Jürg Kramer: Irrationality of √2 and Arakelov Geometry

Jürg Kramer, Humboldt-Universität zu Berlin

Time: Wed 2009-09-09 16.00

Location: Room 3721, department of mathematics, KTH, Lindstedtsvägen 25, 7th floor

Starting with the well-known proof of the irrationality of √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 on the set of rational points on algebraic varieties and how it can be further generalized by means of Arakelov Geometry to higher dimensional objects in order to measure their arithmetic complexity.

Kollokvier 2009

Titel Datum
Sandra Di Rocco: Interaction between Convex and Algebraic Geometry 2009‑12‑16
Alexander Gorodnik: Arithmetic Geometry and Dynamical Systems 2009‑11‑18
Laurent Bartholdi: Insanely twisted rabbits 2009‑11‑18
Nils Dencker: The spectral instability of differential operators 2009‑11‑04
Peter Jagers: Extinction: how often, how soon, and in what way? 2009‑10‑21
Norbert Peyerimhoff: Expander graphs — some background and new examples 2009‑10‑07
Saharon Shelah: Hilbert's First Problem and the number four 2009‑09‑23
Jürg Kramer: Irrationality of √2 and Arakelov Geometry 2009‑09‑09