This project on pure mathematics concerns analytic number theory and additive combinatorics, as well as their connections to ergodic theory and higher order Fourier analysis. The central topics in this research are randomness properties of the primes and the Möbius function. Relating to the randomness of the Möbius function, the conjectures of Chowla and Sarnak will be studied in this project. Regarding the primes, the aim of this research is to establish new Gowers norm estimates for the primes. These are expected to have applications to combinatorial and dynamical questions about the primes.

2024