This is a brief, informal and very elementary introduction into the work of Pila and others about counting rational points on analytic and, more generally, definable sets. We also discuss some of the most spectacular applications.
Cite this article
Alexey Beshenov, Margaret Bilu, Yuri F. Bilu, Purusottam Rath, Rational points on analytic varieties. EMS Surv. Math. Sci. 2 (2015), no. 1, pp. 109–130DOI 10.4171/EMSS/10