Minimizers of discrete measures and energy integrals.

Abstract: We shall survey various results and conjectures about energy minimization problems that arise in different fields: electrostatics, discrete and metric geometry, discrepancy theory and uniform distribution, signal processing etc. While in many natural examples optimizing the energy imposes uniform distribution, we shall pay special attention to the opposite effect -- when minimizers exhibit clustering or discretization, or are supported on small or lower dimensional subsets. We shall also touch upon energies that depend on interactions of three or more particles, rather than just pairwise interactions, and describe difficulties that arise in this setting.

classical analysis and ODEsfunctional analysisrepresentation theoryspectral theory

Audience: researchers in the topic

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