Chennai Mathematical Institute


Fields Medal Lecture Series
Date: Friday, March 10, 2023
Time: 2:00 pm to 3:00 pm
Venue: Seminar Hall
Difference between consecutive primes

R. Balasubramanian
Institute of Mathematical Sciences, Chennai.


In 2013, James Maynard announced the following spectacular theorem: Theorem. For any fixed k ≥ 2, there exist k integers (h1, ... , hk) such that for infinitely many n, one has all the integers n + h1, ... , n + hk are primes. In particular, there exists an integer h ≤ 600 with the property that there exist infinitely many pairs of prime numbers of the form (p, p + h).

In this lecture we try to explain the new ideas which Maynard uses as compared to Goldston-Pintz-Yildrim and Y. Zhang.