edited by Koji Hasegawa (Tohoku University), Takahiro Hayashi (Nagoya University), Shinobu Hosono (University of Tokyo), & Yasuhiko Yamada (Kobe University)

In 2007, Professor Akihiro Tsuchiya of Nagoya University reached the retirement age of sixty-three. He has played a significant role in mathematical physics over the decades, most particularly in the foundation of conformal field theory, which was the first nontrivial example of a mathematically rigorous quantum field theory.

This volume is the proceedings of the international conference at the occasion. Included are: Conformal field theories and related topics such as solvable statistical models, representation theory of affine algebras, monodromy preserving deformations, and string theories. Readers interested in these subjects will find exciting and stimulating insights and questions from these articles.

Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America

• The Triplet Vertex Operator Algebra W(p) and the Restricted Quantum Group Ū_q(sl₂) at q =e^πi/p (Kiyokazu Nagatomo & Akihiro Tsuchiya)
• Representation Theory of W-Algebras, II (Tomoyuki Arakawa)
• Chiral Potts Model and the Discrete Sine-Gordon Model at Roots of Unity (Vladimir V Bazhanov)
• Modular Forms and Elliptic Genera for ALE Spaces (Tohru Eguchi, Yuji Sugawara & Anne Taormina)
• Fermionic Formulas for Characters of (1,p) Logarithmic Model in ϕ_2,1 Quasiparticle Realisation (Boris Feigin, Evgeny Feigin & Il'ya Tipunin)
• Quantization of Soliton Systems and Langlands Duality (Boris Feigin & Edward Frenkel)
• Quantizing the Bäcklund Transformations of Painlevé Equations and the Quantum Discrete Painlevé VI Equation (Koji Hasegawa)
• Quantum Groups and Quantization of Weyl Group Symmetries of Painlevé Systems (Gen Kuroki)
• On Frenkel–Mukhin Algorithm for q-Character of Quantum Affine Algebras (Wakako Nakai & Tomoki Nakanishi)
• Perverse Coherent Sheaves on Blow-Up. I. A Quiver Description (Hiraku Nakajima & Kōta Yoshioka)
• Differential Fay Identities and Auxiliary Linear Problem of Integrable Hierarchies (Kanehisa Takasaki)