On the MLC Conjecture

Abstract: The MLC Conjecture, on local connectivity of the Mandelbrot set, is one of the central open problems in Holomorphic Dynamics. It turned out to be intimately related to many other geometric themes of the area: Fatou's Conjecture on the density of hyperbolicity, self-similarity features of the Mandelbrot set, Lebesgue measure of Julia sets, and so on. We will give an introduction to this problem and an update on its current status.

Mathematics

Audience: learners

TMC Distinguished Lecture Series

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