## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

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Wednesday, January 15, 2014 — 4:00 PM EST

It is a long standing conjecture, since antiquity, that there exist infinitely many consecutive prime numbers that are separated by 2, which is of course the closest possible distance. The prime number theorem shows that the gap between pn and pn+1 is on average log pn. It is surprising then that even proving the existence of infinitely many gaps smaller than some constant multiple of the average has proved difficult for the century that ensued the proof of the prime number theorem. In a breakthrough paper in 2009, Goldston, Pintz, and Yildirim proved that for any small constant c > 0, there exist infinitely many primes p, q such that |p − q| < c log p. In doing so they were able to relate the gaps between prime problems with a famous conjecture of Elliott and Halberstam, the first time anyone was able to connect the bounded gap problem to a major and fundamental conjecture in number theory. In May 2013, Yitang Zhang announced a proof of the existence of bounded gaps between primes and just six months later, James Maynard gave a drastically different and technically innovative proof which led to far superior estimates on the size of the gaps. In this talk I will give a brief outline of the arguments of GPY, Zhang, and Maynard.

Location

MC - Mathematics & Computer Building

4062

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Indigenous Initiatives Office.