Curvature testing in metric polyhedral complexes and lunar exploration.

Murray Elder
Texas A&M University

If someone hands you a complex built out of Euclidean polyhedra, then
how could you check that it is non-positively curved?
In this talk we will see that there is a practical algorithm that can
decide whether or not a 3-dimensional metric polyhedral complex is locally
CAT(0). We will also see that in fact there is a (not-so-practical)
algorithm for complexes of ANY dimension. The first procedure is very
geometric, and the second uses techniques from computational algebraic
geometry.

This is joint work with Jon McCammond.