My research interests are in orthogonal polynomials and operator theory. In particular, I am interested in exploring what properties of orthogonal polynomials are preserved under perturbations of their corresponding linear functionals. I am also curious about the the roles of orthogonal polynomials in semigroup theory and their connections with stochastic processes.
4. R. Bailey, S. Costa, M. Derevyagin et al. Hamiltonians that realize perfect quantum state transfer and early state exclusion. Quantum Inf Process 24, 51 (2025). https://doi.org/10.1007/s11128-025-04667-z. Full Text 3. R. Bailey and M. Derevyagin. DEK-type orthogonal polynomials and a modification of the Christoffel formula. J. Comput. Appl. Math. 438 (2024), Paper No. 115561. ArXiv 2. R. Bailey and M. Derevyagin. Complex Jacobi matrices generated by Darboux transformations. J. Approx. Theory 288 (2023), Paper No. 105876, 33 pp. ArXiv 1. R. Bailey and E. Gunawan. Cluster algebras and binary subwords. Order 39 (2022), no.1, 55–69. ArXiv
1. R. Bailey and E. Gunawan. Cluster Algebras and Binary Words. Sem. Lothar. Combin. 82B (2020), Art. 81, 12pp.
2. R. Bailey. Orthogonal Polynomials and Perfect State Transfer. 2024. arXiv: 2412.16351 [quant-ph]. url: https://arxiv.org/pdf/2412.16351 ArXiv 1. B. Akwei et al. Convergence, optimization and stability of singular eigenmaps. 2024. arXiv: 2406.19510 [math.PR]. url: https://arxiv.org/abs/2406.19510. ArXiv
1. R. Bailey, F. Baudoin, M. Gordina, T. Campos, A. Gannon, B. Hanzsek-brill, C. Marrs, A. Neuschotz, T. Rabe, and E. Winters. A Characterization of Fractional Gaussian Fields on S1 and the d-Torus. (preprint), 2022.
14. Third Joint SIAM/CAIMS Annual Meetings. "Orthogonal Polynomials and Perfect State Transfer" (August 2025) 13. AMS Spring Eastern Sectional Meeting. "Orthogonal Polynomials and Perfect State Transfer" (April 2025) 12. University of New Mexico Analysis Seminar. "DEK-Type Orthogonal Polynomials (The Extended Version)" (April 2024) 11. University of Hartford Mathematics Colloquium. "A Random Walk Along the Theory of Orthogonal Polynomials" (March 2024) 10. JMM Special Session: Numerical Analysis, Spectral Graph Theory, Orthogonal Polynomials, and Quantum Algorithms. "A new perspective on an old example" (January 2024) 9. AWM JMM 2024 Poster Session and Workshop. "DEK-Type Orthogonal Polynomials" (January 2024) 8. SIAM Quantum Walks on Graphs Workshop. "Orthogonal Polynomials and Quantum Walks on Graphs" (April 2023) 7. JMM Special Session: Orthogonal Polynomials and their Applications III. "A Modification of the Christoffel Formula" (January 2023) 6. Bridgewater State University Math Seminar. "Darboux Transformation and Exceptional Orthogonal Polynomials" (December 2022) 5. Advances In Operator Theory and Applications to Mathematical Physics. "Modification of the Christoffel Formula" (November 2022) 4. SIAM Quantum Computing Workshop. "Probability in Quantum Computing" (March 2022) 3. AMS Spring Eastern Sectional Meeting. “The Dubov-Eleonskii-Kulagin Polynomials and a Modification of the Christoffel Formula” (March 2022) 2. Formal Power Series and Algebraic Combinatorics. Presented “Cluster Algebras and Binary Words” poster (July 2019) 1. WIMIN at Smith College. “Binary Words and Antichains of Posets” (September 2018)