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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.