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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

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Table of Contents

Front/Back Matter

• View this volume's front and back matter

Morningside lectures

• Problems in moonshine
• The Ornstein-Uhlenbeck 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 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

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