Quantitative equidistribution and Wasserstein distance

(Joint work with T. Untrau) Many equidistribution theorems in number theory are proved by means
of the Weyl Criterion and quantitative bounds for $L$-functions or related quantities. It is natural to
want to translate these statements into quantitative equidistribution results in terms of distances
between probability measures. Wasserstein metrics provide an intrinsic and highly flexible framework
for such statements. The talk will survey the underlying definitions and give examples of applications,
including a version of Deligne's Equidistribution Theorem. We will also present some natural questions
which arise from this perspective.