From High-School Problems to Advanced Research in Arithmetic Geometry
Time and place
1 PM on Thursday, April 8th, 2010; NAC 6113
Jurg Kramer (Humboldt University)
Abstract
Title: From High-School Problems to Advanced Research in Arithmetic Geometry
Abstract: Starting with the well-known proof of the irrationality of $\sqrt{2}$, we would like to show in our talk how this proof has significantly influenced the development of modern Diophantine Geometry. A key notion in this respect is the height of a rational point on an algebraic curve or, more generally, on an algebraic variety. It will be shown how this notion can be used to derive results about the set of rational points on algebraic varieties and how it can be further generalized by means of Arakelov Geometry to higher dimensional cycles in order to measure their arithmetic complexity.
