Tori Noquez : The Pila-Wilkie Theorem

Posted by Victoria Noquez , part of the Louise Hay Logic Seminar.

At

Oct. 4, 2012, 3 p.m.

In

SEO 427

Abstract

We will go over the proof of the main theorem in Pila and Wilkie's 2006 paper The Rational Points of a Definable Set. It says that for $X$, a subset of $\mathbb R^n$, which is definable in an o-minimal expansion of $\mathbb R$, there are (in a suitable sense) very few rational points of $X$ which do not lie on some connected semialgebraic subset of $X$ of positive dimension.