Research and Publications

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. 


[7] Jacqueline Anderson, Emerald Stacy, Bella Tobin. On a slice of the cubic 2-adic Mandelbrot set. preprint (2024), available at arxiv: 2401.09394.

[6] Angelica Babei, Lea Beneish, Manami Roy, Holly Swisher, Bella Tobin, Fang-Ting Tu. Generalized Ramanujan-Sato series arising from modular forms. preprint (2022), available at arxiv: 2202.13253. To appear.

[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. preprint (2021), available at arXiv: 2109.033392. To appear.

[2]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.

[1] 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.