Speaker: Yitwah Cheung (Tsinghua University)
19 November, 2021 14:30 UTC
Abstract: There is a natural generalization of the concept of convergents of the continued fraction to higher dimensions that does not involve any specific choice of norm. In this talk, I will motivate this concept from several different angles, within the framework of staircases, which is a rectilinear version of Kleinian sails. I will describe some results about dual convergents and illustrate the method of our approach towards constructing slowly unbounded A-orbits by sketching the proof of dichotomy of Hausdorff dimension phenomenon obtained in joint work with P. Hubert and H. Masur.