Title: Falconer type theorems: How many points do you need to guarantee many patterns?
Speaker: Eyvindur Palsson - Virginia Tech
Abstract: Finding and understanding patterns in data sets is of significant importance in many applications. One example of a simple pattern is the distance between data points, which can be thought of as a 2-point configuration. Two classic questions, the Erdos distinct distance problem, which asks about the least number of distinct distances determined by N points in the plane, and its continuous analog, the Falconer distance problem, explore that simple pattern. Questions similar to the Erdos distinct distance problem and the Falconer distance problem can also be posed for more complicated patterns such as triangles, which can be viewed as 3-point configurations. In this talk, I will give an introduction to both the discrete and continuous questions, report on recent progress, and share some exciting open questions.
