Speaker: Ethan White (UIUC)
Title: Extremal configurations in the plane
Abstract: Many central problems in extremal geometry can be phrased by fixing a property P held by k-tuples of points, and then asking for how many k-tuples in a set of n points does the property P hold. Two problems in this class are the Erdos unit-distance problem, and a problem of Pach and Sharir on unit-perimeter triangles. We will discuss new results on these problems. In the former problem we characterize the structure of point sets with many unit-distances, and in the later we present significantly improved lower bounds on the number of unit-perimeter triangles.