On the problem of local connectivity of the Mandelbrot set

When

November 8, 2023 | 2:30 p.m. – 3:30 p.m.
Refreshments provided

Where

University Hall 4004

Speaker

Dzmitry Dudko

Abstract

The Mandelbrot set encodes how the dynamics of a quadratic polynomial depends on the parameter. In the 1980s, A. Douady and J. Hubbard conjectured that the Mandelbrot set is locally connected -- the MLC conjecture. This conjecture would result in a simple abstract ``pinched disk'' model for the Mandelbrot set with various consequences. Since the 1990s, local connectivity has been established for a large class of parameters, but the full conjecture is still open. In the talk, we will first discuss the motivations for the MLC conjecture and its relation to the renormalization theory. Then, we will outline recent developments in the area. Based on a joint work with Misha Lyubich.