One of the most interesting developments in arithmetic geometry during the last 30 years come from the discovery of the complexity of the distribution of rational solutions of polynomial equations. We will first explain what it means to be equidistributed for such solutions, then we will describe several well known examples for which "obvious" solutions of the equations are far more numerous than they ought to be, thus preventing equidistribution. During the second part of the talk, we will introduce the notion of slopes and explain its uses and limitations with respect to equidistribution and explore its relations to heights on projective bundles.

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