We review the famous Yomdin-Gromov Lemma about smooth reparametrizations of semialgebraic sets, and state a version of this lemma for holomorphic reparametrizations and semialgebraic sets defined over ℚ. We then introduce o-minimal theory and illustrate how it can deeply impact diophantine geometry.
This video was produced by Tel Aviv University as part of its algebra seminar.
