Allan Greenleaf (Rochester) Title: Erd\H{o}s-Falconer Configuration Problems Abstract: In discrete geometry, there is a large collection of problems due to Erd\H{o}s and various coauthors starting in the 1940s, which have the following general form: Given a large finite set $\mathcal P$ of $N$ points in $d$-dimensional Euclidean space, and a geometric configuration (a line segment of a given length, a triangle with given angles or a given area, etc.), is there a lower bound on how many times that configuration must occur among the points of $\mathcal P$? Relatedly, is there an upper bound on the number of times any single configuration can occur? One of the most celebrated problems of this type, the Erd\H{o}s distinct distances problem in the plane, was essentially solved in 2010 by Guth and Katz, but for many problems of this type only partial results are known. In continuous geometry, there are analogous problems due to Falconer and others. Here, one looks for results that say that if a set $A$ is large enough (in terms of a lower bound on its Hausdorff dimension, say), then the set of configurations of a given type generated by the points of $A$ is large (has positive measure, say). I will describe work on Falconer-type problems using some techniques from harmonic analysis, including estimate for multilinear operators. In some cases, these results can be discretized to obtain at least partial results on Erd\H{os}-type problems.