Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: The reach of an algebraic variety
Seminar | November 5 | 5-6 p.m. | 939 Evans Hall
Madeleine Weinstein, UC Berkeley
The reach of a real algebraic variety is its distance to its medial axis, the locus of points in Euclidean space that have more than one nearest point on the variety. The reach is important in topological data analysis because it determines the density of sample points needed to compute the persistent homology of a variety. We discuss algebraic properties of bottlenecks and curvature, which together determine the reach.