Polynomial Progressions in Topological Fields and Their Applications to Pointwise Convergence Problems

We will discuss multilinear variants of Weyl's inequality for the exponential sums arising in pointwise convergence problems related to the Furstenberg-Bergelson-Leibman conjecture. We will also illustrate how to use the multilinear Weyl inequality to derive quantitative bounds (in the spirit of Peluse and Prendiville) in Szemeredi's theorems for polynomial progressions in topological fields.