Algebraic Dynamics Seminar: Sullivan’s Dictionary, Limits of deformations, and Modular Laminations
ALGEBRAIC DYNAMICS, SEMINARS
March 23, 2023 4:00 pm - 6:00 pm
Science Center 232
Jeremy Kahn - Brown University
Sullivan’s dictionary between Kleinian groups and rational maps reveals how many objects, such as limit sets and Julia sets, are different names for the same thing. On a deeper level, it provides conjectures in one field that are analogs of well-known theorems in the other. One such well-known theorem, proven by W. Thurston, is the compactness of the space of representations (in Isom(H^3)) of the fundamental group of a compact 3-manifold with acylindrical boundary. The analog of this theorem for rational maps was conjectured by C. McMullen in the early 1990’s. Because there is no quotient three-manifold for a rational map, new tools are needed to study degenerating sequences of deformations. We introduce the concept of an invariant modular lamination as a limit of degeneration and use it to prove this conjecture.
For more information, please see: Algebraic Dynamics Seminar at Harvard