Non-archimedean and tropical geometry

This talk deals with the interplay between tropical varieties and non-archimedean analytic varieties in the sense of Berkovich. The Berkovich space associated to a variety over a field with a non-archimedean valuation contains a lot of points which are not visible in algebraic geometry. Under certain conditions these additional points are helpful to find tropical varieties inside Berkovich spaces. After an introduction explaining tropicalizations and Berkovich spaces, we will discuss some results from joint work with Joseph Rabinoff and Walter Gubler.