Vortrag im Schwerpunkt Reelle Geometrie und Algebra
Freitag, 27. November 2009, um 14:15 Uhr in F426 (Oberseminar) Margaret Thomas (Konstanz) Mild Parameterization and the Rational Points of Definable Sets Abstract
We shall review the connection between the notion of parameterization and the problem of bounding the number of rational points lying on certain subsets of the reals. This connection was first explored by Pila and Wilkie in the context of o-minimal expansions of real closed fields. In particular, we shall focus on mild parameterization and on sets definable in the (o-minimal) expansion of the real ordered field by restricted Pfaffian functions. We shall outline some results of Pila giving a logarithmic bound for certain definable sets and aim to give an indication of some generalisations of these results.
