3:00–4:00 pm Eckhart Hall, Room 202
Geometry and Topology at Many Scales
Abstract:
In 1979, Kaufman constructed a remarkable surjective Lipschitz map from a cube to a square whose derivative has rank 1 almost everywhere. This strange property arises from its multiscale structure; it is constructed by starting with a simple map and adding more and more complexity at smaller and smaller scales. In this talk, we will introduce some ideas in multiscale and nonsmooth geometry -- what can you construct by perturbing a map or surface at many scales, and what are the limits of such constructions? Examples include: bounding the complexity of maps and surfaces, the geometry of the Heisenberg group, and topologically nontrivial maps from \(S^m\) to \(S^n\) with derivative of rank \(n-1\).