An intersection of CS and harmonic analysis: approximating matrix p to q norms

In Fourier restriction theory, we bound exponential sums whose frequencies lie in sets with special properties, e.g. random sets or curved sets. Bourgain, Demeter, and Guth developed decoupling inequalities to show that such functions enjoy square root cancellation behavior. This theory lies in the larger context of bounding matrix p to q norms, which is well-studied in the CS literature. We will discuss a new polynomial time algorithm inspired by Fourier restriction theory of myself, Guth, and Urschel which reduces the multiplicative error of computing matrix 2 to q norms from roughly n^{1/q} to n^{1/2q}, where n is the size of the matrix.