James A Maynard - Primes and the Riemann Hypothesis

Abstract: The Riemann Hypothesis is often called 'the most important unsolved problem in mathematics'. If true, it would have many fantastic implications for the distribution of prime numbers. However, it turns out that we don't need the full strength of the Riemann Hypothesis for several of these implications; we can sometimes prove similar results if we can show that any counterexamples to the Riemann Hypothesis are 'rare'.

I'll give a gentle introduction to these ideas, including recent work (joint with Larry Guth) that has improved our understanding of these exceptions, and correspondingly our understanding of the distribution of primes.