KIAS Workshop

The Zero Problem: Theory and Applications

The Zero Problem is a family of decision problems about whether a given numerical expression is equal to zero. Many applications depend the solution of the zero problem. Such decision problems are often reduced to the computation of effective bounds. Techniques developed in transcendental number theory, diophantine approximations, and effective algebraic computations have proved useful here. It is also closely related to singularity theory. In recent years, the development of new software to perform real computation have proliferated. One genre of such software, as represented by LEDA, CGAL and Core Library provides guaranteed sign computation which ultimately depends on the zero problem. The derivation of sharp zero bounds has major impact on the efficiency of such software. In particular, the combination of sharp zero bounds with highly efficient numerical approximations algorithms can lead to practical and adaptive algorithms. The zero problem also sheds considerable light on the current interest on the foundations of real computation. A viable theory of real computation must be able to properly account for the complexity of such computations.

This workshop will bring together an interdisciplinary group of leading researchers in areas that address the mathematical foundations and theory of zero problems, as well as application areas that depend on the zero problem. Application areas include computational geometry, computational topology, optimization algorithms, computer-aided geometric design (CAGD), computational number theory, computational topology, and automatic theorem proving.

Tutorials in several of these topics are planned. We encourage students to attend this workshop. This workshop is sponsored by KIAS (Korea Institute for Advanced Study).