Quasiconformal Equivalence of Cantor Sets
发布时间：2024年03月08日
浏览次数：1109
发布者: He Liu
主讲人： Hiroshige Shiga(Kyoto Sangyo University)
活动时间： 从 2024-03-13 09:00 到 09:50
场地： 线上
Cantor sets appear in many fields of mathematics. In this talk, we are interested in Cantor sets in the complex plane $\mathbb C$.
We recognize those sets have two aspects. One is that they are compact and totally disconnected perfect subset of $\mathbb C$ and another is that their complements are Riemann surfaces of infinite type of genus zero. We consider the quasiconformal (= qc) equivalence of Cantor sets from the two aspects.
In the first part of the talk, we show qc-equivalence or non-qc-equivalemce of Cantors set which are obtained from some dynamical systems. In the second part, we focus on Cantor sets which are generalized ones of the middle one-third Cantor set and consider their qc-equivalence in terms of sequences of $(0, 1)^{\mathbb N}$ which give those Cantor sets.
Finally, we exhibit some conjectures about qc-eqivalence of Cantor sets and their moduli spaces.
We recognize those sets have two aspects. One is that they are compact and totally disconnected perfect subset of $\mathbb C$ and another is that their complements are Riemann surfaces of infinite type of genus zero. We consider the quasiconformal (= qc) equivalence of Cantor sets from the two aspects.
In the first part of the talk, we show qc-equivalence or non-qc-equivalemce of Cantors set which are obtained from some dynamical systems. In the second part, we focus on Cantor sets which are generalized ones of the middle one-third Cantor set and consider their qc-equivalence in terms of sequences of $(0, 1)^{\mathbb N}$ which give those Cantor sets.
Finally, we exhibit some conjectures about qc-eqivalence of Cantor sets and their moduli spaces.
Zoom Meeting ID: 181 155 584
