Title: A new large sieve method in combinatorics
Abstract: We discuss a new method of converting local congruence restrictions into global information, based on the Chinese remainder theorem. Despite their simplicity, the general principles behind it seem to have a wide variety of applications, leading to new results for several longstanding problems in combinatorics, discrete geometry and number theory. We will survey some of these recent developments, and discuss how these ideas are also connected with the recent breakthrough counterexample for the unit distance conjecture, as well as other unexpected constructions. Based on joint work with Ernie Croot, Junzhe Mao, Adam Sheffer, and Kyle Yip.
