Geometry of Polynomial Shift Locus and the Space of Trees
发布时间:2024年07月12日
浏览次数:646
发布者: He Liu
主讲人: Yan Mary He(University of Oklahoma)
活动时间: 从 2024-07-25 21:00 到 22:00
场地: 线上
Location: Zoom (ID: 813 9122 3119, Password: 184255)
The degree d \ge 2 shift locus S_d consists of affine conjugacy classes of complex polynomials whose critical points all escape to infinity under iterations of the polynomial. We relate generic points in the shift locus S_d to metric graphs. Using thermodynamic metrics on the space of metric graphs/Culler-Vogtmann outer space, we obtain a distance function on S_d. We show that S_d is incomplete if and only if d \ge 3 and the metric completion contains a subset homeomorphic to the space of trees PST_d^* introduced by DeMarco-Pilgrim. This is joint work with Hongming Nie.