Dynamics Seminar

Continued fractions have provided a natural playground for several advances in number theory, geometry, topology, dynamics, analysis, and probability theory. I will report on some dimension-theoretic research (see https://arxiv.org/a/das_t_4.html) regarding the fascinating fractals that arise from studying such objects and point to vistas among their conformal cousins in the Fatou–Sullivan dictionary, about which much less is known. The talk will be accessible to anyone whose interests intersect the convex hull of dynamics, fractal geometry and Diophantine approximation, and I hope to present a sampling of open questions and research directions that await exploration.