Too Acute to be True?
October 14, 2020, 12:15 PM - 1:15 PM
Location:
Online Event
Quentin Dubroff, Rutgers University
Let f(d) be the maximum number of points in R^d such that every three form an acute triangle. For decades, it was thought that f(d) should grow linearly until a striking application of the probabilistic method by Erdős and Füredi showed that f(d) grows like C^d for some C>1. A few tiny improvements were made on this until very recently when a series of papers showed that f(d) is at least 2^{d-1}, nearly matching the upper bound of 2^d. I will recount this story, highlighting a few of the most clever arguments, as well as discuss its connection to a problem in coding theory which remains wide open.