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.
1. 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 3. R. Bailey and E. Gunawan. Cluster algebras and binary subwords. Order 39 (2022), no.1, 55–69. ArXiv
1. JMM Special Session: Numerical Analysis, Spectral Graph Theory, Orthogonal Polynomials, and Quantum Algorithms. "A new perspective on an old example" (Jan. '24) 2. AWM JMM 2024 Poster Session and Workshop. "DEK-Type Orthogonal Polynomials" (Jan. '24) 3. SIAM Quantum Walks on Graphs Workshop. "Orthogonal Polynomials and Quantum Walks on Graphs" (Apr. '23) 4. JMM Special Session: Orthogonal Polynomials and their Applications III. "A Modification of the Christoffel Formula" ( Jan. '23) 5. Advances In Operator Theory and Applications to Mathematical Physics. "Modification of the Christoffel Formula" (Nov. '22) 6. SIAM Quantum Computing Workshop. "Probability in Quantum Computing" (Mar. '22) 7. AMS Spring Eastern Sectional Meeting. “The Dubov-Eleonskii-Kulagin Polynomials and a Modification of the Christoffel Formula” (Mar. '22) 8. Formal Power Series and Algebraic Combinatorics. Presented “Cluster Algebras and Binary Words” poster (July '19) 9. WIMIN at Smith College. “Binary Words and Antichains of Posets” (Sept. '18)