Analytic and Tropical Geometry

Analysis and analytic geometry over non-archimedean fields has attracted substantial interest, beginning with work of Tate in the 1970s, and then work of Raynaud, Huber, and Berkovich. Of these, Berkovich's theory has particularly nice topological properties. The basic geometry of Berkovich spaces can be accessed using polyhedral methods, and a process called tropicalization. I will give an introduction to this circle of ideas.