Advanced Studies in Pure Mathematics 2009; 363 pp; hardcover Volume: 55 ISBN10: 493146954X ISBN13: 9784931469549 List Price: US$81 Member Price: US$64.80 Order Code: ASPM/55
 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 contributed talks by young researchers. The scope of this volume reflects a new development for singularity theory and a new direction in mathematics through noncommutativity. This volume aims to inspire not only the specialists in these fields but also a wider audience of mathematicians. Volumes in this series are freely available electronically 5 years postpublication. Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS. Readership Graduate students and research mathematicians interested in analysis. Table of Contents Plenary Lectures  P. Biane  From Pitman's theorem to crystals
 T. Harada  Singularities and selfsimilarity in gravitational collapse
 S. Izumiya  Horospherical geometry in the hyperbolic space
 H. Kanno  Instanton counting and the chiral ring relations in supersymmetric gauge theories
 Y. Kawahigashi  Superconformal field theory and operator algebras
 P. PopescuPampu  Iterating the Hessian: A dynamical system on the moduli space of elliptic curves and dessins d'enfants
 S. V. Ngọc  Quantum Birkhoff normal forms and semiclassical analysis
 K.i. Sugiyama  On geometric analogues of Iwasawa main conjecture for a hyperbolic threefold
 Y. Sugiyama  Partial regularity and its application to the blowup asymptotics of parabolic systems modelling chemotaxis with porous medium diffusion
 T. Yamaguchi  Upper curvature bounds and singularities
 Y. Yomdin and G. Zahavi  Highorder processing of singular data
Research Articles  S. Echterhoff, R. Nest, and H. OyonoOyono  An analogue of Serre fibrations for \(C^*\)algebra bundles
 K. Fujiwara, H. Itoyama, and M. Sakaguchi  Spontaneous partial breaking of \(\mathcal{N}=2\) supersymmetry and the \(U(N)\) gauge model
 K. Gomi  An analogue of the space of conformal blocks in \((4k+2)\)dimensions
 M. Kasatani and Y. Takeyama  The quantum KnizhnikZamolodchikov equation and nonsymmetric Macdonald polynomials
 Y. Konishi  Local GromovWitten invariants of cubic surfaces
 S. Minabe  Flop invariance of the topological vertex
 H. Moriuchi  A table of \(\theta\)curves and handcuff graphs with up to seven crossings
 H. Nagoya  A quantization of the sixth Painlevé equation
 Y. Nohara  Lagrangian fibrations and theta functions
 Y. Ogawa  Generalized Qfunctions and UC hierarchy of Btype
 M. Pichot  The space of triangle buildings
 M. Watanabe  Ends of metric measure spaces with nonnegative Ricci curvature
 S. Yamagata  On ideal boundaries of some Coxeter groups
 T. Yoshida  On manifolds which are locally modeled on the standard representation of a torus
