Abstract

In this lecture I will survery old and new results on the distribution of rational points of bounded height on algebraic varieties, and in particular a conjecture of Yu. Manin on Fano varieties, and the application of ideas from automorphic forms. I will also explain a recent joint work with J. A. Shalika and Yu. Tschinkel on the distribution of rational points of bounded height on certain compactifications of semi-simple groups.



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