New bounds on multilinear exponential sums

We build upon the existing results of multilinear exponential sums over prime fields and extend results beyond the previous barrier of quadrilinear sums to general multilinear sums. This extension is due to some recent results in additive combinatorics due to Shkredov. We also give applications of such sums to bounds of multinomial exponential sums. This is joint work with Bryce Kerr.