Nonarchimedean and Tropical Geometry

Topics covered in this volume include:

• Differential forms and currents, and solutions of Monge-Ampere type differential equations on Berkovich spaces and their skeletons;
• The homotopy types of nonarchimedean analytifications;
• The existence of "faithful tropicalizations" which encode the topology and geometry of analytifications;
Relations between nonarchimedean analytic spaces and algebraic geometry, including logarithmic schemes, birational geometry, and the geometry of algebraic curves;
• Extended notions of tropical varieties which relate to Huber's theory of adic spaces analogously to the way that usual tropical varieties relate to Berkovich spaces; and
• Relations between nonarchimedean geometry and combinatorics, including deep and fascinating connections between matroid theory, tropical geometry, and Hodge theory.