Proceedings of the Workshop “Geometric Aspects of Discrete and Ultra-Discrete Integrable Systems” (March 30 − April 3, 2009, University of Glasgow, UK)

The Guest Editors for this special issue are

Christian Korff (University of Glasgow, UK)
Masato Okado (Osaka University, Japan)
Wolfgang K. Schief (Technische Universität Berlin, Germany)
Tetsuji Tokihiro (The University of Tokyo, Japan)

The satellite workshop Geometric Aspects of Discrete and Ultra-Discrete Integrable Systems (March 30 − April 3, 2009) was part of the Isaac Newton Institute Programme on Discrete Integrable Systems (January 19 − July 3, 2009). It brought together different communities of researchers working on classical and quantum aspects of integrable systems as well as experts on combinatorial representation theory and crystals and this interdisciplinary aspect is reflected in this proceedings volume.

On behalf of the other organisers, Claire Gilson and Jon Nimmo, I would like to express our gratitude to the participants of the workshop, the contributing authors to this volume, the guest editors (Professors Masato Okado, Wolfgang Schief and Tetsuji Tokihiro) and the organisers of the Discrete Integrable Systems programme as well as the support staff of the Isaac Newton Institute.

Papers in this Issue:

On Quadrirational Yang-Baxter Maps

V.G. Papageorgiou, Yu.B. Suris, A.G. Tongas and A.P. Veselov
SIGMA 6 (2010), 033,  9 pages   [ abs   pdf   ps ]

Yang-Baxter Maps from the Discrete BKP Equation

Saburo Kakei, Jonathan J.C. Nimmo and Ralph Willox
SIGMA 6 (2010), 028, 11 pages   [ abs   pdf   ps ]

Level Set Structure of an Integrable Cellular Automaton

Taichiro Takagi
SIGMA 6 (2010), 027, 18 pages   [ abs   pdf   ps ]

Epsilon Systems on Geometric Crystals of Type A_n

Toshiki Nakashima
SIGMA 6 (2010), 023, 14 pages   [ abs   pdf   ps ]

Zero Action on Perfect Crystals for U_q(G₂⁽¹⁾)

Kailash C. Misra, Mahathir Mohamad and Masato Okado
SIGMA 6 (2010), 022, 12 pages   [ abs   pdf   ps ]

Q-system Cluster Algebras, Paths and Total Positivity

Philippe Di Francesco and Rinat Kedem
SIGMA 6 (2010), 014, 36 pages   [ abs   pdf   ps ]

Bethe Ansatz, Inverse Scattering Transform and Tropical Riemann Theta Function in a Periodic Soliton Cellular Automaton for A_n⁽¹⁾

Atsuo Kuniba and Taichiro Takagi
SIGMA 6 (2010), 013, 52 pages   [ abs   pdf   ps ]