Inserted: 17 jul 2018
Last Updated: 27 jun 2019
Lectures held at Park City 9-13 July 2018
We aim at explaining the most basic ideas underlying two fundamental results in the regularity theory of area minimizing oriented surfaces: De Giorgi's celebrated $\varepsilon$-regularity theorem and Almgren's center manifold. Both theorems will be proved in a very simplified situation, which however allows to illustrate some of the most important PDE estimates.