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

• Pubblicazione: Providence, Rhode Island : , : American Mathematical Society, , [2012]; ©2012
• Descrizione fisica: 1 online resource (170 p.)
• Disciplina: 516.35
• Soggetto topico: Tropical geometry
• Classificazione: 14T0514H7014N1037K1037K20
• Persona (resp. second.): AthorneChris <1957->; MaclaganDiane <1974->; StrachanIan <1965->
• 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.
• Titolo autorizzato: Tropical geometry and integrable systems
• ISBN: 0-8218-9188-X
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910821761303321
• Lo trovi qui: Univ. Federico II
• Serie: Contemporary mathematics, ; 580 . 0271-4132