About Hrushovski and Loeser's work on the homotopy type of Berkovich spaces

TL;DR

This paper surveys Hrushovski and Loeser's research on the homotopy types of Berkovich spaces, highlighting their methods and applications in non-Archimedean geometry and tropical geometry.

Contribution

It provides a comprehensive overview of Hrushovski and Loeser's work and demonstrates how their results can be applied to study pre-images of skeleta.

Findings

Hrushovski and Loeser's work characterizes the homotopy types of Berkovich spaces.

The survey explains applications to non-Archimedean and tropical geometry.

The author illustrates the use of their results in studying pre-images of skeleta.

Abstract

Those are the notes of the two talks I gave in april 2013 in St-John (US Virgin Islands) during the Simons Symposium on non-Archimedean and tropical geometry. They essentially consist of a survey of Hrushovski and Loeser's work on the homotopy type of Berkovich spaces; the last section explains how the author has used their work for studying pre-image of skeleta.