Metric Algebraic Geometry

Metric algebraic geometry is a term proposed for the study of properties of real algebraic varieties that depend on a distance metric. The distance metric can be the Euclidean metric in the ambient space or a metric intrinsic to the variety. In this talk, we introduce metric algebraic geometry through discussion of Voronoi cells, bottlenecks, offset hypersurfaces, and the reach of an algebraic variety. We also show applications to the computational study of the geometry of data with nonlinear models.