Explore the intriguing phenomenon of discrete minimizers in energy integral optimization in this 48-minute lecture by Dmitriy Bilyk from the Hausdorff Center for Mathematics. Delve into the counterintuitive behavior of pairwise interaction energy minimization, where uniform distributions are not always the outcome. Examine cases involving attractive-repulsive energies and weak repulsion, where minimizing measures become discrete or highly non-uniform. Investigate the connections between this phenomenon and various fields, including analysis, signal processing, and discrete geometry.