Math Graduate Student Seminar

One of the most famous open problems in number theory is the twin prime conjecture, which says that there are infinitely many prime numbers at distance two. I will introduce some of the tools used to deal with this problem, such as the Selberg sieve and the Bombieri-Vinogradov theorem, and outline the new ideas that led to the breakthroughs of Zhang and Maynard in 2013, who independently proved that the gap between primes is bounded infinitely often. If time permits, I will touch on the known obstructions towards twin primes, such as the parity problem in sieve theory.