Speaker: Luke Rogers (Cornell)

Title: Smooth cutoffs for functions on fractal sets, and applications


Analysis on rough spaces such as fractals, or metric spaces with a Dirichlet form, is often quite different from analysis on Euclidean spaces. In particular, some tools that we take for granted in the Euclidean context have no counterpart in these settings. Examples include the use of smooth partitions of unity to smoothly partition functions, and convolution with a compactly supported smooth bump function to cut functions off smoothly in a neighborhood of a set. I will talk about some work (joint with Strichartz and Teplyaev) on producing alternatives to these useful tools, and, if time permits, give some indication their applications to a theory of distributions on certain types of fractals.