Energy optimization on the sphere

Many problems, arising in discrete and metric geometry, signal processing, physics, etc, can be reformulated as questions of optimizing discrete or continuous measures. We shall review some of such conjectures, as well as approaches to determining optimal (or at least good) point distributions and measures, and connections to other problems, such as discrepancy, sphere packings etc. We shall also discuss several manifestations of the phenomenon of clustering of minimizing measures, which is often observed theoretically, numerically, or experimentally: in many situations, in particular for some attractive-repulsive potentials, the minimizers of the energy integral happen to be discrete or supported on very thin sets.