Caltech/UCLA Joint Analysis Seminar

UCLA, MS 6627

A longstanding conjecture of Erdős stated that every subset of the integers with positive density contains a sumset B + C = {b + c : b ∈ B,c ∈ C} for two infinite sets B and C. I will talk about joint work with Joel Moreira and Donald Robertson in which we resolve this conjecture. Our proof utilizes ideas and methods coming from Ergodic Theory, including an intersectivity lemma of Bergelson and a novel decomposition theorem for arithmetic functions into structured and random components.