Tools for extracting information from numerically approximated<br/><br/>varieties and schemes

There
are natural situations where one is led to consider numeric approximations
of varieties, schemes, sheaves, ideals, modules, etc. For instance, given a
homogeneous ideal one might be able to determine a reduced primary
decomposition via numerical methods (such as homotopy continuation) whereas
symbolic methods might be too slow or not even apply. This provides
motivation to develop a set of tools to handle and manipulate numerically
approximated varieties and schemes. In this talk, I will discuss some tools
of use for these objects. This is joint work with Dan Bates and Andrew
Sommese.