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FIELD Math:Topology
DATE July 29 (Wed), 2020
TIME 09:00-10:30
PLACE online
SPEAKER Dan Margalit
HOST Kim, Sang-hyun
INSTITUTE Georgia Tech
TITLE Mapping class groups in complex dynamics
ABSTRACT

In joint work with James Belk, Justin Lanier and Becca Winarski, we give a simple geometric algorithm that can be used to determine whether or not a post-critically finite topological polynomial is Thurston equivalent to a polynomial. Our methods are rooted in geometric group theory: we consider a complex of isotopy classes of trees and a simplicial map of this complex to itself that we call the lifting map. Our work extends previous work of Nekrashevych. Similar work has been announced by Ishii-Smillie. We will give several applications of our methods, including a solution to Pilgrim's finite global attractor problem in the case of topological polynomials, the solution to a generalization of Hubbard’s twisted rabbit problem (originally solved by Bartholdi?Nekrashevych), and a new proof of Thurston's theorem for topological polynomials.
* to participate, please visit https://visgat.cayley.kr

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