My primary research focus is on the connection between arithmetic dynamics and arithmetic geometry. Much of my work involves post-critically finite maps, which is a dynamical analogue of CM Abelian varieties. Additionally, I explore the use of dynamical Belyi maps in arithmetic dynamics to help us understand properties of PCF rational maps.
Papers
[10] Alexander J. Barrios, Manami Roy, Nandita Sahajpal, Darwin Tallana, Bella Tobin, and Hanneke Wiersema, Local data of elliptic curves under quadratic twist, Results in Number Theory 11 (2025)
[9] Angelica Babei, Manami Roy, Holly Swisher, Bella Tobin, and Fang-Ting Tu, Supercongruences arising from Ramanujan-Sato series, Results in Mathematics 80 (2025)
[8] Tori Day, Rebecca DeLand, Jamie Juul, Cigole Thomas, Bianca Thompson, and Bella Tobin, Dynamical irreducibility of certain families of polynomials over finite fields, Finite Fields and their Applications 108 (2025).
[7] Angelica Babei, Lea Beneish, Manami Roy, Holly Swisher, Bella Tobin, and Fang-Ting Tu, Generalized Ramanujan–Sato series arising from modular forms, Research Directions in Number Theory: Women in Numbers V, Springer (2024)
[6] Jacqueline Anderson, Emerald Stacy, and Bella Tobin, On a slice of the cubic 2-adic Mandelbrot set, preprint (2024), Available at Arxiv: 2401.09394. To appear in Research Directions in Number Theory, Women in Numbers VI
[5] John Doyle, Paul Fili, and Bella Tobin. Julia sets for stochastic dynamical systems. In preparation.
[4] John Doyle, Paul Fili, and Bella Tobin. Stochastic equidistribution and generalized adelic measures. preprint (2021), available at arxiv:2111.08905.
[3] Jacqueline Anderson, Michelle Manes, and Bella Tobin. Some applications of dynamical Belyi polynomials. La Matematica 3 (2024)
[2]Jacqueline Anderson, Michelle Manes, and Bella Tobin. Cubic post-critically finite polynomials defined over ℚ . Proceedings of the Fourteenth Algorithmic Number Theory Symposium (2020)
[1] Michelle Manes, Gabrielle Melamed, and Bella Tobin. Dessins d’enfants for single-cycle Belyi maps. Research Directions in Number Theory (2019)
My PhD dissertation is Belyi Maps and Bicritical Polynomials.