Polynomial progressions in the primes

Combinatorics Seminar
Friday, January 11, 2013 - 3:00pm
1 hour (actually 50 minutes)
Skiles 005
U. Texas
The Green-Tao theorem says that the primes contain arithmetic progressions of arbitrary length. Tao and Ziegler extended it to polynomial progressions, showing that congurations {a+P_1(d), ..., a+P_k(d)} exist in the primes, where P_1, ..., P_k are polynomials in \mathbf{Z}[x] without constant terms (thus the Green-Tao theorem corresponds to the case where all the P_i are linear). We extend this result further, showing that we can add the extra requirement that d be of the form p-1 (or p + 1) where p is prime. This is joint work with Julia Wolf.