Published on *Department of Mathematics* (https://math.yale.edu)

October 7, 2020 - 4:15pm

A “rubber band” constrained to remain on a manifold evolves by trying to shorten its length, eventually settling on a closed geodesic, or collapsing entirely. It is natural to try to consider a noisy version of such a model where each segment of the band gets pulled in random directions. Trying to build such a model turns out to be surprisingly difficult and generates a number of nice insights, as well as some beautiful algebraic and analytical objects. We will survey some of the main results obtained on the way to this construction.