Quasiconformal Equivalence of Cantor Sets
Time: 2024-03-08
Published By: He Liu
Speaker(s): Hiroshige Shiga(Kyoto Sangyo University)
Time: 09:00-09:50 March 13, 2024
Venue: Online
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
