In 2004 I proved an O(log log H) bound for the number of integer points of height at most H lying on a globally subanalytic curve. (The paper was published in the Journal of Symbolic Logic and so probably escaped the notice of most of you reading this.) Recently, Gareth Jones and Gal Binyamini proposed a generalization of the result to higher dimensions (where the obvious statement is almost certainly false) and I shall report on our joint work: one obtains the (hoped for) (log log H)n bound for (not globally subanalytic but) globally analytic sets of dimension n.
This video is part of the Number Theory Web Seminar series.
