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. Jost, 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.
Morningside lectures: Problems in moonshine by R. E. Borcherds The
Ornstein-Uhlenbeck process on a Riemannian manifold by D. W. Stroock Plenary
addresses: Stochastic PDEs in turbulence theory by W. E Recent developments
of realization of surfaces in $R^3$ by H. Jiaxing Numerical study of
interfacial problems with small surface tension by H. D. Ceniceros and T. Y.
Hou Selected topics in moduli spaces by J. Li A tour of mirror symmetry by B.
H. Lian and S.-T. Yau The scalar curvature equation on $S^n$ by C.-S. Lin
Symplectic isotopy in four dimension by G. Tian Stability in Hamiltonian
dynamical systems by Z. Xia On the behavior of solutions to the compressible
Navier-Stokes equations by Z. Xin Scaling limit of particle systems,
incompressible Navier-Stokes equation and Boltzmann equation by H.-T. Yau
Geometry of algebraic points by S. Zhang Invited addresses: Jordan structures
in Banach manifolds by C.-H. Chu The rationality problem of finite group
actions by M.-c. Kang Hecke algebras and representation ring of Hopf algebras
by Y. Zhu On the Euler numbers of threefolds by M.-C. Chang Vector bundles,
the $S$-duality conjecture of Vafa and Witten, and vertex algebras by W.-p.
Li and Z. Qin Cayley-Bacharach property and $k$-very ampleness by S.-L. Tan
Sharp polynomial upper estimate of number of positive integral points in
tetrahedron and coordinate free characterization of homogeneous polynomials
by K.-P. Lin and S. S.-T. Yau Spectral theory and geometry of locally
symmetric spaces by L. Ji On the first eigenvalue of Laplacian for locally
symmetric manifolds by J.-s. Li DGBV algebras and mirror symmetry by H.-D.
Cao and J. Zhou Harmonic maps on noncompact manifolds by L.-f. Tam Curvature,
bounded cohomology and path integrals by J.-Y. Wu Vanishing theorems for loop
spaces by K. Liu Symplectic forms, 2+1 soliton equations, and supersymmetric
gauge theories by D. H. Phong Quotients, invariant version of Cartan's lemma,
and the minimum principle by X.-Y. Zhou an elementary expose on
equisingularities by T.-C. Kuo and L. Paunescu A proof of the strong Kervaire
invariant in dimension 62 by W.-H. Lin Melvin-Morton conjecture: A survey by
X.-S. Lin The Seiberg-Witten equations and the Milnor torsion by G. Meng The
Bergman kernel function of some Reinhardt domains by S. Gong and X. Zheng On
some problems in several complex variables and CR geometry by X. Huang A KAM
theory for resonant tori and a generalization of Poincare-Birkhoff fixed
point theorem by C.-Q. Cheng Persistence of $C^k$ normally hyperbolic
invariant manifolds for infinite dimensional dynamical systems by P. W.
Bates, K. Lu, and C. Zeng Fine analysis of blow up and applications by Y. Y.
Li Varifold type theory for Sobolev mappings by F. Lin Cellular neural
networks: Pattern and waves by S.-S. Lin Long time behavior of curves
evolving by curvature by X.-P. Zhu Discontinuous solutions to nonlinear
evolutionary partial differential equations by G.-Q. Chen Well-posedness
theory for hyperbolic conservation laws by T.-P. Liu Two-dimensional Riemann
problems for conservation laws in gas dynamics by J. Li and T. Zhang
Boundedness of cascade algorithms in Besov spaces by S. L. Lee and Q. Sun
Circulant preconditioners for ill-conditioned Hermitian Toeplitz matrices by
R. H. Chan, M.-h. Yip, C.-w. Leung, and M. K. Ng What is computational
geometry by R.-H. Wang A survey on circular chromatic numbers of graphs by G.
J. Chang Approximations for color-covering problems by L. Ruan, D.-Z. Du, X.
Hu, X. Jia, and D. Li List of participants.
