Short exponential sums and their applications over function fields by Mark Shusterman
In joint work in progress with Will Sawin, we obtain (square-root) cancellation in quite general incomplete exponential sums for the ring F_q[x] of polynomials in one variable over a finite field. This has applications to problems in arithmetic statistics such as the Bateman-Horn conjecture, and the number of real quadratic function fields with a huge class group.