1.

Record Nr.

UNINA9910821761303321

Titolo

Tropical geometry and integrable systems : a Conference on Tropical Geometry and Integrable Systems, July 3-8, 2011,  School of Mathematics and Statistics, University of Glasgow, United Kingdom / / Chris Athorne, Diane Maclagan, Ian Strachan, editors

Pubbl/distr/stampa

Providence, Rhode Island : , : American Mathematical Society, , [2012]

©2012

ISBN

0-8218-9188-X

Descrizione fisica

1 online resource (170 p.)

Collana

Contemporary mathematics, ; 580 , 0271-4132

Classificazione

14T0514H7014N1037K1037K20

Disciplina

516.35

Soggetti

Tropical geometry

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references.

Nota di contenuto

Introduction  --  Introduction to tropical algebraic geometry --  1. Introduction --  2. Tropical varieties --  3. Drawing curves in the plane --  4. The Fundamental and Structure theorems --  5. The computational approach to tropical varieties --  6. Connections to subvarieties of toric varieties --  References --  Tropical curves and integrable piecewise linear maps --  1. Introduction --  Acknowledgments --  2. Tropical curve theory --  3. Tropical periodic Toda lattice --  4. Periodic BBS --  References --  Counting algebraic curves with tropical geometry --  1. Enumerative Algebraic Geometry --  2. Tropical Geometry --  3. Counting Algebraic Curves tropically --  4. Applications --  References --  Hurwitz numbers, ribbon graphs, and tropicalization --  1. Introduction --  2. The classical viewpoints: covers and permutations --  3. Double Hurwitz numbers and labeled ribbon graphs --  4. From ribbon graphs to permutations --  5. The tropical definition --  References --  Sperner property, matroids and finite-dimensional Gorenstein algebras --  Introduction --  1. Posets and the Sperner property --  2. Matroids --  3. Tropicalization in cluster algebras --  4. Application I: Periodicities of Y-systems --  5. Application II: Dilogarithm identities --  References --  An application of the max-plus spectral theory to an ultradiscrete analogue of the Lax pair --  1. Introduction --  2. Simplified Lax pair --  3. Adding



constraints --  4. Conclusions and projects --  5. Acknowledgement --  References --  A KdV cellular automaton without integers --  1. Introduction --  2. A brief recall of the continuous and the discrete situation --  3. A linear problem for the ultradiscrete KdV equation --  4. Bound states for the ultradiscrete KdV equation --  5. Tau functions and the dressing procedure --  6. The case of degenerate spectrum --  7. Concluding remarks --  References.