Applications of FT-Mollification

In FT-mollification, one smooths a function while maintaining good quantitative control on high-order derivatives. I will 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).

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