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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 /
| Clasificación: | Libro Electrónico |
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| Autor Corporativo: | |
| Otros Autores: | , , |
| Formato: | Electrónico Congresos, conferencias eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, R.I. :
American Mathematical Society,
©2012.
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| Colección: | Contemporary mathematics (American Mathematical Society) ;
v. 580. |
| Temas: |
Algebraic geometry
> Projective and enumerative geometry
> Enumerative problems (combinatorial problems)
Dynamical systems and ergodic theory
> Infinite-dimensional Hamiltonian systems
> Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
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| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- ""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. Finite-dimensional Gorenstein algebras and Lefschetz property""""4. Gorenstein algebras associated to matroids""; ""5. Main result""; ""6. Gröbner fan of _{ }""; ""References""; ""Block triangular bilinear forms and braid group action""; ""1. A quadratic Poisson algebra and its reductions""; ""2. The Dubrovin�Ugaglia bracket and braid group action""; ""3. General block size""; ""4. Quantisation""; ""Acknowledgements""; ""References""; ""Tropicalization method in cluster algebras""; ""1. Introduction""; ""2. Cluster algebra with coefficients""
- ""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""