David Marker : Model Theory and Real Geometry

Posted by , part of the Graduate Student Colloquium.

At

Sept. 9, 2005, 3 p.m.

In

SEO 636

Abstract

In his celebrated Incompleteness Theorem, Godel showed that there is no algorithm to decide which statements about the natural numbers are true. A surprising counterpoint, was provided by Tarski, who proved that there is such an algorithm for the complex field and the real field. Moreover, the methods from Tarski's proof provide interesting geometric and topological information about real algebraic varieties. In recent years, these methods have been extended to allow certain classes of analytic functions, including exponentiation.