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.
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This colloquium is part of the Distinguished Lecture Series (DLS) organized by The (Indian) Mathematics Consortium (TMC), and co-hosted by IIT-B and ICTS-TIFR. For more information about this lecture series, and to register, please visit the homepage of the TMC DLS.