## – Europe/Lisbon

Room P3.10, Mathematics Building — Online

Dot product problems in the fractal setting and barriers to current methods

We begin with a simply stated problem in discrete geometry: at least how many distinct dot products must be determined by a large finite set of points in the plane? This is related to some well-studied problems of Erdos about distances. The distance problems have celebrated variants in the fractal setting, such as the Falconer distance problem, which have seen significant progress in recent years. However, the analogous problems for dot products in the fractal setting have not moved past the most fundamental results. We discuss the barriers to current methods, in hopes of motivating new approaches to overcome these barriers.