03823nam 2200565 450 991082176130332120220819053611.00-8218-9188-X(CKB)3240000000070103(EBL)3113322(SSID)ssj0000760621(PQKBManifestationID)11451215(PQKBTitleCode)TC0000760621(PQKBWorkID)10715596(PQKB)11264446(MiAaPQ)EBC3113322(RPAM)17414463(PPN)197102239(EXLCZ)99324000000007010320120803h20122012 uy| 0engur|n|---|||||txtccrTropical 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, editorsProvidence, Rhode Island :American Mathematical Society,[2012]©20121 online resource (170 p.)Contemporary mathematics,5800271-4132Description based upon print version of record.0-8218-7553-1 Includes bibliographical references.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.Contemporary mathematics,5800271-4132Tropical geometryCongressesTropical geometry516.3514T0514H7014N1037K1037K20mscAthorne Chris1957-Maclagan Diane1974-Strachan Ian1965-Conference on Tropical Geometry and Integrable SystemsMiAaPQMiAaPQMiAaPQBOOK9910821761303321Tropical geometry and integrable systems832891UNINA