We investigate the structure of finite sets A of integers such that A+A is large, presenting a counterexample to natural conjectures in the pursuit of an "anti-Freiman" theory in additive combinatorics. We will begin with a brief history of the problem and its connection to the study of Lambda(4) sets in harmonic analysis, and then we will discuss our counterexample and its construction from error-correcting codes. We will conclude by describing some related open problems. This is joint work with Mark Lewko.
Allison Lewko