Amos Nevo, Technion University
Classical Diophantine approximation seeks to quantify the denseness of the rational numbers in the real numbers. Upon some reflection, one sees that points with rational coordinates are dense in the unit sphere in Euclidean 3-space. But how dense are they ? Such intrinsic Diophantine approximation problems on homogeneous algebraic varieties were raised long ago by Lang. We will describe a recently developed general approach to them, demonstrating the method in many familiar natural examples. We will explain how to derive best-possible results in some cases, and present some intriguing open problems in others. We will not assume any background in Diophantine approximation and the relevant concepts will be defined in the course of the talk.
MC 5479