**Title**: Primes, the zeta function and zero density estimates.

**Abstract**: If we could prove the Riemann Hypothesis, then there would be several fantastic consequences for our understanding of prime numbers. It turns out that even if the Riemann Hypothesis is false and there are some counterexamples to it, we can still obtain many of these consequences for primes provided the counterexamples are suitably ‘rare’. I’ll talk about this picture and recent joint work on possible patterns of counterexamples. As a consequence of our new approach if the zeros of the zeta function lay on finitely many vertical lines then we obtain several results on primes which are essentially as strong as what the Riemann Hypothesis would imply.

Where: Mathematics Hall, room 520

When: Wednesday, November 02, 2022 at 04:30pm