### Preprints still in development

#### Halasz in short intervals (with Adam Harper, Kaisa Matomaki, and Maksym Radziwill)

We show Halasz's Theorem in intervals of length $$x^{7/12}$$ (removing integers with a prime factor larger than the length of the interval). The method extends to intervals of length $$>x^{1/2+\epsilon}$$ but restricting to $$y$$-smooth integers where $$y$$ is significantly smaller than the length of the interval.

Article

#### Anatomy of integers and permutations.

In this article we study the similarities in the anatomies of integers and permutations.

Article