Speaker: Professor Tom Needham, Ohio State University
Title: Geometry of Spaces of Polygons and Curves
Abstract: In this talk we will describe several applications in shape analysis involving moduli spaces of curves. These include finite-dimensional configuration spaces of polygons and infinite-dimensional spaces of smooth curves. The techniques presented can be used to answer questions such as “what is the probability that a random triangle is obtuse?” and “what is the correct (parameterization-invariant) notion of the distance between a pair of plane curves?”. The common theme is to treat the questions geometrically using natural Riemannian metrics on the moduli spaces.