Geometry and Topology at Many Scales - Robert Young (NYU)
Автор: University of Chicago Department of Mathematics
Загружено: 2025-05-07
Просмотров: 223
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.
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