Limit search to available items
Book Cover
E-book
Author Conference on Tropical Geometry and Integrable Systems (2011 : Glasgow, Scotland)

Title 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
Published Providence, R.I. : American Mathematical Society, ©2012

Copies

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