Abstract

The famous Twin Prime Conjecture asks if there are infinitely many pairs of primes which differ by 2. Despite the simplicity of the statement and the fact this has been studied for over 100 years, unfortunately the problem is still completely open.

I will give an overview of the dramatic progress on two questions related to the Twin Prime Conjecture which has happened in the past few years:
(1) Results on bounded gaps between primes by Zhang, Tao and the speaker.
(2) Results on Chowla's conjecture due to Matomaki, Radziwill, Tao and Teravainen.