Consists of the proceedings of the Third International Congress of Chinese Mathematicians, held at the Chinese University of Hong Kong in December 2004. This book features lectures on topics such as algebra, number theory and cryptography; algebraic geometry and algebraic topology; and, geometric analysis; complex analysis and complex geometry.

Dirichlet forms and markov semigroups on non-associative vector bundles by C.-H. Chu and Z. Qian Decomposition principle and random cascades by A. H. Fan and J.P. Kahane Holomorphic motions and normal forms in complex analysis by Y. Jiang On pseudo-Hermitian CR manifolds by S.-Y. Li Recent progress on the Dirichlet problem in Lipschitz domains by Z. Shen Refinable functions with non-integer Dilations by X.-R. Dai, D.-J. Feng, and Y. Wang On Whitney's critical sets by Z.-Y. Wen and L.-F. Xi Applications of Nevanlinna theory to geometric problems by P.-M. Wong Some results on Smale's mean value conjecture by Y. Wang Localized non-blowup conditions for the 3D incompressible Euler equations by J. Deng, T. Y. Hou, and X. Yu Separation of bound state solutions of systems of nonlinear Schr"odinger equations by T.-C. Lin and Y.-W. Hsu The $C^\alpha$ regularity of a class of ultraparabolic equations by Z. Liqun Stability of basic wave patterns for gas motions by T. Yang and H.-J. Zhao On strong near-epoch dependence by Z. Lin Multifractal analysis of branching measure on a Galton-Watson tree by P. M"orters and N.-R. Shieh Convex duality theory for optimal investment by J. Xia and J.-A. Yan Backward stochastic Volterra integral equations by J. Yong Set addition and set multiplication by M.-C. Chang Collineation groups of translation planes by C. Y. Ho Intelligent and informative scientific computing, trends and examples by Q. Du Scattered data interpolation by box splines by Z. Shen and S. Waldron Piecewise function generated by the solutions of linear ordinary differential equation by Z. Wu Step-sizes for the gradient method by Y.-X. Yuan Number-theoretic methods in experimental designs by K.-T. Fang and Y. Wang Ear modeling and sound signal processing by J. Xin The mathematical problem of inertial waves in rapidly rotating planets and stars by X. Liao and K. Zhang Mathematics, mathematics education and the mouse by S. M. Keung.