Stanley Xiao, Department of Pure Mathematics, University of Waterloo
“The Maynard-Tao sieve”
In May 2013, Yitang Zhang proved that there are infinitely many pairs of primes whose difference is at most 70,000,000. Zhang used sophisticated methods involving very fine exponential sum estimates to improve upon the Bombieri-Vinogradov theorem in the case of smooth moduli. Later that year, in November, Maynard and Tao developed (independently) a multi-dimensional sieve that enabled one to show that there are infinitely many pairs of primes whose difference is at most 600. In this talk, we will give a brief introduction to the Maynard-Tao sieve, and its origin as a Selberg sieve.