Recent Progress in Additive Prime Number Theory -- 2009 Moursund Lectures, Day 1

Terence Tao, 2006 Fields Medal Recipient University of California, Los Angeles Lecture one of a three part series Abstract: Additive prime number theory is the study of additive patterns in the primes. We survey some recent advances in this subject, including the results of Goldston, Pintz, and Yildirim on small gaps between primes, the results of Green and myself on arithmetic progressions in the primes, and the results of Bourgain, Gamburd, and Sarnak for detecting almost primes in orbits. The Moursund lecures are an annual lecture series in which the University of Oregon brings a distinguished mathematician to campus. The lecture series is named after Andrew Moursund, who was the Math department's head from 1939 to 1970, and are partly paid for by an endowment formed by Moursund's widow (Lulu Moursund) and son (David Moursund).