Erdos-Folkman Conjecture

A sequence of numbers is complete if the set of its partial sums
contains all but finite positive integers. (For instance the set of
primes is complete.)
Motivated by the study of complete sequences, Erdos and Folkman made the
following conjecture (1966):

Let A be an infinite sequence of positive integers with density at least
cn^{1/2} (for all large
n, A contains at least cn^{1/2} integers between 1 and n), where c is a
sufficiently large constant. Then
the set of partial sums of A contains an infinite arithmetic progression.

Partial results were obtained by Erdos, Folkman, Hegyvari, Luczak and
Schoen. Recently, Szemeredi and I proved the conjecture. In this talk,  I
will discuss the proof and some relevant problems/results.