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Record Nr. |
UNINA9910821761303321 |
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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 |
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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , [2012] |
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©2012 |
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ISBN |
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Descrizione fisica |
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1 online resource (170 p.) |
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Collana |
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Contemporary mathematics, ; 580 , 0271-4132 |
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Classificazione |
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14T0514H7014N1037K1037K20 |
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Disciplina |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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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 |
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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. |
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