### Mathematics Colloquium

# Dzmitry Dudko

### (Jacobs and Stony Brook University)

## "Pacman renormalization and self-similarity of the Mandelbrot set near Siegel parameters"

** Date: ** |
Mon, November 20, 2017 |

** Time: ** |
17:15 |

** Place: ** |
Lecture Hall, Research I |

**Abstract:** One of the prominent features of the Mandelbrot set is its self-similarity. For example, it contains infinitely many copies of itself. The explanation of this phenomenon is provided by the Renormalization Theory which studies operators acting on the spaces of maps. In the talk, we will discuss basic aspects of the theory. Then we will introduce ``Pacman renormalization operator'' responsible for self-similarity of the Mandelbrot set near its main cardioid, and we will give an idea of a proof that the operator is hyperbolic at periodic Siegel parameters. As a consequence, we obtain various scaling results for the Mandelbrot set near its main cardioid.

*The colloquium is preceded by tea from 16:45 in the Resnikoff Mathematics Common Room, Research I, 127.*