Resolution of the Quadratic Littlewood-Offord problem
Consider a quadratic polynomial Q(x_1,...,x_n) of a random binary sequence (x_1,...,x_n). To what extent can Q(x_1,...,x_n) concentrate on a single value? This is a quadratic version of the classical Littlewood-Offord problem; it was was popularised by Costello, Tao and Vu in their study of symmetric random matrices, and has since become a rich source of connections between combinatorics, probability and computer science. In this talk we will discuss a new essentially optimal bound for the quadratic Littlewood-Offord problem, as conjectured by Nguyen and Vu. Joint work with Lisa Sauermann.