Thermodynamic expansions for the Hausdorff dimension of continued fraction Cantor sets via transfer operator perturbation

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 -- https://arxiv.org/a/das_t_4.html -- regarding the fascinating fractals that arise from studying continued fractions and point to vistas among their conformal cousins about which much less is known. The talk will be accessible to those whose interests intersect a convex combination of dynamics, fractal geometry and Diophantine approximation.