study is representation theory. I am mostly interested in the study of the spectrum of graphs and operators arising from models from physics along with the relationship of these spectrum of these objects with other areas of mathematics such as number theory.

Previously, I defined a generalization of Cayley graphs for group-subgroup pairs. The spectrum of these graphs can be computed by using the characters of the underlying group-subgroup pair, extending the well-known case of Cayley-graphs. It is currently on of my research topics to use these graphs for the study of (non-regular) networks, expanders, generalizations of Ramanujan graph and possible applications to cryptography and coding theory. Recently, I have been studying the spectrum of the quantum Rabi model (QRM), a model in quantum optics, and its generalizations. One of the main results of our works is showing that the asymmetric quantum Rabi models (AQRM) only possesses degeneracies for certain parameter choices, a result previously observed by physicists. Currently, I focus on studying the properties of certain orthogonal polynomial families arising from the study of the degeneracies of the AQRM and its relationship with the spectrum. In addition, I am working on the computation of special values of the spectral zeta function of the QRM. It is expected that these two topics will greatly increase our understanding of the spectrum of the QRM and its physical properties.

キーワード harmonic analysis on graphs, orthogonal polynomials, spectrum of Quantum Rabi model, spectral zeta function
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