**2/23/2005**

**Markus Rost**

**Institute for Advanced Study and the University of Bielefeld **

**Examples in Algebraic Cobordism**

Characteristic numbers of differentiable or complex manifolds play an important role in the classical theory of cobordism. In recent years there appeared a surprising relation between this topic and Galois cohomology. It turned out that characteristic numbers give rise to certain birational invariants which are of particular interest over non-algebraically closed fields. In the lecture we will consider various examples which illustrate this new appearance of characteristic numbers in questions from algebra and algebraic geometry.