2023 Program for Women and Mathematics: Patterns in Integers: dynamical and number theoretic approaches

Abstract: In 1985, Maier demonstrated that there are short intervals with an exceptionally large or small number of primes. In this talk, I will discuss an analog of this result for primes in three-term and four-term arithmetic progressions. I aim to highlight the similarities and differences between the proofs of the two cases; the former uses the circle method, whereas the latter requires ergodic theory. This is based on joint work with Mayank Pandey.