### Preprints still in development

#### Exponential sums with multiplicative coefficients and applications (with Regis de la Breteche)

We show that if an exponential sum with multiplicative coefficients is large then the associated multiplicative function is pretentious''. This leads to applications in the circle method, and a natural interpretation of the local-global principle.

Article

#### 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