Graduate Student Colloquium
David Marker
UIC
Model Theory and Real Geometry
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.
Friday September 9, 2005 at 3:00 PM in SEO 636