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First International Congress of Chinese Mathematicians
Edited by: Lo Yang, Chinese Academy of Sciences, Beijing, China, and S.-T. Yau, Harvard University, Cambridge, MA
A co-publication of the AMS and International Press of Boston, Inc..

AMS/IP Studies in Advanced Mathematics
2001; 518 pp; softcover
Volume: 20
ISBN-10: 0-8218-2652-2
ISBN-13: 978-0-8218-2652-2
List Price: US$120
Member Price: US$96
Order Code: AMSIP/20
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See also:

Third International Congress of Chinese Mathematicians - Ka-Sing Lau, Zhou-Ping Xin and Shing-Tung Yau

Fourth International Congress of Chinese Mathematicians - Lizhen Ji, Kefeng Liu, Lo Yang and Shing-Tung Yau

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 co-published with International Press of Boston, Inc., Cambridge, MA.


Graduate students and research mathematicians.

Table of Contents

Morningside lectures
  • R. E. Borcherds -- Problems in moonshine
  • D. W. Stroock -- The Ornstein-Uhlenbeck 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 Navier-Stokes equations
  • H.-T. Yau -- Scaling limit of particle systems, incompressible Navier-Stokes 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 -- Cayley-Bacharach 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 -- Melvin-Morton conjecture: A survey
  • G. Meng -- The Seiberg-Witten 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 Poincaré-Birkhoff 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 -- Well-posedness theory for hyperbolic conservation laws
  • J. Li and T. Zhang -- Two-dimensional 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 ill-conditioned 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 color-covering problems
  • List of participants
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