A New Upper Bound for the Heilbronn Triangle Problem

Explore a lecture on the Heilbronn triangle problem, featuring a new upper bound discovered through joint research. Delve into the structural results that demonstrate how, for sufficiently large n, any configuration of n points within a unit square contains a triangle with an area smaller than n^(-8/7-1/2000). Learn about the collaborative efforts of Cosmin Pohoata, Alex Cohen, and Dmitrii Zakharov in advancing this mathematical concept. Gain insights into the implications of this finding for geometric probability and combinatorics during this hour-long presentation from the Simons Institute.