Tropical and Non-Archimedean Geometry
About this Title
Omid Amini, École Normale Supérieure, Paris, France, Matthew Baker, Georgia Institute of Technology, Atlanta, GA and Xander Faber, University of Hawaii at Manoa, Honolulu, HI, Editors
Publication: Contemporary Mathematics
Publication Year 2013: Volume 605
ISBNs: 978-1-4704-1021-6 (print); 978-1-4704-1410-8 (online)
Over the past decade, it has become apparent that tropical geometry and non-Archimedean geometry should be studied in tandem; each subject has a great deal to say about the other.
This volume is a collection of articles dedicated to one or both of these disciplines. Some of the articles are based, at least in part, on the authors' lectures at the 2011 Bellairs Workshop in Number Theory, held from May 6–13, 2011, at the Bellairs Research Institute, Holetown, Barbados.
Lecture topics covered in this volume include polyhedral structures on tropical varieties, the structure theory of non-Archimedean curves (algebraic, analytic, tropical, and formal), uniformization theory for non-Archimedean curves and abelian varieties, and applications to Diophantine geometry. Additional articles selected for inclusion in this volume represent other facets of current research and illuminate connections between tropical geometry, non-Archimedean geometry, toric geometry, algebraic graph theory, and algorithmic aspects of systems of polynomial equations.
Graduate students and research mathematicians interested in tropical or non-archimedean geometry and algebraic graph theory.
Table of Contents
- Diane Maclagan – Polyhedral structures on tropical varieties
- Brian Osserman and Joseph Rabinoff – Lifting nonproper tropical intersections
- Kaitlyn Phillipson and J. Maurice Rojas – Fewnomial systems with many roots, and an Adelic Tau Conjecture
- Mounir Nisse and Frank Sottile – Non-Archimedean Coamoebae
- Matthew Baker, Sam Payne and Joseph Rabinoff – On the structure of non-archimedean analytic curves
- Mihran Papikian – Non-archimedean uniformization and monodromy pairing
- Antoine Chambert-Loir – Diophantine geometry and analytic spaces
- Filippo Viviani – Tropicalizing vs. compactifying the Torelli morphism
- David Perkinson, Jacob Perlman and John Wilmes – Primer for the algebraic geometry of sandpiles