Challenges for the 21st Century: Proceedings of the International Conference on Fundamental Sciences: Mathematics and Theoretical Physics, Singapore 13-17 March 2000

The International Conference on Fundamental Sciences: Mathematics and Theoretical Physics provided a forum for reviewing some of the significant developments in mathematics and theoretical physics in the 20th century; for the leading theorists in these fields to expound and discuss their views on new ideas and trends in the basic sciences as the new millennium approached; for increasing public awareness of the importance of basic research in mathematics and theoretical physics; and for promoting a high level of interest in mathematics and theoretical physics among school students and teachers. This was a major conference, with invited lectures by some of the leading experts in various fields of mathematics and theoretical physics. Message from Director of Newton Institute......Page 6 Message from Director of Research and Former Dean of Science National University of Singapore......Page 8 Foreword......Page 10 CONTENTS......Page 12 List of Lectures......Page 14 Committees......Page 18 Mathematics......Page 20 A Review of Critical Point Theory......Page 22 Spectrum of Convolution Dilation Operators on Weighted Lp Spaces......Page 70 Data Tuning......Page 91 Gambling with the Truth: Markov Chain Monte Carlo......Page 102 Automorphic Representations and Cohomology of Arithmetic Groups......Page 121 Applied Mathematics Meets Signal Processing......Page 157 Modular Forms and Diophantine Questions......Page 181 Chromatic Graph Theory......Page 202 Glimpses of Nonlinear Partial Differential Equations in the Twentieth Century: A Priori Estimates and the Bernstein Problem......Page 215 Three-Dimensional Subgroups and Unitary Representations......Page 232 Theoretical Physics......Page 270 How Monte Carlo Simulations can Clarify Complex Problems in Statistical Physics......Page 272 The Future of Particle Physics......Page 295 Yang-Mills Duality and the Generation Puzzle......Page 318 The Mathematics of M-Theory......Page 336 Quantum Entanglement and Secrecy......Page 358 What Is Quantum Computation?......Page 370 Aspects of Anomalies in Field Theory......Page 403 Dynamical Chaos and Nonequilibrium Statistical Mechanics......Page 417 General Relativity and Quantum Mechanics......Page 449 Integrable Integral Operators......Page 471 Topics on Fractals in Mathematics and Physics......Page 480 Perturbative Quantum Field Theory......Page 498