Abstract: This talk will be aimed at discussing the connection between capacity theory on projective space and applications to the arithmetic of dynamical systems. For dynamical systems on the projective line, this connection is best known in terms of the equidistribution of points of small canonical height with respect to rational functions. In higher dimensions, the greater complexities of pluripotential theory have impeded progress on the analogous problems in arithmetic dynamics on projective varieties of dimension >1. This talk will discuss how the Fekete-Leja transfinite diameter (and variants thereof) is a promising avenue of future progress on this issue. The centerpiece of the discussion concerns the adaptation of a quantitative lower bound on averages of Arakelov-Green’s functions due to Matt Baker in dimension one.
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