Abstract

Renormalization theory is a powerful technique both in mathematics and physics. In particular, it is essential in the study of the MLC conjecture, which wonders whether or not the Mandelbrot set is locally connected. The main purpose of this seminar is to comprehend the Straightening Theorem, that is an essential result behind the aforementioned technique. In order to approach our aim, we proceed to concentrate on quasiconformal geometry and give some basic background concerning dynamical systems. Lastly, we explore some applications of the cornerstone of this talk within the framework of complex dynamics in the space of cubic polynomials.