Join us at GSAS for an exciting double feature this week! Emily will present on her recent research in Geometric Measure Theory and Garrett will provide a primer in optimal transport. The titles and abstracts are given below.
Rectifiability and anisotropic singular integral operators
Since the work of Mattila and Preiss in 1995, it’s been known that for a Radon measure with reasonable density assumptions, the almost everywhere existence of principal values of the Riesz transform is equivalent to the measure being rectifiable. In ongoing work with Goering, Toro, and Wilson, we extend this result of Mattila and Preiss to anisotropic Riesz kernels. In this talk, we will discuss the motivation in characterizing rectifiable measures in an anisotropic setting.
Introduction to Optimal Transport
Originally posed in the 18th century by Gaspard Monge, the problem central to optimal transport is to transport a unit mass in some shape (i.e. a probability measure) into another shape while doing the least amount of work. This expository talk will provide a friendly introduction to optimal transport via closely considering measures supported on finitely many points.