Abstract: The MLC Conjecture (the Mandelbrot set is Locally Connected) describes how quadratic polynomials depend topologically on a parameter. The Conjecture has many geometric and probabilistic counterparts; all of them are the subject of the Renormalization Theory, which analyzes first-return maps to small neighborhoods of special points. In this talk, we outline the current state of this theory, with particular emphasis on the (near-) zero-entropy or Molecule (satellite and neutral) regimes.

Zoom Meeting ID: 181 155 584