**Contemporary Mathematics**

Volume: 580;
2012;
155 pp;
Softcover

MSC: Primary 14; 37;

Print ISBN: 978-0-8218-7553-7

Product Code: CONM/580

List Price: $62.00

Individual Member Price: $49.60

**Electronic ISBN: 978-0-8218-9188-9
Product Code: CONM/580.E**

List Price: $62.00

Individual Member Price: $49.60

# Tropical Geometry and Integrable Systems

Share this page *Edited by *
*Chris Athorne; Diane Maclagan; Ian Strachan*

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.

#### Table of Contents

# Table of Contents

## Tropical Geometry and Integrable Systems

- Introduction vii8 free
- Introduction to tropical algebraic geometry 112 free
- Tropical curves and integrable piecewise linear maps 2132
- Counting algebraic curves with tropical geometry 4152
- Hurwitz numbers, ribbon graphs, and tropicalization 5566
- Sperner property, matroids and finite-dimensional Gorenstein algebras 7384
- Block triangular bilinear forms and braid group action 8596
- Tropicalization method in cluster algebras 95106
- An application of the max-plus spectral theory to an ultradiscrete analogue of the Lax pair 117128
- A KdV cellular automaton without integers 135146
- 1. Introduction 135146
- 2. A brief recall of the continuous and the discrete situation 138149
- 3. A linear problem for the ultradiscrete KdV equation 140151
- 4. Bound states for the ultradiscrete KdV equation 142153
- 5. Tau functions and the dressing procedure 145156
- 6. The case of degenerate spectrum 149160
- 7. Concluding remarks 153164
- References 154165

#### Readership

Graduate students and research mathematicians interested in tropical geometry and its applications to integrable systems.