Speaker: Malavika Mukundan
Affiliation: Boston University
Title: Dynamical approximation of post-singularly finite entire functions
Date and Time: July 15, 2025, 16:00:00 Hours
Venue: AG-77
Abstract: An entire map is said to be post-singularly finite if the forward orbit of its set of critical and asymptotic values is finite. Such maps play a crucial role in understanding natural families of entire maps. Motivated by previous work of Devaney-Goldberg-Hubbard, Kisaka and others, we ask the following question: Given a post-singularly finite entire function f, can f be realized as the limit of a sequence of post-singularly finite polynomials? In joint work with Nikolai Prochorov and Bernhard Reinke, we show how we may answer this question in the affirmative. Our techniques rely on a program developed by William Thurston that utilizes Teichmüller theory to topologically characterize post-singularly finite holomorphic maps. If time permits, we will explore the current state of this program and the challenges ahead.
Affiliation: Boston University
Title: Dynamical approximation of post-singularly finite entire functions
Date and Time: July 15, 2025, 16:00:00 Hours
Venue: AG-77
Abstract: An entire map is said to be post-singularly finite if the forward orbit of its set of critical and asymptotic values is finite. Such maps play a crucial role in understanding natural families of entire maps. Motivated by previous work of Devaney-Goldberg-Hubbard, Kisaka and others, we ask the following question: Given a post-singularly finite entire function f, can f be realized as the limit of a sequence of post-singularly finite polynomials? In joint work with Nikolai Prochorov and Bernhard Reinke, we show how we may answer this question in the affirmative. Our techniques rely on a program developed by William Thurston that utilizes Teichmüller theory to topologically characterize post-singularly finite holomorphic maps. If time permits, we will explore the current state of this program and the challenges ahead.