Nonarchimedean and Tropical Geometry

Nonfiction, Science & Nature, Mathematics, Geometry
Cover of the book Nonarchimedean and Tropical Geometry by , Springer International Publishing
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Author: ISBN: 9783319309453
Publisher: Springer International Publishing Publication: August 18, 2016
Imprint: Springer Language: English
Author:
ISBN: 9783319309453
Publisher: Springer International Publishing
Publication: August 18, 2016
Imprint: Springer
Language: English

This volume grew out of two Simons Symposia on "Nonarchimedean and tropical geometry" which took place on the island of St. John in April 2013 and in Puerto Rico in February 2015. Each meeting gathered a small group of experts working near the interface between tropical geometry and nonarchimedean analytic spaces for a series of inspiring and provocative lectures on cutting edge research, interspersed with lively discussions and collaborative work in small groups. The articles collected here, which include high-level surveys as well as original research, mirror the main themes of the two Symposia.

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;
  • 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.
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This volume grew out of two Simons Symposia on "Nonarchimedean and tropical geometry" which took place on the island of St. John in April 2013 and in Puerto Rico in February 2015. Each meeting gathered a small group of experts working near the interface between tropical geometry and nonarchimedean analytic spaces for a series of inspiring and provocative lectures on cutting edge research, interspersed with lively discussions and collaborative work in small groups. The articles collected here, which include high-level surveys as well as original research, mirror the main themes of the two Symposia.

Topics covered in this volume include: 

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