Small scale distribution of primes in four-term arithmetic progressions

In 1985, Maier demonstrated that there are short intervals with exceptionally large or small numbers of primes. In this talk, I will discuss adapting Maier's matrix method to look at the small scale distribution of primes in three-term and four-term arithmetic progressions. I aim to highlight the similarities and differences in the proofs for the two cases; the former uses the classical circle method, whereas the latter requires tools from ergodic theory. This is based on joint work with Mayank Pandey.