Description |
1 online resource (x, 155 pages) : illustrations |
Series |
Contemporary mathematics ; 580 |
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Contemporary mathematics (American Mathematical Society) ; v. 580.
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Contents |
""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"" |
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""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"" |
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""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"" |
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""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"" |
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""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"" |
Bibliography |
Includes bibliographical references |
Notes |
English |
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Online resource; title from PDF title page (American Mathematical Society, viewed Nov. 20, 2012) |
Subject |
Tropical geometry -- Congresses
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Tropical geometry
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Algebraic geometry -- Tropical geometry -- Tropical geometry.
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Algebraic geometry -- Curves -- Relationships with integrable systems.
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Algebraic geometry -- Projective and enumerative geometry -- Enumerative problems (combinatorial problems)
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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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Dynamical systems and ergodic theory -- Infinite-dimensional Hamiltonian systems -- Relations with algebraic geometry, complex analysis, special functions.
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Genre/Form |
Conference papers and proceedings
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Form |
Electronic book
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Author |
Athorne, Chris, 1957-
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Maclagan, Diane, 1974-
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Strachan, Ian, 1965-
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LC no. |
2012023440 |
ISBN |
9780821891889 |
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082189188X |
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