edited by Jean-Pierre Bourguignon (Institut des Hautes Études Scientifiques) , Motoko Kotani (Tohoku University) , Yoshiaki Maeda (Keio University) , & Nobuyuki Tose (Keio University)

The two symposia, the Hayashibara Forum and the MSJ/IHÉS joint workshop, were held at the Institute des Hautes Études Scientifiques (IHÉS) in November, 2006. The Hayashibara Forum focused on singularity theory, which has been one of the research areas that has over the years been well represented at IHÉS. The MSJ/IHÉS Joint Workshop, focused on the broad area of noncommutativity, with an emphasis on noncommutative geometry as one of the fundamental themes of 21st century mathematics. This volume contains papers presented at the symposia in the form of invited lectures and contributing talks by young researchers. We believe that the scope of this volume well reflects a new development for singularity theory, and a new direction in mathematics through noncommutativity. This volume are aimed to inspire not only the specialists in these fields but also a wider audience of mathematicians.

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

• Plenary Lectures:
  • From Pitman's Theorem to Crystals (P Biane)
  • Singularities and Self-Similarity in Gravitational Collapse (T Harada)
  • Horospherical Geometry in the Hyperbolic Space (S Izumiya)
  • Instanton Counting and the Chiral Ring Relations in Supersymmetric Gauge Theories (H Kanno)
  • Superconformal Field Theory and Operator Algebras (Y Kawahigashi)
  • Iterating the Hessian: A Dynamical System on the Moduli Space of Elliptic Curves and Dessins D'enfants (P Popescu-Pampu)
  • Quantum Birkhoff Normal Forms and Semiclassical Analysis (S Vũ Ngoc)
  • On Geometric Analogues of Iwasawa Main Conjecture for a Hyperbolic Threefold (K-I Sugiyama)
  • Partial Regularity and Its Application to the Blow-Up Asymptotics of Parabolic Systems Modelling Chemotaxis with Porous Medium Diffusion (Y Sugiyama)
  • Upper Curvature Bounds and Singularities (T Yamaguchi)
  • High-Order Processing of Singular Data (Y Yomdin & G Zahavi)
• Research Articles:
  • An Analogue of Serre Fibrations for C^*-Algebra Bundles (S Echterhoff et al.)
  • Spontaneous Partial Breaking of N = 2 Supersymmetry and the U(N) Gauge Model (K Fujiwara et al.)
  • An Analogue of the Space of Conformal Blocks in (4k+2)-Dimensions (K Gomi)
  • The Quantum Knizhnik–Zamolodchikov Equation and Non-Symmetric Macdonald Polynomials (M Kasatani & Y Takeyama)
  • Local Gromov–Witten Invariants of Cubic Surfaces (Y Konishi)
  • Flop Invariance of the Topological Vertex (S Minabe)
  • A Table of θ-Curves and Handcuff Graphs with Up to Seven Crossings (H Moriuchi)
  • A Quantization of the Sixth Painlevé Equation (H Nagoya)
  • Lagrangian Fibrations and Theta Functions (Y Nohara)
  • Generalized Q-Functions and UC Hierarchy of B-Type (Y Ogawa)
  • The Space of Triangle Buildings (M Pichot)
  • Ends of Metric Measure Spaces with Nonnegative Ricci Curvature (M Watanabe)
  • On Ideal Boundaries of Some Coxeter Groups (S Yamagata)
  • On Manifolds which are Locally Modeled on the Standard Representation of a Torus (T Yoshida)