"Noga Alon is being awarded the 2024 Wolf Prize for his profound impact on Discrete Mathematics and related areas."
I will describe a recent joint work with Matia Bucic and Lisa Sauermann about the investigation of extremal problems in discrete geometry for typical norms.
The results include surprisingly tight solutions of the unit and distinct distances problems for typical norms, as well as a determination of the chromatic number of the unit distance graph for a typical planar norm.
This settles, in a strong form, questions and conjectures of Matousek, of Brass, of Chilakamarri and Robertson and of Brass, Moser and Pach.