Title: Complex continued fractions and beyond

Speaker: Seonhee Lim (Seoul National University)

Abstract: The Hurwitz nearest-integer complex continued fraction for the irrational quadratic field enjoys nice dynamical properties when d=1,2,3,7, and 11. As a consequence, we show that the length of continued fraction of rationals over the set with denominators bounded by n goes to the normal distribution as n goes to infinity. We will briefly mention some generalization of the complex continued fraction map to Kleinian circle packings. (The talk is based on a joint work with Jungwon Lee and Dohyeong Kim, and a joint work with Kangrae Park and Yongquan Zhang.)