19 Equidistribution: Extremal Newtonian-like Configurations, Group Invariant Discrepancy, Finite Fields, Combinatorial Designs, Linear Independent Vectors, Matroids and the Maximum Distance Separable Conjecture
We use the notation 
and 
for measures.
The problem of “distributing well” a large number of points on certain 
-dimensional compact sets embedded in 
(see Figures 19.1–19.6) is an interesting problem with numerous wide applications in diverse areas, for example, harmonic analysis, approximation theory, zeroes of extremal polynomials in all kinds of settings, singular operators, for example, Hilbert transforms, random matrix theory, crystal and molecule structure, electrostatics, special functions, Newtonian energy, extensions, alignment, data science, number theory, manifold learning, clustering, shortest paths, codes and discrepancy, computer vision, signal processing, biology, neuroscience, networks, clustering, optimal transport, and many others. We say the points equidistribute over the set or cover it.
Figure 19.1 , .
Figure 19.2 , .
Figure 19.3 , .
Figure 19.4 Torus, ...
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