Larger Corner-Free Sets in High Dimensions

Explore a 35-minute lecture on the topic of larger corner-free sets in high dimensions, presented by Lianna Hambardzumyan from Hebrew University at the Simons Institute. Delve into the central question of additive combinatorics regarding the size of arithmetic progression-free sets, focusing on high-dimensional generalizations known as corners. Learn about recent advancements in understanding corner-free sets, including improved upper bounds for 2-dimensional corners and the first improvement on high-dimensional corner-free sets since Rankin's original construction. Discover how communication complexity perspectives have been applied to achieve these results, based on joint work with Toniann Pitassi, Suhail Sherif, Morgan Shirley, and Adi Shraibman.