Algebraic Geometry Seminar

Berkovich spaces are a natural setting for analysis on varieties over fields with non-archimedean valuation. They have been studied in a variety of contexts, including tropical geometry and number theory. I will give an introduction to Berkovich spaces, and explain recent connections between the theory of Berkovich spaces and the minimal model program. In particular, I will show that if $X$ is a rationally connected smooth projective variety over the Laurent series $\mathbb{C}((t))$, the Berkovich space is a contractible topological space. This is joint work with Tyler Foster.