3:00–4:00 pm Zoom
Title:
Subset Sums
Abstract:
In this talk, I will discuss novel techniques which allow us to prove a diverse range of results relating to representing integers as subset sums, including solutions to several long-standing open problems in the area. These include: solutions to the three problems of Burr and Erdős on Ramsey complete sequences, for which Erdős later offered a combined total of $350 for their solution; analogous results for the new notion of density complete sequences; the answer to a question of Alon and Erdős on the minimum number of colors needed to color the positive integers less than n so that n cannot be written as a monochromatic sum; the exact determination of an extremal function introduced by Erdős and Graham and first studied by Alon on sets of integers avoiding a given subset sum; and, answering a question of Sárközy and of Tran, Vu and Wood, a common strengthening of seminal results of Szemerédi-Vu, Freiman, and Sárközy on long arithmetic progressions in subset sums. Based on joint work with David Conlon and Huy Tuan Pham.