Algebraic Dynamics Seminar: Sullivan’s Dictionary, Limits of deformations, and Modular Laminations


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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