Tropical Geometry and Integrable Systems
About this Volume
Edited by: Chris Athorne, University of Glasgow, Glasgow, United Kingdom, Diane Maclagan, University of Warwick, Warwick, United Kingdom and Ian Strachan, University of Glasgow, Glasgow, United Kingdom
2012: Volume: 580
ISBNs: 978-0-8218-7553-7 (print); 978-0-8218-9188-9 (online)
This volume contains the proceedings of the conference on tropical geometry and integrable systems, held July 3–8, 2011, at the University of Glasgow, United Kingdom.
One of the aims of this conference was to bring together researchers in the field of tropical geometry and its applications, from apparently disparate ends of the spectrum, to foster a mutual understanding and establish a common language which will encourage further developments of the area. This aim is reflected in these articles, which cover areas from automata, through cluster algebras, to enumerative geometry. In addition, two survey articles are included which introduce ideas from researchers on one end of this spectrum to researchers on the other.
This book is intended for graduate students and researchers interested in tropical geometry and integrable systems and the developing links between these two areas.
Graduate students and research mathematicians interested in tropical geometry and its applications to integrable systems.
Table of Contents
- Diane Maclagan – Introduction to tropical algebraic geometry
- Rei Inoue and Shinsuke Iwao – Tropical curve and integrable piecewise linear map
- Florian Block – Counting algebraic curves with tropical geometry
- Paul Johnson – Hurwitz numbers, ribbon graphs, and tropicalization
- Toshiaki Maeno and Yasuhide Numata – Sperner property, matroids and finite-dimensional Gorenstein algebras
- Leonid Chekhov and Marta Mazzocco – Block triangular bilinear forms and braid group action
- Tomoki Nakanishi – Tropicalization method in cluster algebras
- Sergeĭ Sergeev – An application of the max-plus spectral theory to an ultradiscrete analogue of the Lax pair
- R. Willox, A. Ramani, J. Satsuma and B. Grammaticos – A KdV cellular automaton without integers