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# First International Congress of Chinese Mathematicians

### About this Title

**Lo Yang**, *Chinese Academy of Sciences, Beijing, China* and **S.-T. Yau**, *Harvard University, Cambridge, MA*, Editors

Publication: AMS/IP Studies in Advanced Mathematics

Publication Year:
2001; Volume 20

ISBNs: 978-0-8218-2652-2 (print); 978-1-4704-3802-9 (online)

DOI: https://doi.org/10.1090/amsip/020

MathSciNet review: MR1830155

MSC: Primary 00B25

### Table of Contents

**Front/Back Matter**

**Morningside lectures **

**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 Navier-Stokes equations
- Scaling limit of particle systems, incompressible Navier-Stokes 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
- Cayley-Bacharach 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
- Melvin-Morton conjecture: A survey
- The Seiberg-Witten 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 Poincaré-Birkhoff 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
- Well-posedness theory for hyperbolic conservation laws
- Two-dimensional Riemann problems for conservation laws in gas dynamics
- Boundedness of cascade algorithms in Besov spaces
- Circulant preconditioners for ill-conditioned Hermitian Toeplitz matrices
- What is computational geometry
- A survey on circular chromatic numbers of graphs
- Approximations for color-covering problems