Applications of FT-Mollification II

In FT-mollification, one smooths a function while maintaining good quantitative control on high-order derivatives. This is a continuation of my talk from last week, and I will continue to describe this approach and show how it can be used to show that bounded independence fools polynomial threshold functions over various distributions (Gaussian, Bernoulli, and p-stable). I may also touch on other applications in approximation theory and learning theory.

This talk is based on various works by subsets of Ilias Diakonikolas, Daniel Kane, David Woodruff, and myself.