The conference is concerned with the theory of computability and complexity in analysis, physical sciences, and engineering over the real numbers, which is built on the Turing machine model. This research is an interdisciplinary area between applied analysis and computability and complexity theory, and sometimes also involves works in numerical analysis. The goal of the research is to understand the laws of real number computation, the computability content of existence results in analysis, and the computational complexity of computable operators.
Computability brings to mind computers, which are playing an ever larger role in our society. Computers operate on finite strings of digits. However most mathematical models describe continuous problems ranging from physical phenomena such as electromagnetism and sound waves, to engineering applications such as bridge designs and air flows around airplanes, to financial predictions such as expected investment returns. Continuous models are based fundamentally on the concept of real numbers. Although a large portion of computer resources is devoted to compute the solutions of such continuous problems, real number computation is not as well understood as it should be. There still exists a big gap between the continuous nature of problem from the physical world and the computability and complexity theory of discrete structures. The explosion of Ariane 5 rocket on June 4, 1996, is a drastic example. The problem at the center is that computers operate on finite strings of digits while the real numbers are infinite mathematical objects. The increasing demand for reliable as well as fast software requires a better understanding of real number computation. Computable analysis is a theory which studies the laws of real number computation. Its goal is to bridge the gap between analysis, the mathematical theory of real numbers, on the one end, and computability on the other. It studies which computations in analysis, physical sciences, and engineering are possible and which are not. The research lets us understand why a problem cannot be solved on computers, or provides us with a better understanding of the computability content of a continuous problem and thus better tools for constructing more efficient algorithms. The research outputs of the conference series are substantial. The series has produced five volumes of proceedings containing more than 100 (refereed) papers ranging from theoretical investigations of computability and complexity in analysis to new implementations of exact real arithmetics as well as further developments of existing software packages.
