Nonarchimedean and Tropical Geometry (Simons Symposia) by Matthew Baker,Sam Payne

By Matthew Baker,Sam Payne

This
volume grew out of 2 Simons Symposia on "Nonarchimedean and tropical
geometry" which happened at the island of St. John in April 2013 and in
Puerto Rico in February 2015. each one assembly accumulated a small crew of experts
working close to the interface among tropical geometry and nonarchimedean
analytic areas for a chain of inspiring and provocative lectures on cutting
edge learn, interspersed with full of life discussions and collaborative paintings in
small teams. The articles amassed right here, which come with high-level surveys as
well as unique study, replicate the most topics of the 2 Symposia.

Topics
covered during this quantity include: 

  • Differential kinds and currents, and
    solutions of Monge-Ampere kind differential equations on Berkovich areas and
    their skeletons; 
  • The homotopy forms of nonarchimedean analytifications;
  • The lifestyles of "faithful tropicalizations" which encode the topology and
    geometry of analytifications;
  • Relations among nonarchimedean analytic
    spaces and algebraic geometry, together with logarithmic schemes, birational
    geometry, and the geometry of algebraic curves;

  • Extended notions of
    tropical types which relate to Huber's conception of adic areas analogously to
    the means that ordinary tropical forms relate to Berkovich areas; and 
  • Relations
    between nonarchimedean geometry and combinatorics, together with deep and
    fascinating connections among matroid conception, tropical geometry, and Hodge
    theory.

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