In the Fall of 2021 the De Giorgi Mathematical Research Center resumed the series of Colloquia in Mathematics at Scuola Normale Superiore named after one of the most prominent mathematical figures of the 20th Century.

The De Giorgi Colloquia are held by renowned experts and are targeted to a general mathematical audience. They usually include a historical account

of a mathematical subject, arriving to the current and most relevant results. In this way they are accessible also to students who are willing to enter into research field new for them.

Speakers in the Colloquia Series are asked to provide some notes in the form of a survey or of an extended abstract. Our goal is to have a written memory of the events, which might also give an opportunity for the interested reader to deepen the understanding of the topic and have at hand a list of useful references.