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
[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.
[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.