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Book DetailsAMS/IP Studies in Advanced MathematicsVolume: 20; 2001; 518 ppMSC: Primary 05; 08; 11; 14; 22; 35; 37; 80;
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.ReadershipGraduate students and research mathematicians.

Table of Contents

Morningside lectures

Problems in moonshine

The OrnsteinUhlenbeck process on a Riemannian manifold

Plenary addresses

Stochastic PDEs in turbulence theory

Recent developments of realization of surfaces in $R^3$

Numerical study of interfacial problems with small surface tension

Selected topics in moduli spaces

A tour of mirror symmetry

The scalar curvature equation on $S^n$

Symplectic isotopy in four dimension

Stability in Hamiltonian dynamical systems

On the behavior of solutions to the compressible NavierStokes equations

Scaling limit of particle systems, incompressible NavierStokes equation and Boltzmann equation

Geometry of algebraic points

Invited addresses

Jordan structures in Banach manifolds

The rationality problem of finite group actions

Hecke algebras and representation ring of Hopf algebras

On the Euler numbers of threefolds

Vector bundles, the $S$duality conjecture of Vafa and Witten, and vertex algebras

CayleyBacharach property and $k$very ampleness

Sharp polynomial upper estimate of number of positive integral points in tetrahedron and coordinate free characterization of homogeneous polynomials

Spectral theory and geometry of locally symmetric spaces

On the first eigenvalue of Laplacian for locally symmetric manifolds

DGBV algebras and mirror symmetry

Harmonic maps on noncompact manifolds

Curvature, bounded cohomology and path integrals

Vanishing theorems for loop spaces

Symplectic forms, 2+1 soliton equations, and supersymmetric gauge theories

Quotients, invariant version of Cartan’s lemma, and the minimum principle

an elementary exposé on equisingularities

A proof of the strong Kervaire invariant in dimension 62

MelvinMorton conjecture: A survey

The SeibergWitten equations and the Milnor torsion

The Bergman kernel function of some Reinhardt domains

On some problems in several complex variables and CR geometry

A KAM theory for resonant tori and a generalization of PoincaréBirkhoff fixed point theorem

Persistence of $C^k$ normally hyperbolic invariant manifolds for infinite dimensional dynamical systems

Fine analysis of blow up and applications

Varifold type theory for Sobolev mappings

Cellular neural networks: Pattern and waves

Long time behavior of curves evolving by curvature

Discontinuous solutions to nonlinear evolutionary partial differential equations

Wellposedness theory for hyperbolic conservation laws

Twodimensional Riemann problems for conservation laws in gas dynamics

Boundedness of cascade algorithms in Besov spaces

Circulant preconditioners for illconditioned Hermitian Toeplitz matrices

What is computational geometry

A survey on circular chromatic numbers of graphs

Approximations for colorcovering problems


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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.
Graduate students and research mathematicians.

Morningside lectures

Problems in moonshine

The OrnsteinUhlenbeck process on a Riemannian manifold

Plenary addresses

Stochastic PDEs in turbulence theory

Recent developments of realization of surfaces in $R^3$

Numerical study of interfacial problems with small surface tension

Selected topics in moduli spaces

A tour of mirror symmetry

The scalar curvature equation on $S^n$

Symplectic isotopy in four dimension

Stability in Hamiltonian dynamical systems

On the behavior of solutions to the compressible NavierStokes equations

Scaling limit of particle systems, incompressible NavierStokes equation and Boltzmann equation

Geometry of algebraic points

Invited addresses

Jordan structures in Banach manifolds

The rationality problem of finite group actions

Hecke algebras and representation ring of Hopf algebras

On the Euler numbers of threefolds

Vector bundles, the $S$duality conjecture of Vafa and Witten, and vertex algebras

CayleyBacharach property and $k$very ampleness

Sharp polynomial upper estimate of number of positive integral points in tetrahedron and coordinate free characterization of homogeneous polynomials

Spectral theory and geometry of locally symmetric spaces

On the first eigenvalue of Laplacian for locally symmetric manifolds

DGBV algebras and mirror symmetry

Harmonic maps on noncompact manifolds

Curvature, bounded cohomology and path integrals

Vanishing theorems for loop spaces

Symplectic forms, 2+1 soliton equations, and supersymmetric gauge theories

Quotients, invariant version of Cartan’s lemma, and the minimum principle

an elementary exposé on equisingularities

A proof of the strong Kervaire invariant in dimension 62

MelvinMorton conjecture: A survey

The SeibergWitten equations and the Milnor torsion

The Bergman kernel function of some Reinhardt domains

On some problems in several complex variables and CR geometry

A KAM theory for resonant tori and a generalization of PoincaréBirkhoff fixed point theorem

Persistence of $C^k$ normally hyperbolic invariant manifolds for infinite dimensional dynamical systems

Fine analysis of blow up and applications

Varifold type theory for Sobolev mappings

Cellular neural networks: Pattern and waves

Long time behavior of curves evolving by curvature

Discontinuous solutions to nonlinear evolutionary partial differential equations

Wellposedness theory for hyperbolic conservation laws

Twodimensional Riemann problems for conservation laws in gas dynamics

Boundedness of cascade algorithms in Besov spaces

Circulant preconditioners for illconditioned Hermitian Toeplitz matrices

What is computational geometry

A survey on circular chromatic numbers of graphs

Approximations for colorcovering problems