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).