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.
 John Doyle, Paul Fili, and Bella Tobin. Julia sets for stochastic dynamical systems. In preparation.
 John Doyle, Paul Fili, and Bella Tobin. Stochastic equidistribution and generalized adelic measures. preprint (2021), available at arxiv:2111.08905.
 Jacqueline Anderson, Michelle Manes, and Bella Tobin. Some applications of dynamical Belyi polynomials. preprint (2021), available at arXiv: 2109.033392.
Jacqueline Anderson, Michelle Manes, and Bella Tobin. Cubic post-critically finite polynomials defined over ℚ . Proceedings of the Fourteenth Algorithmic Number Theory Symposium (Steven Galbraith, ed.), volume 4(1) of Open Book Series, pages 23–38.
 Michelle Manes, Gabrielle Melamed, and Bella Tobin. Dessins d’enfants for single-cycle Belyi maps.InResearch Directions in Number Theory, pages 153–159. Springer International Publishing, 2019
My PhD dissertation is Belyi Maps and Bicritical Polynomials.