TARGET will run Complex Dynamics Week in May, 2024, which consists of two mini-courses and a colloquium lecture (in conjunction with KAIX distinguished lecture series).
Here are details:
Department of Mathematical Sciences Colloquium / KAIX Distinguished Lectures in Mathematics
Speaker: John Hubbard
May 23rd, 4:15-5:15PM, E6-1, room 1501
Title: The structure of the Mandelbrot set
Dynamics seminar
Speaker: John Hubbard (Cornell University)
May 23rd, 9:30-11:00AM, E6-1, room 1401
Title: Introduction to Henon maps
Mini-course 1: John Hubbard (Cornell University)
Lecture1: Teichmüller space and its cotangent space (May 22nd, 10:30-11:30AM, E6-1, room 1401)
Lecture2: The classification of homeomorphisms of surfaces, and hyperbolization of 3-manifolds that fiber over the circle. (May 27th, 10:30-11:30AM, E6-1, room 1401)
Lecture3: Thurston's theorem on characterization of rational maps and hyperbolization of Haken manifolds. (May 29th, 10:30-11:30AM, E6-1, room 1401)
Mini-course 2: Insung Park (Stony Brook University)
Title: Topology, geometry, and dynamics of post-critically finite(PCF) rational maps Abstract: Post-critically finite (PCF) rational maps are a fascinating class of dynamical systems with rich mathematical structures. In this minicourse, we explore the interplay between topology, geometry, and dynamics in the study of PCF rational maps.
Lecture1: What are PCF rational maps? (May 22nd, 1:30-2:30PM, E6-1, room 4415)
We begin by introducing PCF rational maps, highlighting their significance in complex dynamics.
Lecture2: Topology of PCF rational maps (May 27th, 1:30-2:30PM, E6-1, room 4415)
W.Thurston's and D.Thurston's characterizations provide powerful frameworks for understanding the topological dynamics of rational maps. We delve into these characterizations, exploring their implications for the dynamics of PCF rational maps. Additionally, we discuss finite subdivision rules and topological surgeries, such as matings, tunings, and decompositions, as tools for constructing and analyzing PCF rational maps in topological ways.
Lecture3: Geometry of PCF rational maps (May 29th, 1:30-2:30PM, E6-1, room 4415)
Geometry of PCF rational maps The topological models for PCF rational maps we discuss define canonical quasi-symmetric classes of metrics on their Julia sets. We investigate the conformal dimensions of Julia sets, which measure their geometric complexity and provide insights into the underlying dynamics. Through this exploration, we uncover the intricate relationship between the topology, geometry, and dynamics of PCF rational maps.