AMS/IP Studies in Advanced Mathematics 2001; 518 pp; softcover Volume: 20 ISBN10: 0821826522 ISBN13: 9780821826522 List Price: US$120 Member Price: US$96 Order Code: AMSIP/20
 The International Congress of Mathematicians was an historical event that was held at the Morningside Center of Mathematics of the Chinese Academy of Sciences (Beijing). It was the first occasion where Chinese mathematicians from all over the world gathered to present their research. The Morningside Mathematics lectures were given by R. Borcherds, J. Coates, R. Graham, and D. Stroock. Other distinguished speakers included J.P. Bourguignon, J. Jöst, M. Taylor, and S. L. Lee. Topics covered in the volume include algebra and representation theory, algebraic geometry, number theory and automorphic forms, Riemannian geometry and geometric analysis, mathematical physics, topology, complex analysis and complex geometry, computational mathematics, and combinatorics. Titles in this series are copublished with International Press of Boston, Inc., Cambridge, MA. Readership Graduate students and research mathematicians. Table of Contents Morningside lectures  R. E. Borcherds  Problems in moonshine
 D. W. Stroock  The OrnsteinUhlenbeck process on a Riemannian manifold
Plenary addresses  W. E  Stochastic PDEs in turbulence theory
 H. Jiaxing  Recent developments of realization of surfaces in \(R^3\)
 H. D. Ceniceros and T. Y. Hou  Numerical study of interfacial problems with small surface tension
 J. Li  Selected topics in moduli spaces
 B. H. Lian and S.T. Yau  A tour of mirror symmetry
 C.S. Lin  The scalar curvature equation on \(S^n\)
 G. Tian  Symplectic isotopy in four dimension
 Z. Xia  Stability in Hamiltonian dynamical systems
 Z. Xin  On the behavior of solutions to the compressible NavierStokes equations
 H.T. Yau  Scaling limit of particle systems, incompressible NavierStokes equation and Boltzmann equation
 S. Zhang  Geometry of algebraic points
Invited addresses  C.H. Chu  Jordan structures in Banach manifolds
 M.c. Kang  The rationality problem of finite group actions
 Y. Zhu  Hecke algebras and representation ring of Hopf algebras
 M.C. Chang  On the Euler numbers of threefolds
 W.p. Li and Z. Qin  Vector bundles, the \(S\)duality conjecture of Vafa and Witten, and vertex algebras
 S.L. Tan  CayleyBacharach property and \(k\)very ampleness
 K.P. Lin and S. S.T. Yau  Sharp polynomial upper estimate of number of positive integral points in tetrahedron and coordinate free characterization of homogeneous polynomials
 L. Ji  Spectral theory and geometry of locally symmetric spaces
 J.s. Li  On the first eigenvalue of Laplacian for locally symmetric manifolds
 H.D. Cao and J. Zhou  DGBV algebras and mirror symmetry
 L.f. Tam  Harmonic maps on noncompact manifolds
 J.Y. Wu  Curvature, bounded cohomology and path integrals
 K. Liu  Vanishing theorems for loop spaces
 D. H. Phong  Symplectic forms, 2+1 soliton equations, and supersymmetric gauge theories
 X.Y. Zhou  Quotients, invariant version of Cartan's lemma, and the minimum principle
 T.C. Kuo and L. Paunescu  an elementary exposé on equisingularities
 W.H. Lin  A proof of the strong Kervaire invariant in dimension 62
 X.S. Lin  MelvinMorton conjecture: A survey
 G. Meng  The SeibergWitten equations and the Milnor torsion
 S. Gong and X. Zheng  The Bergman kernel function of some Reinhardt domains
 X. Huang  On some problems in several complex variables and CR geometry
 C.Q. Cheng  A KAM theory for resonant tori and a generalization of PoincaréBirkhoff fixed point theorem
 P. W. Bates, K. Lu, and C. Zeng  Persistence of \(C^k\) normally hyperbolic invariant manifolds for infinite dimensional dynamical systems
 Y. Y. Li  Fine analysis of blow up and applications
 F. Lin  Varifold type theory for Sobolev mappings
 S.S. Lin  Cellular neural networks: Pattern and waves
 X.P. Zhu  Long time behavior of curves evolving by curvature
 G.Q. Chen  Discontinuous solutions to nonlinear evolutionary partial differential equations
 T.P. Liu  Wellposedness theory for hyperbolic conservation laws
 J. Li and T. Zhang  Twodimensional Riemann problems for conservation laws in gas dynamics
 S. L. Lee and Q. Sun  Boundedness of cascade algorithms in Besov spaces
 R. H. Chan, M.h. Yip, C.w. Leung, and M. K. Ng  Circulant preconditioners for illconditioned Hermitian Toeplitz matrices
 R.H. Wang  What is computational geometry
 G. J. Chang  A survey on circular chromatic numbers of graphs
 L. Ruan, D.Z. Du, X. Hu, X. Jia, and D. Li  Approximations for colorcovering problems
 List of participants
