**AMS/IP Studies in Advanced Mathematics**

Volume: 20;
2001;
518 pp;
Softcover

MSC: Primary 05; 08; 11; 14; 22; 35; 37; 80;

Print ISBN: 978-0-8218-2652-2

Product Code: AMSIP/20

List Price: $120.00

AMS Member Price: $96.00

MAA member Price: $108.00

**Electronic ISBN: 978-1-4704-3802-9
Product Code: AMSIP/20.E**

List Price: $120.00

AMS Member Price: $96.00

MAA member Price: $108.00

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# First International Congress of Chinese Mathematicians

Share this page *Edited by *
*Lo Yang; S.-T. Yau*

A co-publication of the AMS and International Press of Boston

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.

#### Readership

Graduate students and research mathematicians.

# Table of Contents

## First International Congress of Chinese Mathematicians

- Cover Cover11
- Title page v6
- Contents vii8
- Preface ix10
- Inauguration speech xi12
- Chinese essay 1 xiii14
- Chinese essay 2 xv16
- ICCM98 Beijing conference xvii18
- Congratulation speeches xix20
- Jean-Pierre Bourguignon xxi22
- Kun Soo Chang xxiii24
- David Eisenbud xxv26
- Juergen Jost xxvii28
- Seng Luan Lee xxix30
- Toshigazu Sunada xxxi32
- M. Taylor xxxiii34
- Committees of ICCM98 xxxv36
- Morningside Award Medalists xxxix40
- The work of Chang-Shou Lin xli42
- The work of Shou Zhang xliii44
- The work of Raymond Chang xlvii48
- The works of Chong-Qing Cheng li52
- The work of Kefeng Liu lv56
- The work of Tong Yang lvii58
- Photos lix60
- Opening ceremony lxi62
- Speakers of the conference lxxi72
- Morningside lectures 178
- Problems in moonshine 380
- The Ornstein-Uhlenbeck process on a Riemannian manifold 1188
- Plenary addresses 25102
- Stochastic PDEs in turbulence theory 27104
- Recent developments of realization of surfaces in 𝑅³ 47124
- Numerical study of interfacial problems with small surface tension 63140
- Selected topics in moduli spaces 93170
- A tour of mirror symmetry 115192
- The scalar curvature equation on 𝑆ⁿ 129206
- Symplectic isotopy in four dimension 143220
- Stability in Hamiltonian dynamical systems 149226
- On the behavior of solutions to the compressible Navier-Stokes equations 159236
- Scaling limit of particle systems, incompressible Navier-Stokes equation and Boltzmann equation 171248
- Geometry of algebraic points 185262
- Invited addresses 199276
- Jordan structures in Banach manifolds 201278
- The rationality problem of finite group actions 211288
- Hecke algebras and representation ring of Hopf algebras 219296
- On the Euler numbers of threefolds 229306
- Vector bundles, the 𝑆-duality conjecture of Vafa and Witten, and vertex algebras 235312
- Cayley-Bacharach property and 𝑘-very ampleness 241318
- Sharp polynomial upper estimate of number of positive integral points in tetrahedron and coordinate free characterization of homogeneous polynomials 251328
- Spectral theory and geometry of locally symmetric spaces 261338
- On the first eigenvalue of Laplacian for locally symmetric manifolds 271348
- DGBV algebras and mirror symmetry 279356
- Harmonic maps on noncompact manifolds 291368
- Curvature, bounded cohomology and path integrals 297374
- Vanishing theorems for loop spaces 311388
- Symplectic forms, 2+1 soliton equations, and supersymmetric gauge theories 319396
- Quotients, invariant version of Cartan’s lemma, and the minimum principle 335412
- an elementary exposé on equisingularities 345422
- A proof of the strong Kervaire invariant in dimension 62 351428
- Melvin-Morton conjecture: A survey 359436
- The Seiberg-Witten equations and the Milnor torsion 369446
- The Bergman kernel function of some Reinhardt domains 375452
- On some problems in several complex variables and CR geometry 383460
- A KAM theory for resonant tori and a generalization of Poincaré-Birkhoff fixed point theorem 397474
- Persistence of 𝐶^{𝑘} normally hyperbolic invariant manifolds for infinite dimensional dynamical systems 403480
- Fine analysis of blow up and applications 411488
- Varifold type theory for Sobolev mappings 423500
- Cellular neural networks: Pattern and waves 431508
- Long time behavior of curves evolving by curvature 435512
- Discontinuous solutions to nonlinear evolutionary partial differential equations 443520
- Well-posedness theory for hyperbolic conservation laws 455532
- Two-dimensional Riemann problems for conservation laws in gas dynamics 461538
- Boundedness of cascade algorithms in Besov spaces 473550
- Circulant preconditioners for ill-conditioned Hermitian Toeplitz matrices 481558
- What is computational geometry 491568
- A survey on circular chromatic numbers of graphs 497574
- Approximations for color-covering problems 503580
- List of participants 509586
- Back Cover Back Cover1596