Title: Counting isosceles trapezoids
Speaker: Georgios Petridis (University of Georgia)
Abstract: Given $n$ points on the plane (we think of $n$ as a large integer) we aim to bound the number of isosceles trapezoids with all four vertices in the point set. One is interested in this question because it is related to the pinned variant of Erdos’ distinct distances question. One can verify that if the point are the vertices of a regular $n$-gon or $n$ equally spaced points on a line, then there are a constant multiple of $n^3$ ordered isosceles trapezoids ($n^3$ being the trivial upper bound). Are there other examples of point sets that exhibit this trait? What is there to be gained by understanding this question better? In this largely expository talk, I will answer these questions and hopefully more.
